dynamic planning and multicriteria scheduling of … · master production schedule (mps) and...

1IntroductionUvod

In traditional approach, planning and scheduling aretwo separate and successive operations. The processplanning phase is mostly about the physical aspect ofplanning, where a product range, production quantities,machines, tools, material and accessories are selected. Theemphasis in the second, scheduling phase, is on the timeaspect. The plan is the basis to determine the sequence ofoperations across available machines in a way that providesmaximum machines utilisation and timely manufacturing.Differences between planning and scheduling criteria oftenlead to conflict situations or even opposition betweenrespective goals.

Master production schedule (MPS) and capacityrequirement planning (CRP) in the environment ofmanufacturing resources planning (MRPII) are the mostfrequently applied traditional methods in practice. Thissystem is characterised by a hierarchical approach from thetop to the bottom. Goals and restrictions at the lower levelare determined by the results at the higher level. Suchplanning method rarely takes account of the schedulingproblem. Separate treatment of planning and schedulingoften results in plans having to be manually modified. Itleads to significant rearrangement costs and supply delays.Nowadays, such planning does not provide efficientbusiness operations as customers and the market requireflexibility and quick response.

A solution for such problems is the integration ofplanning and scheduling processes. The article presents asolution on the case example of planning the production ofturned parts. Presented is a dynamic planning model and its

453

A Slak, , J Duhovnik. J. Tavčar .

ISSN 1330-3651

UDC/UDK 65.012.122:621.941]:004.421

DYNAMIC PLANNING AND MULTICRITERIA SCHEDULINGOF TURNED PARTS' PRODUCTION

Aleš Slak, , Jože DuhovnikJože Tavčar

Technical innovations in the area of manufacturing logistics are being introduced partially and thus not exploiting their full potential. In order to optimise theefficiency of turning manufacturing processes, the process has been analysed and fundamentally re-engineered. All data from production (operations,quantities, date, time duration of operations, etc.) are now located in ERP system. It provided the necessary condition for the establishment of a robust dynamicplanning model.An update was required for the whole lifecycle of products and means of work. The paper presents the information support and an algorithm fora dynamic planning model, based on a genetic algorithm. Continuous data capturing and planning in real time are a breakthrough in the management of theprocess. Presented are a generalised dynamic planning model and a case example from the production of turned parts, which take account of the singularities ofa real environment. Production capacities have to be linked up with the supply chain and customers. The presented dynamic planning model can be adapted tovarious types of production.

Keywords: Integrated process planning and scheduling, enetic lgorithm, multicriteria schedulingg a

Original scientific paper

U području proizvodne logistike tehničke se inovacije uvode parcijalno te se ne koristi njihov puni potenc U cilju poboljšanja efikasnosti proizvodnihprocesa tokarenja, postupak se analizirao i u potpunosti preradio. Svi se podaci iz proizvodnje (operacije, količine, datumi, vrijeme trajanja operacija itd.) sadanalaze u ERP sustavu. modela dinamičkog planiranja.

za rad. U članku se predstavlja informatička podrška i algoritam za dinamički model planiranja, zasnovan na genetskom algoritmu.Stalno dobivanje podataka i planiranje u realnom vremenu predstavljaju važan napredak u upravljanju tim procesom. Predstavljen je generalizirani modeldinamičkog planiranja i primjer iz proizvodnje tokarenih dijelova se uzimaju u obzir specifično

. Ovaj se model dinamičkog planiranja može adaptirati različitim tipovima proizvodnje.

ijal.

On je osigurao potrebne uvjete za stvaranje Tražili su se ažurirani podaci o cijelom radnom vijekuproizvoda i sredstvima

gdje sti stvarnog okruženja. Proizvodni se kapaciteti morajupovezati s nabavnim lancem i kupcima

K :ljučne riječi genetski algoritam, planiranje i terminiranje integriranog procesa, terminiranje uz više kriterija

Izvorni znanstveni članak

Dinamičko planiranje i terminiranje uz više kriterija u proizvodnji tokarenih dijelova


Technical Gazette 17, (2010),4 453-464

advantages, compared to the existing method of work in theturned parts' production. A genetic algorithm was used tooptimise scheduling. The updated process planningimproved the efficiency of production and reliability ofsupplies. The proposed integrated model is presented insection 4, user interface is presented in section 5. Thegenetic algorithm and the target functions are described insection 6 and experimental results in section 7.

