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Table of Content 1 Introduction Page

1.1 Background 2 1.2 Project Aim & Objectives 5 1.3 Description of the Problem 6

2 Review of Related Works

2.1 Commercial Product 8 2.2 Academic Research Works 10 2.3 Conclusion 14

3 Conceptual Background

3.1 Introduction of GA 15 4 System Analysis

4.1 Basic System Requirements 17 4.2 Assumptions 18 4.3 Detailed Data Flow & Entity Relationship 19 4.4 Genetic Representation 27 4.5 Fitness Functions Analysis 33 4.6 Other special considerations 37

5 System Design

5.1 Structured Charts 40 5.2 Database Design 43 5.3 Process Specifications 44 5.4 Interfaces Design 52

6 Implementation

6.1 Technical considerations 55 6.2 Programs structure 56 6.3 Special programming issues highlight 57 6.4 GA parameters settings 59

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7 System Evaluation

7.1 Evaluation Plan 60 7.2 Evaluation Result Analysis 62

8 Conclusion

8.1 About the Project aims 67 8.2 Further Developments 68 8.3 What has been learnt ? 70

9 References 71 10 Appendix

10.1 Project Plan 72 10.2 Database – Full listing 73 10.3 Installation Guide 79 10.4 System Screen Captures - 10.5 Test Plan – Functional 81

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1. Introduction 1.1 Background In these few years, Enterprise Resource Planning (ERP) system is so popular in the field of manufacturing sector in Hong Kong that almost every manager knows or hears of its necessity and importance to the development of a manufacturing company. However, most of those commercial ERP packages use only planning techniques called Materials Requirements Planning (MRP) and Capacity Requirements Planning (CRP), which is not sufficient to satisfy the need of the SME of different industries in Hong Kong ….. By the end of the 1960s, MRP had already been developed in the USA and Europe. As from it’s naming, MRP mainly concentrates in the planning and scheduling of materials supply to the manufacturing firm. Planned Purchase Order of materials and planned Manufacturing (Production) Order of products or components are the output of the MRP engine, with the input of information about Sales Orders (Required quantity, delivery date of Finished Goods), Inventory Balances, Bill of Materials (Materials Usage, purchase lead time, and production lead time). In short, the basic philosophy of MRP is to ensure that the right number of components (and materials) is planned at the right time to meet the demand for end items (products). But MRP totally ignores the capacity constraints of the manufacturing facilities. It assumes that there is infinite capacity of every work center of the firm. As a consequence of the demand for finite capacity scheduling, two approaches were implemented in commercial ERP package. They are : (1) pre/post-MRP analysis and; (2) Finite Capacity Planning (FCS) The pre/post-approach is executed as a part of the MRP methodology, while the FCS approach is executed as an extension to the shop floor control module. There are two strategies in the pre/post-approach, namely, rough cut capacity planning (RCCP) and Capacity Requirements Planning (CRP). RCCP is executed before the MRP algorithm. It is simply a method of ensuring that bottleneck resources are not overloaded. RCCP is often used in practice, but is limited in its effectiveness.

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CRP on the other hand is executed after the MRP. The CRP first determines whether the schedule is feasible. This is done via a variety of approaches including simulation of machine loading. When a problem is detected CRP provides the user with multiple solution options. These include forward and backward scheduling, midpoint scheduling, and overtime planning. CRP is reported to be unpopular in practice. The main reason for the unpopularity is that considerable user participation is required and the lack of interaction. The FCS approach is broadly interpreted. It encompasses approaches that generate a detailed shop floor schedule from a basic plan. It is the process of creating an operation schedule for a set of jobs that are to be produced on a limited set of resources. Each job is comprised of one or more operations (e.g. drilling, turning, painting, etc.) that must be performed in a specified sequence using the set of available resources (machines, workers, etc.). A schedule assigns a starting and ending time to each operation and sequences the operations across the resources so that no resource conflicts occur (i.e. a given resource is not required to process two operations at the same time). The operations are also assigned in a way that any sequencing constraints are respected (e.g. Operation 2 cannot start until Operation 1 is complete). Traditionally (and currently in a lot of manufacturing firms of Hong Kong), FCS can be done using a manual planning board (sometimes called a Gantt Chart) in which the available resources are listed down the left side and operations are assigned to resource rows and spaced horizontally within each row to represent the passage of time. Each operation is represented by a horizontal bar where the length of the bar represents the duration of the operation. Figure 1 below can be a simple illustration. Resource B Resource A Time In this simple example, Job X consists of two operations that are defined by Sequence Number 1 and 2 and must be performed in that order. Operation 2 cannot begin until Operation 1 is complete, i.e. precedence constraint. That is the reason why job Z-2

Job X-1

Job Y1

Job Z-2 JobY2

Job Z-1 Job X-2

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cannot start just after job Y2 finishes. Here we can note that the schedule shown is merely one of several possible production schedules that can be generated for this very simple two resources, three job problem. In practical problems involving many different resources and many different jobs, the number of possible schedules is enormous (actually it is well known as NP-hard problem which will be further discussed in the next section.). We clearly need an effective method for generating a “good” schedule that meets the production objectives.

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1.2 Project Aim & Objectives “Is there any academic methodology or theory that may be able to solve the practical scheduling problem ?” “Are those theories or methodologies satisfactorily solve the problem, compared with commercial scheduling application software ?” “Any limitation or difficulty that may exist which hinder the commercialization of those methodologies ?” Above are the questions always appeared in the mind of the writer, knowing the practical need described in the last section. Therefore, through this project by designing and programming for an application, the writer wanted to find out the answers. Put it in a formal way, the objective of this project is to develop an application program which can generate recommended production schedules, with the input of a set of job orders and resources, together with their relationships in the practical situation (detailed in the next section – Description of the Problem), considering : 1) Capacity constraints of the manufacturing resources 2) Precedence relationship of the operations of jobs 3) Multiple objectives for evaluating schedules The schedules generated by the program will be presented by telling the planner the start time, and expected end time for each of the operations in the problem set. And also the quality of the schedules would be told by having the “scores” of each of the schedules shown. And last but not least, the performance of this program is critical. The time required to generate a good solution would be investigated and considered as a main factor of the practicality of the program. Performance statistic would be taken for various combinations of parameters to be used by the algorithm. As the performance issue is very crucial in the practical environment, it would be another main issue to be investigated in this project.

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1.3 Description of the Problem In this project, one of the common production shop floor scheduling problems is to be solved. Let us have a number of main job orders. Under each main job order, there are several sub-job orders. The sub-job orders have precedence relationship between each other, just like a tree structure, in which the sub-job orders are to produce the components of the final product, like that of a Bill of Materials. The following diagram tries to illustrate the structure. For each sub-job order, there are several Operations to go through to completely produce the component. Each operation occupies a manufacturing resource (e.g. machine, assembly line), which it is usually regarded as a Work Center in most ERP systems. For each operation, there is “Setup Time” and “Run Time”. Setup Time is the fixed time to start the operation at that Work Center, and Run Time is the time needed to complete one item. For example, the setup time is 0.5 day and the run time is 0.1 day per item unit for an operation, if the quantity to be produced is 20, the total operation time will then be equal to 2.5 days.

Main Job - Product

Sub-Job A – for Component A

Sub-Job B – for Component B

Sub-Job A1 – for Component A1

Sub-Job B1 – for Component B1

Sub-Job B2 – for Component B2

Sub-Job A2 – for Component A2

Sub-Job B3 – for Component B3

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For each Work Center, there is one capacity constraint, i.e. a upper bound of availability, for example, which can be the number of machines in a period of time (e.g. per day or per week). The problem is that now a manufacturer with the above conditions, receives a number of main job orders. The main job order records the quantity of product required, the latest delivery date, and the penalty cost of late delivery. The task of the system is to generate schedule which should satisfy the capacity constraint of all Work Centers used, and minimize the penalty cost if the schedule cannot meet the delivery schedule of all the main job orders. Recommended schedules would be provided by the system, accompanied with the “score” (performance measures) for each of them. The calculation of the “score” is dependent on the emphasis of the planner in evaluating a schedule. Composite scoring can be used for multiple objectives, and weighting of each of them can be adjusted. Make span, idle period of resources, Work-In-Progress level will be used as the performance measures in the system of this project.

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2 Related Works 2.1 Commercial Product One of the commercial scheduling applications is to be investigated below. It is Preactor and it has been integrated with many commercial ERP systems. In this commercial FCS software, two approaches are provided to construct a schedule. The first is named as algorithmic and the second as simulation-based. Algorithmic sequencing is a simple method for schedule construction. The algorithmic sequencer selects a job and then puts each operation for that job on the planning board. It repeats this process until all jobs (and therefore, all operations) have been loaded. Each operation is loaded on its specified resource at the first available time slot that satisfies the constraints for that operation. Although there are a number of very simple heuristic rules that can be used to select the order for loading the jobs on the planning board (for examples, to sort the jobs by a priority value that has been assigned to each job, earliest due date, earliest release date, and smallest remaining slack time….), none of these rules are optimal in a mathematical sense. Each rule represents a different strategy and focus in planning the jobs individually. For example, the due date-related rules (earliest due date, least remaining slack) focus on reducing the number of late jobs, whereas the priority-based rule strives to complete the most important jobs as soon as possible. But in practice, a planner is required to take into all these rules in consideration in the same time as a whole. In contrast to the algorithmic sequencer, the simulation-based sequencer selects and loads an operation at a time. By loading individual operations rather than entire jobs, the simulation-based sequencer has finer control over the way the operations are loaded onto the planning board. This operation-at-a-time loading is the key to the added flexibility in the schedule generation using the simulation-based sequencer. Whichever of two sequencing algorithms described above, they required the planner to construct schedules by “trial and error”, attempting different jobs dispatching / sorting rules, or even moving the operations forward or backward manually. It is because there are often multiple objectives to be satisfied before a final schedule can be made.

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These are not what actually the planners expect from a scheduling tool, because they are working in a highly demanding customer-driven market environment. They expect a tool which can provide them feasible, “good” schedules, taking into consideration of factors of multiple objectives, with minimal manual participation. In this project, the main evaluation method for the program is by comparing the its results with schedules generated by this commercial product.