The change of planning was triggered by therequirement for flexibility and quick response to the marketand consumers' needs. J. Errington [1] presented theadvantages of Advanced Planning and Scheduling (APS),compared to traditional methods.

Computer Aided Process Planning (CAPP) has beenrecognised to play a key role in Computer IntegratedManufacturing (CIM) [3]. Traditionally, nearly allcomputer aided process plannings (CAPP) suppose thatmanufacturing is of secondary importance and that theworkshop has unlimited resources. It triggers unrealisticplans that are unworkable in the manufacturing process.

Planning and scheduling functions often have opposinggoals, which makes their separate treatments less efficient.The other deficiency of separate treatments is not takingaccount of the dynamic manufacturing environment. Timedelay between process planning and the actual beginning

2Literature reviewPregled literature

Here, individual steps ofthe traditional approach are merged in the way that theyallow automatic transition. Tasič et al. [2] presentedadvanced scheduling methods, such as priority rules, usefulalso for sophisticated systems.

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Dynamic planning and multicriteria scheduling of turned parts' production

Tehni ki vjesnikč ,17, 4(2010) 453-464

of the plan can cause the plan to become unworkable. Fixedplans lead to bottleneck situations. Researches have shownthat as much as between 20 to 30 per cent of all plans have tobe modified in order to adjust them to the dynamicmanufacturing environment [4].

Integration between planning and scheduling process istherefore vital as this is the only way to create more realisticplans and schedules. Only this will result in a real computerintegrated manufacturing (CIM) [5]. The integration createsa single space for solutions and provides the basis forefficient integrated solutions that are in the interests of bothplanning and scheduling [6]. It contributes to improvedefficiency of manufacturing resources, shorter throughputtimes, scheduling times and shorter delays. The integrationof planning and scheduling is much more complex and moredifficult to do in practice. The main contribution of thisarticle is to show on a case example the rules and methodshow to introduce dynamic planning and scheduling intopractice. The basis for our work was the existing ERP(Enterprise Resource Planning) information system.

Larsen [13] and Alting [7] arranged differentapproaches to integrated process planning into three types:concept of non-linear process planning (NLPP) or flexibleprocess planning, closed loop process planning (CPP) anddistributed process planning (DPP).

The concept of non-linear process planning is typical ofintegrated process planning and scheduling (IPPS).According to this model, all alternative plans for a productare determined, which is called MPP (multiple processplans) [8]. All these plans are defined regardless of thecurrent situation on the shop floor. A large number ofproducts and alternatives can make individual plansunworkable, and so an optimum result is not possible to beachieved through integration.

Closed loop process planning (CLPP) generates plansby means of a dynamic feedback from the shop floor. It isbetter than NLPP because plans are generated with a view torealistic conditions in the manufacturing environment. Withthis method, the realistic conditions are vital and thedynamic feedback is important for the scheduling process.

Distributed process planning (DPP) performs processplanning simultaneously with the scheduling ofmanufacturing. Process planning is divided into two phases.The first phase is the initial phase where productrequirements are analysed according to its shape, tools,machines etc. When all requirements are clear, the secondphase or final planning begins. During this phase, therequired manufacturing resources and the availableresources are matched. The flexibility of this approachincreases if the required resources are given as alternatives.Examples of such approach are L. Wang and W. Shen [9]and IPPM system by H-C. Zhang [10], followed by IPPS byS. H. Huang et al. [5].

Matching individual planning models has shown thatDPP is the best approach. However, it still requires highperformance hardware and software. NLPP involvesalternative plans, which allows better scheduling flexibility.Such method can be introduced in enterprises without theneed for their reorganisation, compared to DPP and CLPPthat would require reorganisation of planning andscheduling departments. This is due to CLPP and DPPrequiring merging of different separate processes within anenterprise.

Several researchers merged individual approaches inorder to remove the deficiencies and come up with optimumplans. L. Gao et al. [11] presented an integrated process

planning and scheduling model, based on taking theadvantages of NLPP (alternative plans) and DPP(hierarchical approach) models. The model is based on theprinciples of concurrent engineering, where computer-aided planning and scheduling are performedsimultaneously. Usher and Fernandes [3] presented asystem, called PARIS (Process Planning Architecture forIntegration with Scheduling), which divides the dynamicprocess planning into two phases, the static one and thedynamic one. Each phase has its objectives that should bemet. A. Jain et al. [8] and M. R. Razfar et al. [12] tackled thetask in a similar way, by dividing the problem into twomodules.

Nowadays, modern manufacturing systems should beadapted to the changes on the market. They all have thesame objective – the lowest possible manufacturing costs.On the other hand, they wish to meet customers' quality andtimely delivery requirements. M. Starbek et al. [14]developed a method whereby it is possible to predict thedelivery time of a new product on the basis of actualthroughput times of previous products. The suggestedprocedure also allows changes of the calculated deliverytime with regard to confidence and risk level. J

] presented modern techniques together with methodsfor the reduction of throughput times and improved quality.

The importance of artificial intelligence has grown dueto increased complexity of planning problems. Methods,based on a genetic algorithm, for example, are very efficientfor difficult problems. They do not always yield the bestabsolute solution but they find an approximation, goodenough for practice. ] used geneticalgorithms in order to arrange machines and apparatuses ina flexible processing system. They used variabletransferable costs as their target function. Yan and Zhang[17] developed a uniform planning and schedulingoptimisation model for the management of a three-tiermanufacturing system. In order to solve the problem, theyopted for heuristic approach, based on genetic algorithms.They developed an algorithm where they determined theoptimum size of a batch. Park and Choi [18] suggested theuse of genetic algorithms (GA). The target function was theshortest production time of all products, while takingaccount of alternative machines and alternative sequence ofoperations. Using genetic algorithms, A. Kimms [19]solved mixed integer program formulation which he haddeveloped for multi-level, multi-machine scheduling.Zhang and Yan [20] defined the planning and schedulingproblem as nonlinear mixed integer program model. For thepurpose of simultaneous optimisation of production planand scheduling, they presented an improved hybrid geneticalgorithm (HGA). To improve the results, they also usedheuristic rules, i.e. the shortest production time (SPT) andthe longest processing time (LPT). Lee and Kim [21]suggested simulation with a genetic algorithm, linked with asimulation module that calculates the success rate ofplanning, based on combinations between process plans.Total production time and delivery date were used as targetfunctions. To solve the single machine scheduling problem,Valente and Goncalves [22] suggest genetic algorithmapproach with linear earliness penalty and quadratictardiness penalty. They suppose that there is no dead time ona machine. L. Gao et al. [11] suggest the use of a modifiedgenetic algorithm where each function (process planningand scheduling) was given a different chromosomerepresentation. Minimum throughput time of all productswas used as the target function. For the integrated model

. Kopač et al.[15

J. Balič et al. [16


455Technical Gazette ,17, 4(2010) 453-464

they used a mathematical model, which they solved withgenetic algorithms [23]. Lestan Z. et al. [24] developed asimple genetic algorithm for a job-shop problem. They usedmakespan as a target function and the solution is searchedwithout the help of heuristic rules.

In order to achieve optimum plans in a dynamicmanufacturing environment, it is necessary to take accountof the current situation on the shop floor, which traditionalCAPP neglects. Most researchers have focused on a soletarget function, such as throughput time of all products,delivery time, effective utilisation of machines.Manufacturing costs and effective utilisation of machineswere rarely considered. It is important to consider effectiveutilisation of machines in order to cover high investmentcosts and reap economic benefit from them [6]. Researchersare mostly focused on scheduling algorithms and on narrowproblems. Missed are introduction methods and examplesof dynamic planning in the industrial environment.

An integrated process planning and scheduling modelis presented and described in detail for production of turnedparts.

A planning model has been developed whichcomprehensively covers production planning. Constructingthe model has shown that planning should also includematerials and tools purchase as well as product sales. Thismodel has served as a basis to determine a satisfactory planbased on genetic algorithms. Several target functions andcriteria are present in the optimisation procedure. With thegenetic algorithms we improved productivity, utilisation ofmachines and delivery times. Presented are alsoexperimental results and comparison with other authors.