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2.2 Academic Research Works Determining an efficient schedule for the general shop problem has been the subject of research for more than 50 years. And there were numerous papers, researches done on this topic. Job Shop Scheduling Problem is one of the most typical topics found. The classical job shop problem assumes that each job had several operations and exactly one machine (resource) can only perform each operation, and each operation has a single predecessor. There are many variations of the job shop scheduling problem, for examples, flow shop scheduling, multi-objective job shop scheduling, dynamic job shop scheduling, multiple capacitated job shop scheduling… which fitted different criteria or assumptions of the real life conditions into the original structure of the job shop problem. And the original aim of solving the job shop scheduling problem was to find a feasible schedule. From another point of view, some later researches regard the problem as Optimization problem. It is because it is often impossible to obtain feasible solution or there could be more than one feasible solutions. So it is expected that a computer program can give out an optimal or near optimal (good) solution with some pre-set criteria or objectives. The sections below will try to summarize the related work for the two classifications described above. Critical Path Method Critical Path Method is a traditional method came from Operation Research (OR). It provides the resource-unconstrained schedule for a set of precedence-constrained activities with deterministic durations. It gives the shortest possible make span assuming infinite resources. Although useful for obtaining a rough idea of the difficulty of executing a plan, the critical path method does not consider temporal or resource constraints. Linear and Integer Programming Linear Programming is one of the most famous optimization techniques introduced independently by Kantarowitsch in 1939 and by Dantzig in 1949. It is applicable in decision situations where quantities (variables) can take any real values only restricted

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by linear (in-) equalities, e.g. for representing capacity constraints. In case the model solely consists of integer variables, it is called Integer Programming. If the model contains both real and integer variables, Mixed Integer Programming model is given. Although linear programming is very efficient for solving linear programs, problems arise if the objective or constraints are not linear functions. In some cases, non-linear functions may be approximated by piecewise linear functions, and linear programming is still used; however, this is often an inefficient representation of the problem, and a very limited number of functions may be represented this way. These formulations may cause explosively large matrices that are solved very slowly. For example, logical constraints usually require at least two linear constraints to be represented correctly, so a large number of logical constraints creates a huge linear program. This is a common difficulty in scheduling and sequencing problems. Bounded Enumeration Many solution methods search a decision tree generated from the precedence relations in the plan. The root of the tree corresponds to the first task, and the second level of the tree is the set of tasks that can be scheduled once the first task has been scheduled, and so on. The final tree thus represents a precedence feasible set of task sequences. The search consists of traversing the tree until the best root-to-leaf path is found. Enumerative methods are typically bounded using heuristics in order to reduce the size of the tree. It is easy to see how the tree grows quickly with the number of activities. Depending on the precedence relations, each new task can add many branches to the tree. Although pruning algorithm can be used for trimming the tree branches, it requires a new set of heuristics for the scheduling step if the types of constraints are changing. According to some researchers (Sprecher and Drexl), enumerative methods cannot solve large problems; the tree is simply too big. And they still require special heuristics to accommodate variations in resource constraint formulations. Scheduling Heuristics Scheduling heuristics operate on a set of tasks and determine when each task should be executed. The scheduler enforces constraint satisfaction by assigning a task to a resource ( or a resource to a task ) at a time when the resource is available and for the task can be executed. (This is similar to the Algorithmic sequencing described in the

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Introduction section.) Sequencing Heuristics Sequencing heuristics determine the order in which the tasks will be scheduled. These heuristics are often used in combination with decision trees to determine which part of the tree to search or to avoid. Actually it can be regarded as a variation of scheduling heuristics. Constraint Programming Constraint Programming represents a relatively new technique for computing feasible (and optimal) solutions to combinatorial decision problems like those typically arising in scheduling and routing. In the mid 80’, it was developed as a computer science technique by combining concepts of Artificial Intelligence with new programming languages. In the meantime, it has received considerable attention in practice as well as in the Operation Research community, in particular, since it has successfully been included into well-known commercial software systems (e.g. ILOG). Constraint Programming does not reply on mathematical optimization problems but on constraint satisfaction problems which, basically, consist of variables, domains as well as constraints. For each variable, an associated domain defines a set of feasible values which need not necessarily be real or integral. The variables are related to each other by constraints describing restrictions that have to be observed by feasible solutions. In general, constraints need not be simple expressions, in particular, they need not be linear inequalities or equations as common in mixed integer programming. The corresponding constraint satisfaction problem is to assign a value to each variable of its domain such that each constraint is satisfied. Obviously, a Constraint Satisfaction Problem differs from a classical optimization problem by not considering an objective function. That is, solving a Constraint Satisfaction Problem aims at finding feasible solutions to a real-world problem rather than an optimal one. However, a possible objective function can be represented within Constraint Satisfaction Problem by particular constraints and optimized by solving several Constraint Satisfaction Problems consecutively. Among the major advantages of Constraint Programming are the ease of application and the flexibility to add new constraints to existing problems. This is due to the rich set of possible constraint types and to the search algorithms employed being rather

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general. A disadvantage may be the rather poor performance with respect to solution quality and computation time. For a constraint programming approach to be competitive to modern Operation Research methods such as highly developed branch and bound procedures or meta-heuristics (e.g. Genetic Algorithms), the constraints of the problem to be solved should be rather restrictive, like this is (for example) true in production scheduling in case of tight due dates. Simulated Annealing Simulated Annealing approaches require a schedule representation as well as a neighborhood operator for moving from the current solution to a candidate solution. Annealing methods allow jumps to worse solutions and thus often avoid local sub-optimal solutions. Tabu search A tabu search is a meta-heuristic that guides local heuristic search procedures to explore the solution space beyond local optimality. It was introduced by Glover (86) specifically for combinatorial problems. And it was used by some researchers (e.g. Taillard 90’, Nowicki 96’) to tackle flow shop scheduling problem. Genetic Algorithms (Evolutionary Algorithms) Genetic Algorithms (GA) were initially developed by Holland and its associates at the University of Michigan and the first systematic but rather technical treatment was published in Holland (1975). GA has become increasingly popular as a means for solving such optimization problems heuristically, that is, for determining near-optimal solutions within reasonable time. One of the main reasons for this popularity is the relative ease of programming at least a simple genetic algorithm. Furthermore, many researchers have observed empirically that already basic versions of GA will give very acceptable results without excessively fine tuning them for the problem on hand. (Research has been done to investigate the performance of GA on scheduling problems, reference [6]) Finally, since GA work on a representation (coding) of a problem, it is possible to adapt existing procedures to modified problem versions quite easily or to write one general computer program for solving many different problems.

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As mentioned in the previous section, most scheduling problems in the real life manufacturing environment have been proven to be NP-hard, that is, the computational time requirements grows exponentially as a function of the problem size. (For n jobs and m machines in the general job shop scheduling problem, there will be n!m feasible solutions.) And GA is well known as working better with a large population of solutions. One of the earliest suggested uses of genetic algorithms for scheduling was made by Lawrence Davis. In his paper (85), Davis noted the attractiveness of using a stochastic search method due to the size of the search space and suggested an indirect representation in which the genetic algorithm operated on a list which was then decoded to form the actual schedule. 2.3 Conclusion From the papers and researches found for the topic of production scheduling, one can find that each of the above techniques has its own advantage over the others in different area of problems. After consulting the supervisor of the writer for this project, Dr. Andy Chun, Genetic Algorithm is used as the fundamental methodology to solve the problem described in the section 1.3. The writer do hope that this choice can broaden the space for further development of this system because of the favorable trend of GA application in the scheduling field.

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3 Conceptual Background 3.1 Introduction of GA Nature has a robust way of evolving successful organisms. The organisms that are ill-suited for an environment die off, whereas the ones that are fit live to reproduce. Offspring are similar to their parents, so each new generation has organisms that are similar to the fit members of the previous generation. If the environment changes slowly, the species can gradually evolve along with it, but a sudden change in the environment is likely to wipe out a species. Occasionally, random mutations occur, and although most of these mean a quick death for the mutated individual, some mutations lead to new successful species. Darwin’s evolution theory is just trying to state out this concept.

Genetic Algorithms (GA) starts with a set of one or more individuals and applies selection and reproduction operators to “evolve” an individual that is successful, as measured by a Fitness Function. There can be several choices for what the individuals are.

GA simply searches directly in the space of individuals, with the goal of finding one that maximizes the Fitness Function. The search is parallel because each individual in the population can be seen as a separate search. And the key question is how to allocate the searching resources. Clearly, we should spend most of our time on the most promising individual. But we are taking the risk of getting stuck on a local maximum if we ignore the low-scoring ones.

Before we can apply GA to a problem, we need to answer the following questions :

What is the fitness (objective) function ? How is an individual represented ? How are individuals selected ? How do individuals reproduce ?

Fitness Function – it usually depends problem, but generally speaking, it is a

function that takes an individual as input and returns a real number as output. Representation – in some classic GA approach, an individual is represented as a

string over a finite alphabet. Each element of the string is called a gene.

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Selection Strategy – usually randomized, with the probability of selection

proportional to fitness. In other words, if individual A scores twice as high as B on the fitness function, then A is twice as likely to be selected for reproduction than is B. Usually selection is done with replacement, so that a very fit individual will get to reproduce several times.

Reproduction – which is accomplished by cross-over and mutation. All the

individuals that have been selected for reproduction are randomly paired. For each pair, a cross-over point is randomly chosen. And each gene can be altered by random mutation to a different value, with small independent probability.

If the GA has been designed well (actually this is an art), the population will converge to an optimal solution to the problem. Convergence is the progression towards increasing uniformity. A gene is said to be converged when 95% of the population share the same value. The population is said to be converged when all of the genes have converged.

But unfortunately it is important to note that GA are stochastic iterative processes and they are not guaranteed to converge. Therefore, a termination condition may be needed to specify. It can be a fixed maximal number of generations or the attainment of an acceptable fitness level. That is the reason why it is noted that “good” solution will be obtained by using GA, but not optimal solution. NOTE In this project, some of the detailed GA processes, e.g. selection, reproduction, will not be investigated. Standard GA methods from the GA engine provided are used, e.g. crossover method, mutation method…

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4 System Analysis 4.1 Basic System Requirements The system is required to provide an interface for the user to input the following information. - quantities, latest delivery dates, and penalty costs about the main job orders - the relationship between the main job orders and their corresponding sub-job

orders - the operations sequence of each of the job orders, both main and sub jobs - the Work Center used by each operation - the setup time and the run time of each operation on the Work Center - the capacity constraint of each Work Center. And the system is required to transform the above information into formats for GA to generate solution described previously. After running GA, the program is required to transform the output of GA to user understandable format : - start time and end time of each operation of sub-job orders - “scores” of the schedules Diagram is used to illustrate the system functions as below.

Planner

Main/sub job info.

Work Center info..

Operation info.

Start time / End time of operations

Scores of suggested schedules

AI Scheduling system

Basic Info.

Results

Parameters for GA

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4.2 Assumptions In real life situation, there are a lot of factors required to be included in the scheduling considerations. It would need a long period of time of development to cater for all of them in the system. To limit the scope of the project and make sure the project will be completed on time, there are several assumptions made for the problem. They are listed as below : - one operation can be executed on one resource only, no ‘parallel’ run on more than

one resource will be considered ; - each operation once started must be performed to completion (no pre-emptive

priorities); - no rework operation will be considered; - the capacity constraint of each resource is static over time, that is, not vary with

time; - there is only one capacity constraint for each Work Center, no secondary

constraint will be considered; - there is only one sequence of operations in a job, no alternative sequence will be

considered; - the sequence of the operations is linear; - no alternative resource for operation, that is, each operation can be defined to

occupy a particular resource only; - all operations can be started at any time, that is, there is no limitation of the start

time of any of the operations; - operation can start only after its predecessors finish; there is no overlapping of

operations in the schedule; - there is no fix pre-defined slack time allowed between operations; - setup time for each operation is fix no matter what is the sequence of operations; - all resources operate on the same time basis, e.g. 8 hours per day, or 24 hours per

day; - no holiday or down time of resources will be taken into consideration, it is

assumed that the resources will be available continuously ; - all operations are allocated again at each scheduling process, no previous schedule

information will be considered.

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4.3 Detailed Data Flow Data Flow Diagrams are used to show the information flow as below :

1.0 Process

Basic

Info.

Planner Basic Info.

Basic Information

Validated data

2.0 Process

inputted

info.

Planner Weightings

for GA scores

3.0 Run

Scheduling

engine

Planner

Validated data

Parameters for GA run

Results

Planner

Schedules &

running log

Schedules &

running log

All Basic Info.

4.0 Convert to

user readable

format Results in Gantt

Chart / Table format

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DFD 1.0 Basic Information Data Flow :

1.1 Process

Item Info.

1.2 Process

Work Center

Info.

1.3 Process

Operation

Info.

1.4 Process

Job Orders

Info.

Planner Basic Information

Item Info.

Work Center

Info.

Operation Info.

Job Orders Info.

Validated data

Validated data

Validated data

Validated data

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DFD 1.1 Item Info. Data Flow :

1.1.1 Verify

& Add Item

Info.

1.1.2 Search

& List Item

Info.

1.1.3 Verify

and Update

Item Info.

1.1.4 Delete

Item Info.

Planner

New Item Info.