Planning and scheduling of products in the productionof turned parts ranks among complex problems. Annumber of products should be scheduled across annumber of machines in the way that they are manufacturedand delivered to the customer in time. Each product has atleast one alternative plan that includes several operations. Italso represents the end product. Each operation isperformed on a single machine. Currently, plans are mademanually and everything depends on a single person whorelies on his or her experiences. Some products aresubjected to planning according to MRP system. It is aknown fact that such system does not always lead toworkable plans, which makes it almost unusable in adynamic environment. For this reason planners extendproduct's throughput time and thus deliberately extenddelivery times. In turn, it creates longer queues, less flowthrough the production, less effective utilisation ofmachines and higher production costs. Current planningdoes not provide any feedback on the situation ofmanufacturing resources and response to any change on theshop floor (machine failure, urgent order) is poor. The

2.1A survey of the current situation and new approach todynamic planning

3Problem description: Planning and scheduling in theproduction of turned parts

Postojeće namičstanje i novi pristup di kom planiranju

Opis problema: Planiranje i terminiranje u proizvodnjitokarenih dijelova

nm


number of items for a single operation is not known and thewhole potential of the information system is not exploited. Itresults in high consumption of time to coordinate plans andscheduling causes conflicting situations.

Because process planning and scheduling are closelyrelated functions, their integration in such environment isvital for the creation of an optimum plan.Adynamic processplanning and scheduling model is presented below.

Fig. 1 shows the whole dynamic process planning andscheduling model. It is basically divided into two parts – thepart where all alternative plans for each product aredetermined and the optimisation part with the geneticalgorithms approach. The first part could be termed as astatic part or pre-planning phase, with the emphasis onspecifying various plans according to available resourcesand specifying production quantities and material needs.The second part involves all dynamics, which is why thispart is called the dynamic part or the final planning phase,where target functions as well as realistic conditions in themanufacturing environment are considered. It means thatthe available resources are matched with the required ones.If current capacity does not meet the requirements, an extraplan should be included in the process. In practice it meansthat a product is being manufactured simultaneously on twomachines.

First, all orders are collected, followed by making arough plan by means of gathering the information on theavailable capacity of regular orders that are alwaysmanufactured on a single machine. For other orders,alternative plans are prepared according to other availableresources. This is followed by specifying material needs andcapacity for all production quantities.

4Integration of process planning and schedulingfunctionsIntegriranje funkcija planiranja i terminiranja procesa


Figure 1Slika 1

Integrated process planning and scheduling modelModel integriranog planiranja i terminiranja procesa.

456 Tehni ki vjesnikč ,17, 4(2010) 453-464

When alternative plans, manufacturing procedure(sequence of operations), required quantities of materialand tools are available, the second phase begins, for whichthese are the input data. This is called the scheduling phaseand its key role is to schedule all product operations acrossmachines in the way that scheduling criteria are met. Prior todetail planning, materials and tools stocks are checked in thesystem. Detailed planning of manufacturing plan is subjectto timely delivery of materials and tools by suppliers.Specifying the optimum plan, the target function is theminimum throughput time of all products and minimumtotal costs. At the same time, another aim is to achieve themost effective utilisation of machines, reduction of set-uptimes for the first operation and to minimise order delays.

Once the satisfactory schedule has been completed, it isconsidered as a working frame. If urgent orders arrive afterthe schedule had been completed, certain tasks are givenhigher priority. If an order has been cancelled or there is anequipment failure, a new schedule should be created. Due tothe above-mentioned reasons it again functions as a frame.If there are no modifications, the optimum schedule shouldtake place on the shop floor

The following assumptions have been specified for thesolution of such problem:

Only one product can be produced on one machine atthe same timeEach product can be machined independently from theother productsEach product has from one to three alternative plans(different CNC machines)The sequence of operations is predefined for eachproduct in the alternative plan.The size of a batch is divided into equal smaller units,such as packaging units which are tracked throughoutthe manufacturing process.

The integration of process planning and scheduling hasled to the shift from manual scheduling to automated,computer-aided planning. Defining a detailed time when themanufacturing process of an order will start and when it willend, including delivery time, is the biggest advantage. Eachoperation on a product has a specified start time and endtime. For example, it is specified when and how manyproducts should be ready for galvanic coating. A planner isnow able to check in any given moment which products arebeing produced on which machines and how many of themare on each operation. Such planning method gives aplanner a more supervisory role as he or she can follow viathe information system what is going on at the shop floorand is informed whether an order is behind or ahead ofschedule.

Manual method included a lot of verbal communicationwith the shop floor, physical checks of machines on theprogress of the work, which is now no longer necessary.Automated planning and scheduling system also allowscontrol over finished products, material and tools. Dynamicplanning requires consistency in the monitoring of productson each operation throughout the manufacturing process.This information allows an accurate prediction of howmany products can be finished in a short period of time. Thisis important in case of increased demand for a product by acustomer. The most important thing for managing a

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4.1Advantages and disadvantages of dynamic planningPrednosti i nedostaci dinamičkog planiranja

dynamic manufacturing environment is a quick andefficient response to changes, such as machine failure,maintenance work, and urgent orders. This means, if themachine is broken, then the new borders are put into theplanning system. Products which have already been put onthe machine have the status "in progress" and they cannot becanceled, but the products with the status plan can berescheduled. This status is written in ERP system. Likewiseis with the urgent orders. This can be done any time,response time to get a new plan is 15 minutes on average.Information from the production is automatically updated inERPsystem every 30 minutes.

Managing changes of materials and tools delivery datesby suppliers could be a drawback of dynamic planning. Ifmaterials and tools are out of stock or they are not suppliedon the planned date, the plan is unworkable and should bedelayed by at least one day, which can trigger delays in thesupply of end products.

Manufacturing information system is the backbone forthe planning and managing of production, which is why theexisting information system within the dynamic planningmodel has been complemented rather than replaced.All dataare stored in the ERP information system. In order tocalculate the optimum plan and schedule, data are exportedand optimisation of the plan with genetic algorithms isperformed. The collected data are then returned to theinformation system. The whole system of data managementand integrated process planning and scheduling is shown inFig. 2.

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5User interface between ERP system and scheduleoptimisation softwareKorisni programa zaoptimizaciju terminiranja

čko sučelje između ERP sustava i

ERP System: BaanManufacturing system

Planner

Oracle Discoverer4.1

Integrated ProcessPlanning &

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Figure 2Slika 2

Data flowchartDijagram toka podataka.

Data are exported from the information system with theOracle Discoverer 4.1. application. Process planning andscheduling is performed once a day or at a request into apurpose built software application (relational base MSAccess, Visual Basic). Later, transition to Oracle base andC++ is planned. A genetic algorithm was used and it provedvery fast, with good conversion results. This local base is

Dynamic planning and multicriteria scheduling of turned parts' production A Slak, , J Duhovnik. J. Tavčar .


the groundwork for planning on the basis of the data fromthe basic information system. The optimisation procedureresults in a detailed plan and schedule of productsmanufacturing. It serves as input information and enablesthe planner to generate manufacturing product tasks withinthe ERPsystem.

The Oracle Discoverer application allows access to thedata base, located in the information system. Each ERPsession has a table with data that are also visible in thesession itself. Necessary tables (information) for theintegrated planning method are specified in the OracleDiscoverer application. Besides, the application also allowsdata filtering, additional equations-based restrictions,similar data pooling etc. The selected data are exported intothe local relational base that functions as the basis forplanning and scheduling. The relational data base is createdin MS Access. The whole relational database set-upprocedure was subjected to normalisation, which was usedin order to establish relationships between the data and todetermine links between the attributes from different tables.The links were of both simple (1:1) and complex (N:1) type.Fig. 3 shows the relational database that serves as the basisfor the plan. Each field is written in the same way as in thetable in the ERP (Baan) system. The same goes for tablesnames.

A purpose application has been created for theoptimisation process. On the basis of the ERP informationsystem it schedules the activities on the shop floor in realtime. Genetic algorithms have proved to be an efficientmethod for product scheduling. The presented planning andscheduling method is performed once a day or at the requestof the planner.