Item No.

and /or

Description

Basic Info. (Item Master)

Item No.

and /or

Description

New Item Info.

Updated Item Info. Verified Updated Item Info.

Item No. to be deleted

Item No. to be deleted

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DFD 1.2 Work Center Information Data Flow :

1.2.1 Verify

& Add Work

Center Info.

1.2.2 Search

& List Item

Info.

1.2.3 Verify

and Update

WC Info.

1.2.4 Delete

Item Info.

Planner

New WC Info.

WC code

and /or

Description

Basic Info. (WC Master)

WC code

and /or

Description

New WC Info.

Updated WC Info. Verified Updated WC Info.

WC code to be deleted

WC code to be deleted

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DFD 1.3 Operation Information Data Flow :

1.3.1 Verify

& Add Oper.

Info.

1.3.2 Search

& List Oper.

Info.

1.3.3 Verify

and Update

Oper. Info.

1.3.4 Delete

Oper. Info.

Planner

New Oper. Info.

Oper code

and /or

Description

Basic Info. (Oper. Master)

Oper code

and /or

Description

New Oper. Info.

Updated Oper. Info. Verified Updated Oper. Info.

Oper. No. to be deleted

Oper. No. to be deleted

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DFD 1.4 Job Order Information Data Flow :

1.4.1 Verify

& Add Job

Info.

1.4.2 Search

& List Job

Info.

1.4.3 Verify

and Update

Job Info.

1.4.4 Delete

Job Info.

Planner

New Job Info.

Job No. and

/or

Description

Basic Info. (Job Master)

Job No. and

/or

Description

New Job Info.

Updated Job Info. Verified Updated Job Info.

Job No. to be deleted Job No. to be deleted

1.4.5 Set

relations of

Jobs

Job Nos. to be related

Relationship of Jobs

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DFD 3.0 Run Scheduling Engine

Basic Information

3.1 Convert Basic

Info. to format

for Genetic

Representation

Planner

Data in GA representation

Jobs, Job relations,

Work Center Info.

Converted Data

3.2 Feed into

Data and required

parameters, and

run GA engine

Converted Data

GA parameters

3.3 Convert result

to understandable

/ meaningful

format

Result in GA

representation

Result

Result in

meaningful format

Log file

Execution Log

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Entity Relationship Diagram

Job Order Has Operation

Item

Precedence Related

Work Center

Item No

Description

Done in

Job No.

Quantity

Due Date

Operation Code

Seq. No.

Description

Setup Time

Run Time

Capacity Consumption Factor

Capacity Over Capacity Cost

Delay Cost

Storage Cost

CriticalDescription

Precedence Job Order No.

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4.4 Genetic Representation Before starting any further analysis or design work, it is essential to design and define the meaning or representation of the gene of a chromosome used in the GA. The writer has spent a period of time to find out and study various representation design. Explained in detail in the reference [7], for any genetic algorithm, the representation should be a minimal, complete expression of a solution to the problem. A minimal representation contains only the information needed to represent a solution to the problem. A complete representation contains enough information to represent any solution to the problem. If a representation contains more information than is needed to uniquely identify solutions to the problem, the search space will be larger than necessary. Whenever possible, the representation should not be able to represent infeasible solutions. If a chromosome can represent an infeasible solution, care must be taken in the objective function to give partial credit to the chromosome for its “good” genetic material while sufficiently penalizing it for being infeasible. In general, it is much more desirable to design a representation that can only represent feasible solutions so that the objective function measures only optimality, not feasibility. A representation that includes infeasible increases the size of the search space and thus makes the search more difficult. And the following sections try to explain different methods found.

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(1) By Dispatching Priority of Operations As from reference [2], the chromosome is partitioned into equally sized blocks of genes which is named as subchrome. One subchrome is used to encode a preference list for each resource. Within a subchrome a list of operation / job preferences (dispatch rules) is encoded, for the resource the subchrome relates to. Dispatch rules allow the program to choose the next operation / job to be processed for resource that becomes free, from any number of operations / jobs that are waiting to be processed in the input buffer of resource. Reading a subchrome from left to right gives us the operation / job to be chosen with the highest priority through to the lowest. For example, the chromosome for a four resource, four operation problem would be :

1320 0123 1023 3210 If we consider the third subchrome 1023, we have the operation choice preference list for the third resource. This means that if operations / jobs ids 0, 1, and 2 have stacked up in the input buffer of the third resource, then when the third resource is ready to process a new operation / job, the program should choose operation / job id 1 to be processed next as it has the highest priority of the waiting operations / jobs. This design of gene representation will require a simulation process after which the timing details (i.e. the start time, end time of each operation / job) can be found. This method leads to redundancy of gene representation. If there are n resources and m operations / jobs, there will be n x m genes. But actually the program do not need to know every priority of operation / job (even some has been allocated). This is undesirable because the performance of GA processing will become longer. When the input pool of data is large, the performance degrade would be significant.

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(2) By Sequence of Job No. As from reference [9], for a n-job and m-operation scheduling problem, a chromosome with a string containing n x m genes will be constructed. Each gene is interpreted as the first unscheduled operation of the job specified by the job number at the matrix of jobs and operations. The first unscheduled operation belonging to the job at each position in order is scheduled on the designated resource at the earliest time it can be started. For example, following is a typical chromosome for the 3x3 scheduling problem in matrix table a :

3 2 3 1 2 1 2 1 3 Table a :

Job No. Operation 1 Operation 2 Operation 31 (M1,t1) (M2,t2) (M3,t3) 2 (M2,t4) (M3,t5) (M1,t6) 3 (M1,t7) (M3,t8) (M2,t9)

where Mn represent the Resource used, and tn represent the time duration required. Schedule thus represented : Again, this method will also lead to redundancy of representation. Or if we modify it by limiting the number of genes to the number of operations, the problem may be solved.

J3 J1

J2

J3 J2

J1

J2

J3

J1

Time

M3

M2

M1

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(3) By sequence of Job No. in subchrome of resource This method is described in reference [8]. This is actually a combination of the methods described above. A chromosome is divided into subchromes and each subchrome represents a resource. Within the subchrome, it is a sequence of Job / Operation No., instead of priority of Job / Operation. Basically this method has similar drawback as described in the previous methods. (4) By “relative” time duration This is a method described in reference [7]. A single chromosome contains an array of numbers. Each number is associated with an operation and indicates the period of time from the latest finish of all the operation’s predecessors to the start of the operation. The times are measured relative to other operations, not to an absolute reference. As a result, precedence feasibility is assured for every schedule. For example, the chromosome is like :

T1 T2 T3 T4 T5 T6 T7 where Tn are the “relative” time Using this method, the length of a chromosome is the number of operations in the problem, and thus the redundancy problem will not be found here.

Time

Oper 1 Op2

Oper 5 Oper 4

Oper 3

Oper 7

T5

T7

T1 T2 T3

T4

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(5) Genetic Representation used in this project Quite obviously as described in the previous sections, the method of “relative” time should be the most appropriate one to be applied in the project. It is because it not only satisfies all the criteria described in the introduction paragraph of this section – Genetic Representation, and also it is readier to makes room for the further development of the application to cater for other requirements, such as consideration of alternative operating modes (e.g. alternative resources). It is because each gene, by this method, represents an operation, and in most case the alternativeness bases on an operation, not resource. So then one can build on this gene representation with other corresponding representation, to every operation (gene) in the problem set. However, in this project, a simple necessary modification is made to the method of “relative” time duration. Each chromosome is built up by a number of sub-chromosomes. Each sub-chromosome represents a Main Job in our problem. And so each gene will associate with an operation under a Main Job, that is, the operations of all the sub-jobs will be regarded also under a Main Job. The operations of all sub-jobs (of a main job) will be gathered under one sub-chromosome with the non-arbitrary order. Let us have an example to illustrate, say, we have 2 main jobs and the tree representation of their relationship with their own sub-jobs as follow : Then the chromosome will have 8 genes (equal to total number of operations), and each gene will store the “relative” time for a particular operation. The following order

Main Job A

1) Oper. A1 2) Oper. A2

Sub-Job A1

1) Oper A11 2) Oper A12

Sub-Job A2

1) Oper. A21

Main Job B

1) Oper. B1

Main Job B1

1) Oper. B11 2) Oper. B12

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will be the order of operations assigned to the chromosome.

A11 A12 A21 A1 A2 B11 B12 B1

The first gene now will represent the operation A11 in the example. Note that the sequence of the operation is not arbitrary. The operation should have all its precedent operations already been assigned a gene representation. We shall discuss it in detail in the Section 5.4 – Process Specification. (6) Comparison Below the writer try to summarize the characteristics of the methods described in this section for genetic representation.

Method Completeness Uniqueness Non-Redundancy Feasibility included

(1) Dispatching priority Y N N N

(2) Job Sequence Y N N N

(3) Job sequence in resource subchrome

Y N N N

(4) “Relative” time Y Y Y Y

(5) modified “relative” time Y Y Y Y

As a short conclusion, the genetic algorithm operates on the structure of the chromosome without considering what the chromosome means in the schedule space. As a result, the constraints are coupled to the search algorithm only through the genetic operators, that is, “initialization”, “crossover”, and “mutation”, and the objective measures are completely decoupled from the search algorithm. The following section will discuss the objective (fitness) functions used in this project in detail.

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4.5 Fitness Functions Analysis Apart from the finalization of Genetic Representation, the design of Fitness Functions is very critical as well, because this would greatly affect the database structure design. The writer would like to spend a section to discuss the reasons behind these functions as below. In this program, 5 fitness functions are used to evaluate the quality of the schedules generated from the chromosomes in the population pool : (1) Over-Capacity of Work Centers (2) Over-Due of Main Job Orders (3) Make Span of all Job Orders (4) Idle period of Critical Work Center(s) (5) Work-In-Progress (WIP) level of components, or degree of Just-In-Time (JIT) The total or final score of a chromosome will then be the sum of the values of multiplying each of the score with their corresponding weightings. And the smaller the total score, the better the schedule a chromosome represents. (1) Over-Capacity of Work Centers

As from the definition of the objective of this project, capacity consideration is the first rule to be considered. Jobs should be assigned and scheduled on the individual resource under the capacity constraint. In the analysis of real life situation, however, we always find there may be no strict constraint of capacity of some resources. For example, in order to complete the operation to meet the order due date, overtime work will be arranged. In other words, capacity constraint can be broken at a cost. In order to provide this kind of flexibility, a field “Over Capacity Cost” (OT_Cost in table WC) is assigned to the Work Center Master such that the planner can take into account of the possibility of Over-Capacity. Of course, if the capacity of a resource is strictly restricted, the value of the field should be set to a value as large as allowed, say, 9999999, so that no over-capacity allocation arrangement will be scheduled on this resource.

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(2) Over-Due of Main Job Orders

It will be meaningless if there is no constraint of meeting the delivery date of an order during the scheduling process. Same as the capacity constraint, on-time delivery or due-date constraint should be a primary consideration. Also the same as the Over-Capacity issue, it is possible that an order can be delivered after the pre-set delivery date, at a cost ! A popular example in the real life is that the goods can be delivered by air or express to the end customer, instead of shipping or other cheaper transportation means, if the production cannot meet the due date. Or even worse, there may be term stated on the sales contract that a penalty cost will be charged for the delay. Therefore, in the design of this fitness function, a field “Delay Cost” (DelayCost in table JO) is implemented on each Main Job Order. It is the basis for the penalty cost per time unit (Time Unit will be discussed in the next section). With the consideration of both “Delay Cost” and “Over-Capacity Cost”, the scheduling engine can make a trade-off “decision” in order to minimize the total cost, which should be a reasonable basis for the scheduling problem in the real life.