Genetic algorithms (GA) are a method of evolutionarycomputation. Evolution can be defined as the optimisationprocess where living organisms are becoming increasinglyadapted to the environment where they live. Evolution canbe simulated on a computer and used to solve problems in a

6Genetic algorithm-based approach for productionschedulingPristup terminiranju proizvodnje baziran na genetskomalgoritmu

variety of fields. Genetic algorithms are a random searchtechnique, not requiring detailed knowledge about aproblem that is being optimised.

Fig. 4 shows the application of genetic algorithmsprocedure. The CAPP system initially specifies allalternative plans and other information of any importancefor the calculation of the optimum plan of integrated processplanning and scheduling. Other data include delivery dates,stock information, materials and tools supply. In the nextstep, a population is randomly generated. It consists of alarge number of different possible plans. On the basis oftarget functions and restrictions, each chromosome of theinitial population is evaluated. The evaluation process isthen carried out, with better and better solutions beingsought on the basis of selection, reproduction, crossover andmutation until the required condition is reached. When thegoal is reached, the optimum schedule for each task is alsocompleted.

Optimization process with GA

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Course of the application of genetic algorithmsTok primjene genetskih algoritama

Genetic algorithms represent solutions of problems instructures, called chromosomes. The collection ofchromosomes is called a population and specificchromosomes in the population are individuums.

Dinamičko planiranje i terminiranje uz više kriterija u proizvodnji tokarenih dijelovaA Slak, , J Duhovnik. J. Tavčar .

Figure 3Slika 3.

A elational data base in MS AccessRelacijska baza podataka

ru uMS Access


A population in any given time is called a generation.The goal of genetic algorithms is to create new generations.Although the population can change from generation togeneration, the size of the population and the structure ofchromosomes remain the same. They operate withcharacters, representing parameters. Proper specification ofparameters or chromosome syntax is an important step. Ithas an effect on subsequent work with genetic algorithmsand on the share of workable solutions in the search area interms of a large number of plans and restrictions. Theliterature has so far presented the chromosome in a numberof ways [25]. Below are presented the chromosome, theevolutionary function with restrictions and geneticoperators. The chromosome has been adapted to the needsof the production of turned parts.

Job-based representation of chromosome has beenchosen to represent the chromosome of the given problem.The manufacturing type in the company is by orders. Oneproduct is represented by one gene in the chromosome. Thegene is represented by two pieces of information, with thefirst one being the number of the alternative plan accordingto which the product will be manufactured while the otherone specifies whether tools presetting will take place(number 1) or not (number 0). The gene can be extended toother characteristics. The chromosome is shown in Fig. 5.The chromosome is made up of a group of genes. In our casethis is the schedule of all products to be manufactured. Itmeans that the chromosome represents permutation oftasks. Representation of the chromosome by productsbelongs to direct approaches, where the solution is built inthe chromosome. Genetic algorithms are used for thecreation of the chromosomes whose objective is to find abetter schedule. First, operations of the first product in thechromosome are scheduled across machines. They arefollowed by the second product's operations and so on to thelast one in the chromosome.

5.1Chromosome epresentationrPredstavljanje kromozoma

found. The GA principle is similar to natural evolution.Only the strongest individuals survive, creating a new andmore advanced population of descendants by means ofgenes mutations and their crossover.

The shortest makespan and minimum manufacturingcosts were set as target functions and manufacturingrestrictions and customers' requirements were considered.Delivery time is the most important of the customer'srequirements. Other restrictions and criteria are describedlater on. Special emphasis is on the products where one ofthe operations is performed at an outsourcer. Together withthe making itself, the manufacturing time also involvesmachine set-up and finishing times. Total costs consist ofmanufacturing costs, labour costs and depreciation costs.

While choosing an alternative manufacturing plan for aproduct, heuristic priority rules can be of assistance. Theshortest processing time (SPT) was used for the initialschedule. Later, the rule saying that products with theearliest due date (EDD) are scheduled first is also applied. Iftwo products are scheduled for the same machine, theproduct with the earlier due date is manufactured first.