(3) Make Span of all Job Orders

Make Span is a very common criteria to be considered in the Job Shop Scheduling Problem described in academic papers. The objective of using this criteria is to minimize total period of time occupying the resources by the jobs. It would avoid the scattering of jobs over the planning board, specially in the case of only a few jobs exist in the scheduling problem. In this project, it is also taken into account.

(4) Idle period of Critical Work Center(s)

In the real life scheduling problem, there is / are always bottlenecked Work Center(s). They are usually special processing machinery, e.g. Surface Mounted Technology (SMT) machine in the electronic industry, CNC machine center in the metal processing industry. As they are usually very expansive, it is not possible for a manufacturer to purchase too many of them and they become the bottleneck of the whole manufacturing process.

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Therefore, a special scheduling technique or criteria will be used for those critical Work Centers. In the situation that there are too many jobs (operations) to be scheduled on those bottlenecked Work Center, the scheduling engine need to only consider Over-Capacity and Over-Due criteria, as described above. However, in the case that there are idle periods of the Work Center, the planner should “crowd” as far as possible all the jobs (operations) together and make room(s) as large as possible on the planning board so that later jobs can be assigned easier onto those bottleneck Work Centers. This is desirable because once a schedule is confirmed and released to the production floor, less change should be made as far as possible in the next scheduling result compared to the released one. The following diagrams try to illustrate the idea : In this project, a flag “Critical” is implemented for each Work Center such that the described technique will be applied to them. And the fitness function will count on the number of idle periods, the less it is, the better score will be assigned. In the

Time

Bottleneck (Critical) Work Center

Scattered schedule – not desirable

Time

Bottleneck (Critical) Work Center

Crowded schedule – Desirable

Diagram 4.5a

Diagram 4.5b

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above example, the number of idle period of diagram(4.5a) is 4, while that of diagram (4.5b) is 2. Apart from above, the desire of minimizing “slack time” between operations in a work center can also be handled by using this fitness function.

(5) Work-In-Progress (WIP) level of components, or degree of Just-In-Time (JIT)

It is also a popular idea in nowadays manufacturing concept that the components should be supplied “Just-In-Time” to its next process or even Product delivery. The main purpose is to minimize the level of Work-In-Progress stock in the shop floor. To include this concept into the scheduling process, a field “Storage Cost” per Time Unit (StorageCost in table JO_Oper) is implemented which will be used to calculated the total cost of storing the WIP after each operation. The scheduling engine will count it in the evaluation scores.

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4.6 Other special considerations

To fit the system requirements into the GA engine, and also to provide user-friendly features, there are 5 more special issues to be discussed and determined before the actual start of the design and implementation work. The 5 issues are : (1) Time Unit definition (2) Maximum Allowed values of “Relative” time (3) GA termination criteria (4) Other GA issues (5) 3 Best Results record (6) Logging for schedule run

(1) Time Unit Definition

As the GA engine used in this project do not accept real number as the gene value, integer value is used. However, to provide the flexibility of setting the time gratuity of the schedule, that is by week, by day, by hour, or even by minute, the concept of “Time Unit” is introduced. Basically, all the time related variables used in the program will base on Time Unit. And the conversion of the values of the variables to the actual date and time will make use of the field “Time Unit per Day” (TimeUday in table Parameter) which stores the number of Time Unit in a day. For example, it should be set as 24 if the time gratuity is in hour and full day running is assumed, or it should be 8 if only 8 hours-day work is assumed. The schedule results, i.e. the start time and end time of operations, not only be represented by date, but also in proportion of a day. That proportion value is calculated by using “Time Unit per day” as the basis.

(2) Maximum Allowed values of “Relative” time

As an essential parameter supplied to the GA engine, the maximum integer value to be randomly generated at the initialization stage (the very beginning stage of generating the first pool of chromosome for the GA) to the gene is to be determined first. In the genetic representation used in this project, this max. value is actually the max. allowed “relative” time duration to be considered.

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This value could be defaulted as the maximum due time (in Time Unit) of Main Job Order in the problem set. However, the writer think that it would be more flexible to allow the user to set this value manually before starting the scheduling process. It is because it will reach the “optimal” or “sub-optimal” results in a shorter processing duration if this value is set as an “appropriate” smaller value, and this is practical in the case that the relative time between operations needed to be limited in a certain range (somehow similar to the JIT concept), or the scheduling engine is required to consider a lot of jobs / operations and they are usually crowded together. Of course, there will be drawbacks of setting too small this value. “Optimal” result may not be obtained because the “relative” time is limited in a certain range. So it must be very careful to set this value. Generally speaking, if not so many jobs are in the problem set or the range of scheduling period is long, this value should be set around the due time of the Main Job with maximum due date.

(3) GA termination criteria

Termination criteria is also to be defined before executing the scheduling process. In this project, fix number of generations will be used. Therefore, “Number of AI scheduling cycles” is allowed to be set before the execution. It will be the number of cycles that the GA engine runs on and ends. Of course, the larger the value it is, the longer the engine will run, but the better result could be obtained. Please refer to the screen capture (1) in the Appendix section 10.4 for the discussion above.

(4) Other GA issues

Apart from the two parameters for GA discussed, the writer also paid attention to the following parameters used in GA computation : - mutation probability - population size - mating pool size - crossover probability

However, the writer think that these parameters should not be set by general user because the outcome of wrongly assigning values to those parameters is not

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guessable by the writer. Therefore, they are hard-coded in the program. On the other hand, the writer has tried to do a small evaluation test against different combinations of the values of those parameters. The result and conclusion are discussed in section 6.4.

(5) 3-Best Results Record

As discussed in the introduction of application of GA in scheduling problem, it should not be expected that an optimal solution can be obtained. Near-optimal or “good” solution is more realistic. And moreover, we have 5 types of fitness functions used in this program, and there may be case that total scores of different resulted schedule can be the same, but the individual score can be different. Therefore, the program is designed to keep 3 best results (least score) after the scheduling process. One can view the breakdown of the scores of individual fitness function for each of the 3 best results, and choose the one more suitable to apply practically. To keep the 3 results, 3 sets of fields are included in the tables storing the results in the database, they can be found in table Parameter and GeneInfo. (Details will be discussed in the next section.) Please refer to Appendix 10.4 (2) for the system screen.

(6) Logging for schedule run

Performance is also one of the issues to be reviewed at the end of the project. Time taken to generate a good schedule is needed to be logged down so that the performance can be compared. At the same time, the parameters used in the execution are also logged down, e.g. “number of operations” considered in the process, the values of weightings…. And if there is any exception found, the problem will also be logged down. Text file is used to keep the log in the project. Please refer to Appendix 10.4 (3) for the system screen.

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5 System Design 5.1 Structured Charts

Structured Charts are used in the design stage of the program development. Important Structured Charts are shown below :

AI Scheduling System

Process Basic Information

Process GA Parameters

Execute GA scheduling

Convert GA results

Validated Basic Info.

Validated Parameter

Validated Basic Info. & Parameters

GA schedule results

GA schedule results

Process Basic Information

Process Item Data

Process Work Center Data

Process Operation Data

Process Job Orders Data

Validated Item Info.

Validated Work Center Info.

Validated Operation Info.

Validated Job Order Info.

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The diagram below is a template for Basic Information processing, it is basically the same for Item Data, Work Center Data, Operation Data and Job Order Data.

Process Job Orders Data

Process Main Job Order Basic Data

Process Main Job Operation Data

Process Sub-Job Basic Data

Process Sub-Job Operation Data

Validated Main Job Basic Info.

Validated Main Job operation Info.

Validated Sub-job Basic Info.

Validated Sub-job Operation Info.

Validated Main Job Basic Info.

Validated Main Job & Sub-job Basic Info.

Validated Job Orders Info.

Process Item Data

Add new record

Search existing record

Modify existing record

Delete existing record

New Item Info.

Existing Item Info.

Updated Item Info.

Validated Item Info.

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As a remark, “GA acceptable format” just simply means the Gene Representation discussed in the corresponding section previously. And the “meaningful” format means the Start Time and End Time of each operation. Note that the Start Time and End Time will be converted to user acceptable format – Start Date and End Date by the module – Convert GA Results. For more detail about the design of these core parts of AI Scheduling system – Data Conversion, Execute GA process and Convert GA Results, the writer will have a detailed discussion on them in the section 5.3 – Process Specifications.

Execute GA engine

Convert Basic Info. & Parameter to GA acceptable format

Feed the converted format and start GA calculation

Convert the result from GA calculation to meaningful format

Converted format

GA schedule results

Schedule result in GA format

Validated Basic Info. & Parameters

GA schedule results

Validated Basic Info. & Parameters

Converted format

Schedule result in GA format

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5.2 Database Design

Basically from the ER diagram shown in section 4.3, the skeleton of the database structure can be built. In addition with data used in GA computation, the whole database can then be built. The detailed database full listing is included in the Appendix section. And a brief introduction of the tables designed is given below.

Table name Main Functions Basic Information JO To store the user input information about Job Orders. WC To store the basic information about Work Centers used in the

system. Item To store the basic information about Item to be processed in the

manufacturing operation. Oper_WC To store the information about Operation. JO_Oper To store the Operations (Routing) required to complete the Job

Order. Parameter To store the parameters used in the GA scheduling, and the

scores breakdown of the best 3 results. Users To store the login user information. Tables used in GA calculation GeneGAInfo (Temporary DataSet)

To store the basic information of each gene used in the GA evaluator, and store the temporary data (StartTime and EndTime) used in the GA calculation.

GeneInfo To store initially the gene information from the conversion of user input data into gene representation (relation of gene with Job Order and Operation), and also keep the final result of the GA to facilitate output to user interface (i.e. Start Date and End Date)

MainJO (Temporary DataSet) To store temporarily the result of GA evaluator for the comparison of end time and due time for the Main Job Order.

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5.3 Process Specifications

As mentioned above, the writer will try to list the detailed process specifications used for the 3 core functions of the GA scheduling process in this section. It should be highlighted here that the GA engine used in this project is provided by the writer’s supervisor, Dr. Andy Chun. What the writer need to do is to convert the basic information into the format of Gene Representation discussed and modify (override) the evaluation function used in calculating the score for the chromosome, feed and start the GA computation, and finally convert back the gene information to a schedule. In short, the 3 functions are : (1) Gene Converter (RunSchedule.vb) (2) Evaluator (StartGA.vb) (3) Result Assigner (Converter) (AssignResult.vb)

(1) Gene Converter

Basic Concept To assign the operation of jobs onto the genes of the chromosome, make

sure that the operation of jobs of a main job is always assigned before those operations nearer to the root in the tree of operation of jobs of Main Job. “Stack” method is used.

Each main job is represented by a sub-chromosome. All sub-chromosomes will be catenated to form the whole chromosome

with no marking gene is used to separate the sub-chromosome.

Check Data (in Database) validity 1) Check table WC if it is empty; 2) Check table JO if it is empty; 3) Check table JO_Oper if it is empty; 4) Check table Oper_WC if it is empty; If any of the above table has no record, message to alert the user that : “No Data of ???? ! Please check first and start the Scheduling again.” Where ???? depends on which kind of data is missed, WC – Work Center JO – Job Order JO_Oper – Operation Oper_WC – Operation / Work Center relations

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Increment the Log Number of Scheduling Execution Update the field “Log_no” in table Parameter by 1 Create DataSet and get data from Database 1) Create Data Tables for :

- GeneGAInfo - GeneInfo - WC - JO - JO_Oper - Oper_WC

2) Fill the data tables from the database tables correspondingly Calculate and store the number of WCs (WC_No) 1) start from 0, assign for each record in table WC to WC_No with increment of Using Stack to convert the tree of Jobs to Genes Spec. Detail Add one more field – EXPLODED (Boolean) [default as False] – to the datatable of JO, which is used to record whether the JO has been exploded to find its successors in the stack. 1) Clean up the datatable GeneGAInfo, GeneInfo and MainJO. For each ACTIVE (Active = 1) main job in JO, perform all the following steps : 1) Select from table JO all the sub-jobs of the same main job to form a temp

collection (e.g. ABC); 2) Create a STACK. 3) Find the record of Root – the Final Product – PredJO_No = 0 (or JO_No =

MainJO_No), and get its value of JO_No; PUSH it to the Stack. 4) If there is more than one record found, write to the log file “Main Job XXX is

not properly relating its sub-job !”, and exit this loop, to another Main Job. 5) If EXPLODED is True, jump to step (8). 6) Select the records from ABC where PredJO_No = JO_No found in (3); 7) If found record exist, Push all of them to the Stack, and set the value of

EXPLODED of the Root (or original JO) to True. 8) If not found any record as from (6), Pop from the stack, and execute

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ASSIGN [another method to assign the values to tables GeneGAInfo and GeneInfo and MainJO] to pass the information of that JO for assignment.

9) If Stack empty, exit the loop. 10) If not empty, get the JO_No value of the topest item from the Stack, and

pass it back to step (5) above, that is, Loop back to step (5). 11) Add a record to table MainJO, with information :

Field Name Value MainJO_No Current MainJO_No DueTime { DueDate (in JO) - StartDate (input by user before executing

the AI Scheduling)} * TimeUday (in table Parameter) Accu_EndTime - Overdue_Cost DelayCost (in JO) StorageCost StorageCost (in GeneGAInfo where MainJO_No = this

MainJO_No and SucGene = 0 )

ASSIGN method : Obtain from calling object the following information – - JO_No (this) GeneCount is used to store the number of Gene exist in the chromosome, initialized as zero at the very beginning. 1) Select from JO_Oper where JO_No = past into JO_No order by

OperSeq_No in Ascending order; 2) For each record from (1), 3) Add record to GeneInfo, with information :

Field Name Value Gene_No GeneCount + 1 JO_No JO_No past in MainJO_No MainJO_No in table JO where JO_No is the past in OperSeq_No OperSeq_No (this) OperCode OperCode in the table JO_Oper where JO_No is the past in

and OperSeq_No = this OperSeq_No WC_Code WC_No in table JO_Oper where JO_No = past-in, and

OperSeq_No= this StartDate - EndDate -

4) Add record GeneGAInfo, with information :

Field Name Value Gene_No GeneCount + 1 PredGene / SucGene

1) if this JO_No is the ending leaf of the tree, i.e., there is no record found in table JO where PredJO_No = this JO_No,

2) further from (1), and if it is the first Operation of this JO_No, i.e., smallest OperSeq_No among the operations of this Job, then assign PredGene = 0;

3) from (2), if not the first Operation, then PredGene =

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GeneCount [i.e. its previous gene]; 4) and further from (3), locate at the record in GeneGAInfo

where Gene_No = GeneCount, and assign its SucGene=GeneCount+1;

5) from (1), if this JO_No is not the ending leaf, and if it is the first Operation of this JO_No,

6) from (5), and if there is more than one son (i.e. more than one record in table JO where PredJO_No = this JO_No), then assign PredGene = -1;

7) and from (6), find all the records in the JOIN table of GeneGAInfo & GeneInfo & JO where PredJO_No = this JO_No and largest OperSeq_No within each set of same JO_No in GeneInfo, then assign SucGene = GeneCount +1;

8) from (6), if there is only one son, then assign PredGene = GeneCount;

9) and from (8), locate at the record in GeneGAInfo where Gene_No = GeneCount, and assign its SucGene = GeneCount + 1;

10) Assign this record SucGene =0. MainJO_No MainJO_No in table JO where JO_No is the past in WC_No WC_No in table WC where WC_Code = WC_Code in

JO_Oper, and OperSeq_No = OperSeq_No of this Gene (GeneInfo)

StartTime - EndTime - OperTime {Qty (in JO where JO_No = JO_No past-in) * RunTime (in

JO_Oper where JO_No = JO_No past-in and OperSeq_No = OperSeq_No of this Gene (GeneInfo))} + SetupTime (in JO_Oper where JO_No = JO_No past-in and OperSeq_No = OperSeq_No of this Gene (GeneInfo)

StorageCost StorageCost in table JO_Oper where JO_No = JO_No past-in and OperSeq_No = OperSeq_No of this Gene (GeneInfo).

CapConsume CapacityCFactor in table JO_Oper where JO_No = JO_No past-in and OperSeq_No = OperSeq_No of this Gene (GeneInfo)

5) GeneCount +=1 6) Loop back to (2) Call the GA_Core to start the GA calculation

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(2) Evaluator 1) Get data to DataSet from DB for table :

GeneGAInfo, MainJO (get DueTime, OverdueCost, store AccuEndtime), WC (get Capacity Limits)

Check the DataSet are not empty such that the calculation will not be invalid. 2) Get parameters from other programs :

objective weights (wt?), 3) Define parameters used internally :

- Score of Chromosome (Score) to be past back and initialized as zero, WC occupation array (WC[(WC_No, TimeRange)]) all initialized with value=zero,

- WC_No = DataSet.Tables(WC).Rows.Count and TimeRange = Greatest DueTime (MaxDueTime) + 10*TimeUday ,

- Total Make Span variables ( MinTime, MaxTime) in Time Unit initialized with zero,

- Number of Idle Periods (NumIdle) initialized as zero - Flag identifying Continuity of Occupation of Work Center (Cont) initialized as

False - Over Capacity Score variable (OverCapS) initialized as zero - Over Due Score variable (OverDueS) initialized as zero - Make Span Score variable (MakeSpanS) initialized as zero - Just-In-Time Score variable (JITS) initialized as zero - Total Score variable (TotalS) initialized as zero

4) Starting from the first gene of the chromosome to the last gene, - calculate the End Time (EndTime) :

if PredGene = 0, StartTime=Gene Value and EndTime=StartTime+OperTime else if PredGene = -1 (means multiple predecessor), sort out from GeneGAInfo that SucGene = Gene_No and find the one which has greatest EndTime, then StartTime= EndTime of the found gene + Gene Value and EndTime = StartTime + OperTime; JITS=EndTime of the found gene ((greatest EndTime) – EndTime of other genes)*StorageCost of the gene. else find the EndTime of gene with Gene_No = PredGene, then StartTime = EndTime of the found gene + Gene Value and EndTime = StartTime +

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OperTime - Update MainJO : if AccuEndTime < EndTime, then AccuEndtime = EndTime

where MainJO.MainJO_No = GeneGAInfo.MainJO_No - Update Capacity consumed by WC (WC[]) : If

EndTime > TimeRange, reDim WC[] array and TimeRange = EndTime, then For y=StartTime to EndTime, Update WC[WC_No,y] = WC[WC_No,y] + GeneGAInfo.CapConsume

- If StartTime < MinTime, MinTime = StartTime. - If EndTime > MaxTime, MaxTime = EndTime.

5) Calculate the scores of the chromosome : - Over Capacity : For x = 1 to WC.Rows.Count and for y = 1 to TimeRange, if

WC[x,y] – WC.Capacity > 0, OverCapS = OverCapS + OTCost*(WC[x,y]-Capacity)

- Main JO Over Due : For all records in MainJO, check if MainJO.AccuEndTime > MainJO.DueTime, then OverDueS = OverDueS + OverDueCost * (MainJO.AccuEndTime – MainJO.DueTime) Else (MainJO.AccuEndTime < MainJO.DueTime) , JITS = (MainJO.AccuEndTime – MainJO.DueTime) * StorageCost

- Make Span : MakeSpanS = MaxTime – MinTime - Number of Idle Periods :

For critical Work Center(s), Initialize Cont = No For x = 1 to TimeRange, if WC(WC_No,x) = 0

if Cont=No, then NumIdle = NumIdle+1 and Cont=Yes endif else if WC(Wc_No,x) <> 0, then Cont = No

- Calculate the Final Score : Final Score = OverCapS * WT_OC + OverDueS * WT_OD + MakeSpanS * WT_MS + NumIdle*WT_ID + JITS*WT_JIT

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(2) Result Assigner (Converter) 1) Connect to DataTable : GeneInfo

Check the DataSet are not empty such that the calculation will not be invalid. 2) Get parameters from table Parameter :

objective weights (wt_??) 3) Define parameters used internally :

- Score of Chromosome (Score) to be past back and initialized as zero, WC occupation array (WC[(WC_No, TimeRange)]) all initialized with value=zero,

- WC_No = DataSet.Tables(WC).Rows.Count and TimeRange = Greatest DueTime (MaxDueTime) + 10*TimeUday ,

- Total Make Span variables ( MinTime, MaxTime) in Time Unit initialized with zero,

- Number of Idle Periods (NumIdle) initialized as zero - Flag identifying Continuity of Occupation of Work Center (Cont) initialized as

False - Over Capacity Score variable (OverCapS) initialized as zero - Over Due Score variable (OverDueS) initialized as zero - Make Span Score variable (MakeSpanS) initialized as zero - Just-In-Time Score variable (JITS) initialized as zero - Total Score variable (TotalS) initialized as zero

4) Starting from the first gene of the chromosome to the last gene, - calculate the End Time (EndTime) :

if PredGene = 0, StartTime=Gene Value and EndTime=StartTime+OperTime else if PredGene = -1 (means multiple predecessor), sort out from GeneGAInfo that SucGene = Gene_No and find the one which has greatest EndTime, then StartTime= EndTime of the found gene + Gene Value and EndTime = StartTime + OperTime; JITS=EndTime of the found gene ((greatest EndTime) – EndTime of other genes)*StorageCost of the gene. else find the EndTime of gene with Gene_No = PredGene, then StartTime = EndTime of the found gene + Gene Value and EndTime = StartTime + OperTime

- Convert the StartTime and EndTime to Date - Save the calculated StartDate and EndDate into GeneInfo

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- Update MainJO : if AccuEndTime < EndTime, then AccuEndtime = EndTime where MainJO.MainJO_No = GeneGAInfo.MainJO_No

- Update Capacity consumed by WC (WC[]) : If EndTime > TimeRange, reDim WC[] array and TimeRange = EndTime, then For y=StartTime to EndTime, Update WC[WC_No,y] = WC[WC_No,y] + GeneGAInfo.CapConsume

- If StartTime < MinTime, MinTime = StartTime. - If EndTime > MaxTime, MaxTime = EndTime.

5) Calculate the scores of the chromosome : - Over Capacity : For x = 1 to WC.Rows.Count and for y = 1 to TimeRange, if

WC[x,y] – WC.Capacity > 0, OverCapS = OverCapS + OTCost*(WC[x,y]-Capacity)

- Main JO Over Due : For all records in MainJO, check if MainJO.AccuEndTime > MainJO.DueTime, then OverDueS = OverDueS + OverDueCost * (MainJO.AccuEndTime – MainJO.DueTime) Else (MainJO.AccuEndTime < MainJO.DueTime) , JITS = (MainJO.AccuEndTime – MainJO.DueTime) * StorageCost

- Make Span : MakeSpanS = MaxTime – MinTime - Number of Idle Periods :

For critical Work Center(s), Initialize Cont = No For x = 1 to TimeRange, if WC(WC_No,x) = 0

if Cont=No, then NumIdle = NumIdle+1 and Cont=Yes endif else if WC(Wc_No,x) <> 0, then Cont = No

- Calculate the Final Score : Final Score = OverCapS * WT_OC + OverDueS * WT_OD + MakeSpanS * WT_MS + NumIdle*WT_ID + JITS*WT_JIT

6) Save the scores into the DataTable : Parameter 7) Update the database tables of Parameter and GeneInfo. 8) Write to Log File for case :

- those Main JO which DueTime is negative;

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5.4 Interfaces Design It is relatively simple in the design of interfaces flow of this program. Let us illustrate the flow by diagram below : First, a login interface is provided to allow the user input the ID and password. Then a main menu is seen on which one can choose which sub-function is to be called. For those sub-functions for Basic Information manipulation, a list of existing records is to be shown, and searching function is provided, as well as an “ADD record” function. After selecting the record to be managed or to add new record, the detail information screen is displayed, allowing the user to manipulate the information by using buttons provided.

ID : _______ Password : ________

Sub-function 1

Sub-function 2

Sub-function 3

…..

Record 1 Record 2 Record 3 ……

Searching function

Add record

Detail info. 1 : _________

Detail info. 2 : _________

Detail info. 3 : _________ ……

“Cancel” Button

“Edit” Button

Delete Button

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The “Edit” Button is to tell the program the input or update process of data is finished and confirmed, while the “Cancel” Button is to abort the process and back to previous screen or menu. For the relatively complicated Job orders input, the screen layout is designed as : For execution function (e.g. AI schedule processing), the execution interface will be displayed once it is chosen on the main menu, allowing the use input essential information before the execution. Finally, if the work in the system is finished, the user can properly logout the system, and the original login screen will be shown again. Apart from the general flow described above, the writer would like to highlight three special interfaces used in the system. The main reason for these special interfaces is to

Parameter 1 :__

Parameter 2 :__

… Start & Cancel execution button

ID : _______ Password : ________

Parent Job Details Operation of the Parent Job

List of Sub-jobs

Add Sub-Job Button

Edit Parent Job Button

Cancel Button

Add Operation Button

Edit and Delete Operation Buttons

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facilitate the user to acquire the information in a graphical mode. They are : (1) Tree structure display of Job orders relationship and ; (2) Gantt Chart display of schedule result. (3) Calendar type of Date entries

(1) Tree Structure (2) Gantt Chart (3) Calendar

Main job – |__Sub-Job – | |__Sub-Job | |__Sub-Job | | |__Sub-Job— |__Sub-Job |__Sub-Job |__Sub-Job |__Sub-Job

Work

Centers

or Jobs

Time

Year Month

1 2 3 ….

Sun. Mon. Tue. Wed. Thur. Fri. Sat.

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6 Implementation 6.1 Technical consideration Because there already provided libraries (functions) to be used for basic GA computation, that is, the basic GA engine is ready. In considering programming language used in the project, 3 commonly used languages can be chosen, as the libraries of GA mentioned can be called by them. They are Java, C# and VB.Net. And for the sack of easier pick-up, VB.Net is selected, because the writer did not familiar with any one of them before the project started. Another important issue to be determined before start programming is that the system should be Web-based or Windows-based. As the global trend is going toward the side of Web-based application, the writer decided to have this system be put on the Web. ASP.NET is used then in order to make it happen, accompanied with the use of VB.NET. For the data storage issue, Microsoft SQL server is used as the database engine in this project. The main reason is that it is widely used in SME of Hong Kong. And it can provide some basic database management facilities, e.g. security, data integrity, user-friendly interface (as the writer is familiar with the management of MS SQL server). And more important, it is claimed in the technical document by Microsoft that using SQL server connection, instead of other database engines, together with VB.NET would have better performance. Actually the database adapter used in VB.NET for SQL server is special and different from other database connection adapter. Other database engines are not considered. For examples, Microsoft Access has limitation in database size and fields definition. Oracle may be a little bit too complicate and not so popular in Hong Kong SME.

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6.2 Program Structure

Three tier system structure is used in the program implementation. They are respectively :

- Presentation layer - Business Logic layer (Application layer) - Database Access layer

Presentation Layer The Presentation layer is a Web layer, provides access for clients to the application in a browser.

Business Logic Layer The Business Logic layer, contains the implementation of the various business rules and logic.

Data Access Layer The Data Access layer provides data services to the Business Logic layer , and access the data from data source..

The main advantage of using this multi-tier architecture is that the application would be more portable and flexible. Just modify the database name and password in the file “web.config”, the application can be connected to another SQL server. And as the Business Logic layer is basically separated from other layers, any modification of the scheduling process logic can be flexibly done without great change in other layers. The maintainability of the program is thus also more favorable.

Data Source

Presentation

Data Access

Business

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6.3 Special programming issues highlight

In this section, the writer is going to discuss some special programming issues during the program coding stage in this project. They are :

- Use of DataSet - Graphical Representation of Tree structure for Job relation - Graphical Gantt Chart Representation of Schedule - Searching features

Use of DataSet

In the programs of GA Evaluator (StartGA.vb) and GA Results Assigner (AssignResult.vb), they need to frequently acquire information from the database and write back temporary calculation results to the database in every cycle of calculating scores for each chromosome in the population pool. If every times the programs have to build the database connection and transfer data, this would greatly decrease the performance of the program, as we know that system I/O (access to hard disk) is usually the bottleneck of program execution. In studying VB.NET, the writer found that the language provides a solution to this issue – DataSet. The DataSet object is central to supporting disconnected, distributed data scenarios with ADO.NET. The DataSet is a memory-resident representation of data that provides a consistent relational programming model regardless of the data source. In other words, the programs need to access the memory (RAM), instead of the hard disk, in every access to the database data. It is now only required to load the related tables once from the hard disk at the beginning of the program and write the updated data back to the hard disk at the end of the program.

Graphical Representation of Tree structure for Jobs relation

As mentioned in the System Design section, to provide a user-friendly representation, a graphical representation of Tree view is done. It is actually achieved by using VB.NET to write a recursive program. It begins with the shared Sub() ShowJO, and it call the shared function ShowChildJO ,and keep call ShowChildJO till no more sub-Job. These are included in JobOrders.vb file in BusinessLogic folder. The screen capture below demonstrates the result.

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Graphical Gantt Chart Representation of Schedule Apart from presenting the schedule in table format, Gantt Chart view is also provided by the system. It is achieved by calculating the width and position of bars representing the jobs to html format, using VB.NET. Two special features are implemented here :

(1) Gantt Chart by Work Center / Job Orders (2) Color highlight for all operations of sub-jobs under a specified

Main Job The screen captures in the following pages try to illustrate the features.

Searching Feature

In all the ‘first’ screens for going into Basic Information Management functions (e.g. Item Data), a searching feature is provided by the system. It is useful when the number of records increases to significant amount, such that the user cannot view all the records in one screen. Two searching criteria are provided – the key code or number and its description. The screen capture on the following pages demonstrates this feature in the system :

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6.4 GA parameters settings As mentioned in section 4.6.(4), the writer has performed a small-scaled experiment on the quality of the results of schedule with the GA parameters settings. The experiment was done by executing the scheduling program with the same set of Job orders, execution cycle, maximum allowed ‘relative’ time, and weightings of scores, but varying the combination of values of the parameters : mutation probability, population size, mating pool size, crossover probability. The experiment result is summarized below : Population Size

Mating Pool Size

Crossover Prob.

Mutation Prob.

OverDue Cost

OverCap Cost

JIT Cost

Best Total Score

100 80 0.7 0.1 0 100 418 5330 100 80 0.8 0.1 0 90 434 5386 100 90 0.7 0.1 0 130 386 5305 50 45 0.7 0.1 0 50 306 3707 50 40 0.6 0.1 0 290 413 7174 50 40 0.7 0.1 0 80 364 4587 50 40 0.8 0.1 0 200 394 6083 40 36 0.7 0.1 0 70 543 6278 40 32 0.7 0.1 0 40 237 2917 40 28 0.7 0.1 0 30 307 3518 60 54 0.7 0.1 0 170 846 10305 60 54 0.7 0.1 0 300 754 10689 60 48 0.7 0.1 0 50 409 4740 25 20 0.7 0.1 0 280 679 9733 No. of Cycles = 300 No. of job operations = 14 Max. allowed ‘relative’ time = 150 It should be admitted that the experiment was quite small in scale and may not reflect the real picture, but for those cases which gave extreme results, e.g. total score above 10,000 and below 4,000 , the writer has repeated the testing and took the average values. So, the table of results still has its value of reference in the project. Highlighted in the table the combination (40, 32, 0.7, 0.1), it gave the lowest total score (2917), meaning that its result has best quality among the combination tested in the experiment. And it is used by the writer in the program for the evaluation part of the project.

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7 System Evaluation 7.1 Evaluation Plan It is really not easy to evaluate an application system because it can be graded from different criteria or different points of view, e.g. accuracy, user-friendliness, performance, functionality, flexibility, extensibility, maintainability….. And even worse is that some of the criteria is subjective in nature, e.g. functionality and user-friendliness. Therefore, the writer would limit the evaluation criteria to those listed below, not hoping to include all, but put effort on what the writer thinks most important. (1) Feasibility of result (2) Quality of result, in terms of Over-Due Time and Operation Slack Time (3) Repeatability of result generation / Performance of the scheduling engine (4) Time required to obtain quality result The criteria are used because the objective of the project is to generate a production schedule for a set of jobs / operations on a set of manufacturing resources, and they are usually what a real world planner doubts about a scheduling software. To have a bench mark reference, a commercial scheduling system – Preactor is used (its evaluation version 9.0). The 2 theories of scheduling of this package have been introduced in the section 2.1 already. And the writer will use its “algorithmic sequencing” method – a more popular method (because it is much more economic and affordable to the SME of Hong Kong) – in the comparison with the program of this project. For the sample data used in the evaluation, five main job orders, with 14 operations are used, from MJ-01 to MJ-05. The details about them is listed on the next page :

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Level Job No. Main Job No. Item No. Quantity

Main Job Due Date Precessor Operation

Work Center

Setup Time

Run Time

0 MJ-01 MJ-01 Product-01 10 2003/1/11 MJ-01 OP03 WC03 3 1

.1 SJ-01 MJ-01 COMPONENT-01 10 MJ-01 OP02 WC02 2 2

..2 SJ-011 MJ-01 COMPONENT-02 10 SJ-01 OP01 WC01 3 5

.1 SJ-02 MJ-01 COMPONENT-03 10 MJ-01 OP04 WC04 3 3

..2 SJ-021 MJ-01 COMPONENT-05 10 SJ-02 OP05 WC05 1 1

..2 SJ-022 MJ-01 COMPONENT-04 20 SJ-02 OP06 WC06 2 2

0 MJ-02 MJ-02 Product-02 10 2003/1/9 MJ-02 OP05 WC05 2 2

.1 SJ-02-1 MJ-02 COMPONENT-04 10 MJ-02 OP06 WC06 3 2

0 MJ-03 MJ-03 Product-03 10 2003/1/4 MJ-03 OP03 WC03 1 1

.1 SJ-03-1 MJ-03 COMPONENT-05 10 MJ-03 OP04 WC04 1 1

0 MJ-04 MJ-04 Product A 10 2003/1/6 MJ-04 OP03 WC03 1 1

.1 SJ-04-1 MJ-04 COMPONENT-04 10 MJ-04 OP04 WC04 1 1

0 MJ-05 MJ-05 Product A 10 2003/1/15 MJ-05 OP03 WC03 1 1

.1 SJ-05-1 MJ-05 COMPONENT-04 10 MJ-05 OP04 WC04 1 1

Time Unit per day = 10 or 10 hours per day Schedule Start Date = 1st of Jan

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7.2 Evaluation Results Analysis (1) Feasibility A sub-set of the sample job orders is used in this part because it will be too difficult to observe the result if too many operations are considered. In this part, only two main job orders are considered, MJ-01 and MJ-02, they have totally 8 operations. The result generated by the AI scheduling system (this project) and that generated by Preactor (using backward scheduling & prioritize by order Due Date) can be seen in the following pages. Table of comparison of results : Criteria AI scheduling Preactor Number of operations scheduled 8 6 Number of Over-Due Main Job Nil Nil Number of Over-Capacity Nil Nil It is very obvious that the outcome from Preactor is not feasible because there are still 2 operations not been allocated. The reason for that is Preactor, under the algorithm sequencing method, allocate all the operations of the MJ-02 (with earlier Due Date) first, which occupies the Work Center WC05 and WC06. When MJ-01 is scheduled, the operations of sub-jobs SJ-021 and SJ-022 which are also going to use the Work Center WC05 and WC06 respectively have to be allocated with start date beyond the schedule start date (1st Jan). This violates the Preactor’s scheduling process, so the two operations are not allocated. By the AI Scheduling system, one can note that the engine can start the operations SJ-021 and SJ-022 earlier and make room for the operations of MJ-02, such that the due date of both main jobs can be met and no infeasible (operation started before the schedule date) solution will be generated. In short, compared with Preactor, the AI Scheduling system is more likely giving feasible solution, just thinking that the case will be worse if the example is made more complicate with more operations. As a special remark here, we can make use another more advance mode (APS mode) of Preactor to generate a schedule for MJ-01 and MJ-02. But the result is still not satisfactory :

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Criteria AI scheduling Preactor Number of operations scheduled 8 8 Number of Over-Due Main Job Nil 1 Number of Over-Capacity Nil Nil This time all operations are allocated, but with the main Job MJ-01 Over-Due ! See the screen capture follows.

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(2) Quality of Result In order to avoid any further infeasible solution generated by Preactor, making the comparison become meaningless, the APS mode is used in this section.

Over-Due Time (in day) Slack Time between operations by Work Center (in day) Main Job

Orders AI scheduling

System Preactor AI scheduling System Preactor

MJ-01 to MJ-05 0.1 7.6 11.7 9.34

MJ-01 to MJ-04 0 7.6 9.6 5.34

MJ-01 to MJ-03 0 7.6 11.7 14.41

MJ-01 to MJ-02 0 7.6 0.6 1.07

MJ-01 0 0 - -

MJ-01,03,04,05 0 0 8.9 5.53

MJ-01,03,04 0 0 7.1 8.03

MJ-01,03 0 0 11.1 10.6

Average 0.0125 3.8 9.87 7.76

Although the sample size is not large, the result does clearly show the difference. Over-Due performance is much better by using AI Scheduling system (304%), while for the Slack Time performance , Preactor performs better (78%).

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(3) Repeatability It is also important that same result should be generated by a scheduling system every time it is executed with the same set of input, because this will give confidence to the user that the result will not vary time from time and the system is reliable. The writer has performed an simple experiment on the AI Scheduling System, by executing the scheduling process repeatedly with different values of GA cycles. And only Main Job MJ-01 is used. The following table shows the result of the experiment.

No. of Cycles

Execution duration (sec.)

Total Scores (Result 1)

Total Scores (Result 2)

Total Scores (Result 3)

Range of Total Scores (Result 1)

48 130 150 160 49 274 284 294 48 200 220 230 300

49 129 149 150

145

64 109 109 129 63 193 213 213 65 88 108 109 400

64 211 231 231

123

127 88 109 109 129 109 129 129 128 109 129 129 800

127 88 108 109

21

Actually, comparison of the total scores of various executions is an indirect way to estimate the result repeatability of scheduling engine. It is clear from the above result that the more the number of cycles the engine runs, the smaller the range will be obtained, i.e. it will become more repeatable. On this issue, Preactor performs far better. It is because it is basically a rule-based scheduler. The operations are allocated by exactly the same rules each time. There will be no different result generated by Preactor no matter how many times the set of jobs are repeatedly scheduled. It can be concluded that “repeatability” is a major drawback of using AI Scheduling engine. The only resort would be using longer execution time, which can be deduced from the analysis result above. It is easy to understand as GA itself requires the stage of convergence of results, as described in the section of introduction of GA.

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(4) Time required Below summarizes the time taken to generate the results in (2) above, by the AI Scheduling engine :

Main Job Orders

Time taken (sec.)

MJ-01 to MJ-05 181

MJ-01 to MJ-04 169

MJ-01 to MJ-03 156

MJ-01 to MJ-02 142

MJ-01 122

Average 154

As a conclusion from the result, the engine only took about 2 - 3 minutes to generate an acceptable result (as discussed in (2) above). The time performance of the system is acceptable. But of course, compared with Preactor, it is much longer, as Preactor only took a second to generate the results. In this sense, Preactor performs better than the GA engine.

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8 Conclusion 8.1 About the Project Aims In fact, at the end of the project, a workable scheduling program has been produced, using an academic methodology – Genetic Algorithms – as the core engine. Although the discussion in the last section has shown that the program (or GA) has drawbacks like lack of repeatability and comparatively worse time performance, it performs its power of generating feasible schedule and higher quality results, it did show its “intelligence”. Capacity constraint and jobs precedence relationship have been proven to be successfully considered by the GA engine. There is basically no violation of them in nearly all the examples quoted in this report. Meanwhile, the program provides the flexibility of releasing the capacity constraint (lower the “Delay Cost” of the Main Job), the trade-off is the “Over-Capacity Cost” of the related Work Center. In addition, other objective functions can be designed to guide the GA engine to generate a practically sensible schedule. The example in this project is the Just-In-Time criteria which leads to a result of less Work-In-Progress level. The other example is the “Number of Idle period” of Critical Work Center. It is basically coming from one of the popular production management concept – Theory of Constraint (TOC), which stresses that a critical work center must be scheduled with jobs such that its utilization rate can be as high as possible. To conclude, GA has proved itself a promising algorithm to successfully solve the jobs shop scheduling problem. Actually, the writer has read some papers [18,19] about the practical use of GA (or Evolutionary Algorithms) in the real world environment. One [18] claimed that the scheduling system should be integrated with Plant Data Acquisition system so that the update of the schedule can be promptly spread out to all the Work Centers concerned. This would then greatly improve the possibility of the commercialization of GA (EA) use in scheduling field. Another interesting sociological issue was suggested [19] that the key is to give confidence to the company management by generating schedules “similar” to those produced by hand at the company. This can be done by adjusting the values of the parameters used by GA. At the end, an “intelligent” system is required to prove its reliability and stability to the commercial world.

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8.2 Further Developments Rooms for further developments of this project are so many that it cannot be listed completely. The writer just tries to summarize those are important below. (1) Alternative Work Centers This is very useful in the real world environment. An operation is now limited to be done on a pre-defined resource. However, it is always case that the operation can also be done on another resource, but with different conditions, e.g. different setup time and run time. If this issue is considered, the software should be able to suggest a more practical schedule, with the suggestion of which Work Center the operation should be placed on. (2) Materials consideration Now in this project, only the production resources constraints are considered, however, the supply of materials is not taken into account. In real world, an operation cannot be started if the required materials have not been received and ready to use. Purchasing activity is needed to be considered at the same time. (3) Order splitting There would be case that in order to meet the deadline of delivery, more than one resources will be used for a job in parallel. This may shorten the whole Make Span of an order but may induce cost. (4) Setup time saving It can consider the sequence of jobs / operations on a resource so that there is the possibility of saving the setup time. This may happen if the jobs / operations are very similar in nature, or even exactly the same. (5) Operations locking Facility should be provided such that some of the operations released in the last schedule can be kept and locked. It is necessary because it is not possible or economic to stop those running operations. And usually scheduling is a continuous process

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which need to take into consideration of last released schedule. (6) Resource working calendar There is an assumption that the schedule is on a continuous calendar in this project, i.e. no holiday or resource down time. A working calendar for each of the resources should be considered. (7) Secondary Capacity Constraint of Resources More than one Capacity Constraint can be considered, e.g. tooling availability, labor availability…, for a Work Center in the scheduling process. (8) Reports or Documents printout Resource Utilization Report, Detailed Job Order Schedule List,… should be provided also by the system.

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8.3 What has been learnt ! This project has provided the writer a chance to realize how Artificial Intelligence be used to solve a practical problem, and its power and limitations. Modeling of the problem is the most difficult part, which affect very much the outcome of the project. Besides, through actually coding by VB.NET, the writer totally understand the benefits of using Object-Oriented approach to construct a program. (The writer has written procedural programs quite a long time ago.) Although the initial design stage may be longer, the development time will be saved much, as OOP has the concept of inheritance. More than that, in this project, the writer has done the planning well for the programming. A detailed process specification was prepared before actual coding. This made the programming smoother than expected. At the end, the writer would like to thank again for the advice and assistance given by Dr. Andy Chun during the period of the development of the project.

Thank you !

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9 References 1) Stuart Russell, Peter Norvig. Artificial Intelligence – A Modern Approach 2) Practical Handbook of Genetic Algorithms Vol. 1 3) Preactor User’s Guide. The CIMulation Centre Ltd. 1998 4) Hartmut Stadtler, Chrisoph Kilger. Supply Chain Management and Advanced

Planning 5) Andy Chun Hon Wai. Introduction to GA Programming 6) Emma Hart, Peter Ross. A systematic investigation of GA performance on jobshop

scheduling problems. 7) Matthaw Bartschi Wall. A Genetic Algorithm for Resource-Constrained

Scheduling, 1996 8) Shigenobu, Isao, Masayuki. An efficient Genetic Algorithm for Job Shop

Scheduling Problems 9) Y. Song, JG. Hughes, N. Azarmi, C.Voudouris. A Genetic Algorithm with an

incomplete representation for the Job Shop Scheduling Problems 10) Philip Husbands. Genetic Algorithms for Scheduling 11) Y.Li, KF. Man, KS. Tang, S.Kwong and WH. Ip. Genetic Algorithm to production

planning and scheduling problems for manufacturing systems 12) Burhaneddin Sandikci. Genetic Algorithms 13) SG. Ponnambalam, V.Ramkumar and N.Jawahar. A multi-objective genetic

algorithm for job shop scheduling 14) Ilog Optimization Suite White Paper, 2001 15) PB. Nagendra and SK. Das. Finite Capacity scheduling method for MRP with lot

size restrictions, 2001 16) U.Al-Turki, C. Fedjki and A.Andijani. Tabu search for a class of single machine

scheduling problems, 2001 17) Philip Husbands and Frank Mill. Scheduling with Genetic Algorithms 18) J.Kaschel, Tobias Teich, Bernd Zacher. Real-time dynamic shop floor scheduling

using Evolutionary Algorithms, 2000 19) Emma Hart, Peter Ross, Jeremy A.D Nelson. Scheduling Chicken Catching – An

Investigation into the Success of a Genetic Algorithm on a Real World Scheduling Problem, 1999.

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10 Appendix

10. 1 Project Plan Period Task Description Milestone July-Aug Learn the basic concept of GA 16-Aug-02Aug Prepare the Interim report 23-Aug-02Aug Confirm the project scope and project details 31-Aug-02Sept Pick up VB.NET programming language 30-Sept-02Sept Try to call / use the GA libraries with simple programs 30-Sept-02Sept Design and build the database structure for the system of the

project 30-Sept-02

Sept Design the Interfaces and flow of the system 30-Sept-02Oct Build the interface to accept external data and put them into the

database 21-Oct-02

Oct Confirmation of modeling the problem of the project into GA 21-Oct-02Nov Programming for the transformation of the external data to GA

parameters 15-Nov-02

Nov Programming for the transformation of the outcome of GA to user interface

20-Nov-02

Nov Performance Analysis of the system 25-Nov-02Dec System Fine Tune 25-Dec-02Dec Prepare the Final report 25-Dec-02Dec Prepare for the representation 28-Dec-02

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10. 2 Database Full Listing Table : JO To store the user input information about Job Orders. Key Field Name Data Type Length Null Default Description PK JO_No varchar 12 N Job Order Number MainJO_No varchar 12 N Related Main JO No. FK Item_No varchar 20 N Job Finished Item No. Qty decimal 9 N Quantity DueDate datetime 8 Y Due Date of the Main JO Active int 4 N 1 Active =1, Non-Active

=0 DelayCost decimal 9 Y Cost for delay per time

unit. PredJO_No varchar 12 N Predecessor JO No. Table : JO_Oper To store the Operations (Routing) required to complete the Job Order. Key Field Name Data Type Length Null Default Description PK JO_No varchar 12 N Job Order No. PK OperSeq_No int 4 N Sequence No. of

Operations to complete the Job.

FK OperCode varchar 6 N Operation Code FK WC_Code varchar 6 N Work Center Code to

be occupied by the operation.

SetupTime int 4 N 0 Setup Time in Time Unit

RunTime Int 4 N Time (in Time Unit) used to process one unit of item.

StorageCost Decimal 9 N 0 Storage Cost of the Item per Time Unit finished by this operation

CapacityCFactor Decimal 9 N 1 Consumption Factor of Capacity of the Work Center for the operation for whole operation.

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Table : Oper_WC To store the information about Operation. Key Field Name Data Type Length Null Default Description PK OperCode varchar 6 N Operation Code OperDes Varchar 30 Y Operation

Description PK WC_Code varchar 6 N Work Center Code to

be occupied by the operation.

SetupTime int 4 N 0 Setup Time in Time Unit

RunTime Decimal 9 N Time (in Time Unit) used to process one unit of item.

StorageCost Decimal 9 N 0 Storage Cost of the Item per Time Unit finished by this operation

CapacityCFactor Decimal 9 N 1 Consumption Factor of Capacity of the Work Center for the operation for whole operation.

Table : WC To store the basic information about Work Centers used in the system. Key Field Name Data Type Length Null Default Description PK WC_Code varchar 6 N Work Center Code WC_No int 4 Y Work Center

Number; used for WC_Description varchar 30 Y Description OT_Cost decimal 9 Y Cost for Over-Time

(Over-loading) Cost per Time Unit per Capacity Unit.

Capacity int 4 N Capacity of the Work Center per Time Unit.

Critical Varchar 1 N 0 Identify Critical Work Center; If yes, =1; if no, =0

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Table : Item To store the basic information about Item to be processed in the manufacturing operation. Key Field Name Data Type Length Null Default Description PK Item_No varchar 20 N Item No. ItemDes varchar 50 Y Item Description Table : Parameter To store the parameters used in the GA scheduling, and the scores breakdown of the best 3 results. Key Field Name Data Type Length Null Default Description PK VKey Int 4 N Virual Primary Key for

DB update purpose only, no actual meaning.

WT_OC decimal 9 N 0 Weighting for Over Capacity of Work Center

WT_OD decimal 9 N 0 Weighting for Over Due of Job Order.

WT_MS decimal 9 N 0 Weighting for Make Span of all Job Order.

WT_ID decimal 9 N 0 Weighting for Number of Idle Periods of Critical Work Center.

WT_JIT decimal 9 N 0 Weighting for Degree of JIT of Operation Arrangement.

TimeUday int 4 N 24 The basic conversion factor of system Time Unit per day.

TotalScore_1 decimal 9 N Store the total score of result 1.

TotalScore_2 decimal 9 N Store the total score of result 2.

TotalScore_3 decimal 9 N Store the total score of result 3.

OCScore_1 decimal 9 N Store the Over-Capacity score of result 1.

ODScore_1 decimal 9 N Store the Over-Due score for result 1

MS_1 decimal 9 N Store the Make Span score for result 1

IDScore_1 decimal 9 N Store the Idle period score of result 1

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JITScore_1 decimal 9 N Store the JIT score of result 1

OCScore_2 decimal 9 N Store the Over-Capacity score of result 2

ODScore_2 decimal 9 N Store the Over-Due score for result 2

MS_2 decimal 9 N Store the Make Span score for result 1

IDScore_2 decimal 9 N Store the Idle period score of result 2

JITScore_2 decimal 9 N Store the JIT score of result 2

OCScore_3 decimal 9 N Store the Over-Capacity score of result 3

ODScore_3 decimal 9 N Store the Over-Due score for result 3

MS_3 decimal 9 N Store the Make Span score for result 1

IDScore_3 decimal 9 N Store the Idle period score of result 3

JITScore_3 decimal 9 N Store the JIT score of result 3

Log_No Integer 4 Y Scheduling Log Number Table : Users Key Field Name Data Type Length Null Default Description PK ID nvarchar 20 N User ID Name nvarchar 50 N User name Password nvarchar 12 N Password to login Table : GeneGAInfo (Temporary DataSet) To store the basic information of each gene used in the GA evaluator. Key Field Name Data Type Length Null Default Description PK Gene_No int 4 N Gene ID PredGene int 4 N 0 Predecessor gene id SucGene int 4 N 0 Successor gene id MainJO_No varchar 12 N Main job belonged to WC_No int 4 N Work Center used by

the corresponding operation

StartTime int 4 Y 0 To be found by GA Core.

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EndTime int 4 Y 0 To be found by GA Core.

OperTime int 4 Y Calculated StorageCost Decimal 9 N 0 Storage Cost of the Item

per Time Unit. [from Oper_WC Table]

CapConsume Decimal 9 N 0 Capacity Consumption Ratio by this operation.

Table : GeneInfo (Database Table) To store initially the gene information from the conversion of user input data into gene representation (relation of gene with Job Order and Operation), and also keep the final result of the GA to facilitate output to user interface. Key Field Name Data Type Length Null Default Description PK Gene_No int 4 N Gene id JO_No varchar 12 N Job Order Number from

GeneConverter MainJO_No varchar 12 N Main Job Order number belonged

to, generated from GeneConverter OperSeq_No int 4 N Sequence No. of Operations to

complete the Job, generated from GeneConverter.

OperCode varchar 6 N Operation Code, from GeneConverter.

WC_Code varchar 6 N Work Center occupied, from GeneConverter.

StartDate_1 datetime 8 Y Result EndDate_1 datetime 8 Y Result StartTime_1 Decimal 9 Y Result EndTime_1 Decimal 9 Y Result StartDate_2 datetime 8 Y Result EndDate_2 datetime 8 Y Result StartTime_2 Decimal 9 Y Result EndTime_2 Decimal 9 Y Result

StartDate_3 datetime 8 Y Result EndDate_3 datetime 8 Y Result StartTime_3 Decimal 9 Y Result EndTime_3 Decimal 9 Y Result

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Table : MainJO (Temporary DataSet) To store temporarily the result of GA evaluator for the comparison of end time and due time for the Main Job Order. Key Field Name Data Type Length Null Default Description PK MainJO_No varchar 12 N Main job no. DueTime int 4 N Main job due time

calculated Accu_EndTime int 4 N To store temporarily

the end time of the main job

Overdue_Cost decimal 9 N To store the main job overdue cost or penalty cost

StorageCost Decimal 9 N Storage cost of storing the Final Product.

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10.3 Installation Guide The following is only a brief guideline of installation of this Web-Based application. It assumes that the reader has fundamental knowledge of IIS and MS SQL server. Pre-requisite Following software must be successfully installed beforehand :

- Microsoft Windows 2000 or above - Internet Information Services (IIS) has been setup - Microsoft SQL server 7.0 or above

Installation steps (1) Copy from the CD-R the folder “AISchedule” and files in the folder to the path :

Drive :\Inetpub\wwwroot Disable the “Read Only” property of all the copied files

(2) Start MS SQL server Enterprise Manager and create a new database. Write down the database name as it will be used in step (5) below.

(3) If you want to restore the sample data used in the evaluation part of this project,

you can restore the database directly (if so, the SQL server version must be 2000 or above) from the backup file named “AI_DB_Backup”, stored under the folder Database.

(4) If you want to create a blank database, you can execute the sql script

“AI_Create_Tables” in SQL server Query Analyzer. The script file is also stored under the folder Database.

(5) Edit the file (by Notepad maybe) web.config under the directory AISchedule just

copied, modify the corresponding information in Italic form below : <appSettings> <add key="ConnectionString" value="Data Source=localhost;

Initial Catalog= Database name ; uid= Database User ID; pwd= Database User Password"/>

</appSettings>

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(6) Start the IIS Manager and locate at the sub-folder “AISchedule” under Default

Web Site folder, right click and choose to open the Property page. On the new Windows come up, locate at the tab-page “Directory” and note the area “Application Program Settings” at the lower part of the Windows. Click the “Create” button and the field “Application name” will now be filled by “AISchedule”. Click confirm to leave the Windows and close the IIS Manager.

(7) Carefully check the access right to the folder “AISchedule” and you may start

Internet Explorer and type “//localhost/aischedule” at the address field. (8) The system login screen should be seen and the user ID will be defaulted “Admin”.

If you restore the sample data, you may now login with password “123”. If you create a blank database, you can now create a new user for yourself by clicking at the link “Create New User”.

(9) If you are using a blank database, and you have login the system. You should build

up your own set of data in the following sequence : - Item Master - Work Center Master - Operation Master - Job Order Information - Parameter

(10) After then, you can try to execute the AI Scheduling process by inputting necessary parameters.

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10.5 Test Plan - Functional Below is a part of the Testing Plan used. Test Item Expected Result Pass Error Found User Management Create new user Add record to

table : User Y

User the newly created user to login the system

Successfully login to the main menu of the system

Y

Edit the user’s password and re-login Successfully login Y Try wrong password to login Login failure Y User Logout link to logout the system Successfully logout Y Item Master Management Add new item with description Successfully added

to the table Item Y

Add new item without entering Item No. Error message prompted and not allowed to write to table

Y

Add existing Item Error message prompted and not allowed to write to table

Y

Edit Item Save change to the table

Y

Delete an existing Item Successfully deleted from table

Y

Search by Item No Show only records of item satisfying the searching criteria

Y

Search by Description Show only records of item satisfying the searching criteria

Y

Search by combination of Item No and Description

Show only records of item satisfying the searching criteria

Y

To show all record Show all existing records

Y

Work Center Management Add new Work Center Successfully added

to the table : WC Y

Add new Work Center without Work Center Code

Error prompted and no record is added

Y

Add existing Work Center Error prompted and Y

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no record is added Add character to field “OT Cost” Error prompted and

no record is added Y

Add character to field “Capacity” Error prompted and no record is added

Y

Edit Work Center Save change to the table

Y

Delete an existing Work Center Successfully deleted from table

Y

Search by Work Center Code Show only records of Work Center satisfying the searching criteria

Y

Search by Description Show only records of Work Center satisfying the searching criteria

Y

Search by combination of Work Center Code and Description

Show only records of Work Center satisfying the searching criteria

Y

To show all record Show all existing records

Y

Operation Management Add new Operation Successfully added

to the table : Oper_WC

Y

Add new Operation without Operation Code

Error prompted and no record is added

Y

Add new Operation without Work Center Code

Error prompted and no record is added

Y

Add existing Operaiton & Work Center combination

Error prompted and no record is added

Y

Add non-exist Operation & Work Center combination, with existing Operation

Successfully added (Combined Keys)

Y

Add character to field “Setup Timet” Error prompted and no record is added

Y

Add character to field “Run Time” Error prompted and no record is added

Y

Add character to field “Storage Cost” Error prompted and no record is added

Y

Add character to field “CapacityCFactor” Error prompted and no record is added

Y

Edit Operation Save change to the table

Y

Delete an existing Operation Successfully deleted from table

Y

Search by Operation Code Show only records of Operation

Y

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satisfying the searching criteria

Search by Description Show only records of Operation satisfying the searching criteria

Y

Search by combination of Operation Code and Description

Show only records of Operation satisfying the searching criteria

Y

To show all record Show all existing records

Y