Mathematical model symbols:– Number of orders or work orders– Number of items on the bill of material– Number of machines on the shop floor– Number of alternative plans for product

– Number of operations for product's plan

– -operation for product's plan

– Ordered quantity of product

– Quantity of product's workpieces, overlapping with

the next operation– Time of operation's overlap on machine

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for operation on machine

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– Time of the performance of operation on machine

– Set-up and finishing times of machine for operation

– The earliest beginning of operation on machine

– The earliest end of operation on machine ( )

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– Throughput time for all operations, performed on

machine , i.e. total time when a machine is engaged inthe performance of all planned operations– Set-up time of machine for operation

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machine– Product priority

– Scheduled delivery date of product to the customer

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c – Manufacturing costs for one piece of product (all

operations, materials, tools)– Labour costs

– Depreciation cost for machine

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ChromosomeKromozom

When the target function of the chromosome iscalculated it has to be decoded back to the solution of theproblem, which means the schedule of products. During theencoding it is of utmost importance to keep the subsequentsolution of each chromosome decoded within the possiblespace of the given problem. This feature is called feasibility.When the generated chromosome cannot be decoded into asolution, correcting techniques are applied. They change anillegal chromosome into a legal one. This feature is calledillegality. For permutations, the technique with a PMXoperator is very useful. It is basically a two-point crossoverwith the correction procedure.

The relational database contains information onproducts that is used for the purpose of orders scheduling.The list of genes or the chromosome represents one possibleschedule on the shop floor. Using GA, a satisfactoryschedule, as close to the optimum as possible, should be


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– Combined weighted function– Weight of delay– Costs of 1 day delay of the delivery date

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All restrictions have to be considered for a satisfactorymanufacturing schedule of turned parts. They are listedabove. Below, they are presented in a mathematical form.

Restrictions:a) Only one product can be processed on each machine atthe same time:

Target functions:a) Minimum throughput time of all tasks and operations

on a single machine:

c) Minimum total manufacturing costs for all products:


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� � (3)

� �� , , , ,

i ilP G M

p i pz ilkj s ilkj il w i

l=0 j=1

c c c c�� k=1

Processing costs:

, , ,w i ssc i o ic c Q� ; 1,...,i N�

Machine costs:

, , ,s ilkj op ilkj a jc t c�

Set-up and finishing time costs:

, ,pz ilkj pz ilkj dc t c�

d) Maximum utilisation of all machines:

1

1

minM

j

j

MU

mnu�

� � ��

�(4)

,

1

max,

1

N

wilkj

ij

j

t

mnut

�

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� ; 1,...,j M�

e) Combined weighted function

� �, ,

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If, , 'd i d i

d d�

then , ' ' ' , ´ , ' ' '(1 )p i l k j p ilkj ii j w i l k jt t D t�� (6)

b) Sequence of operations is predefined for each productin the alternative plan:

, , , ( 1) ' , ( 1) 'es ilkj w ilkj pz il k j es il k jt t t t� �� (7)

1,...,i N� ; 0,...,i

l P� ; 1,...,il

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c) Only one alternative plan can be selected for oneproduct.

Assumption: ( 1)il i lw w ��

0

1iP

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l

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d) Operation is performed simultaneously or sequentially.Product's throughput times change because operation

can be performed simultaneously or sequentially.Throughput time for product i where operations are

performed sequentially:

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1

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il

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Throughput time for product where operations areperformed simultaneously:

i

� �1

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1

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p i pz ilkj po ilkj mo ilkj op ilG j

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e) Throughput times for each operation and product costshave to equal or exceed 0:



, 0pilkjt � ; ,0

pic � (11)

1,...,i N� ; 0,...,i

l P� ; 1,...,il

k G� ; 1,...,j M� (12).

Target functions equations are written from (1) to (5).Taking account of all objectives can be termed as a multi-objective problem. The most important objectives toachieve are minimum throughput time (1), timely delivery(2) and minimum total costs (3). It is necessary to achievethe highest possible efficiency of machines (4), whichreduces dead time on a machine. Combined weightedfunction (5) is composed of total costs and delays.

Restrictions that appear in the algorithm are writtenfrom (6) to (10). Equation (6) determines that a machine canproduce only one product at a time. The sequence ofoperations for two different products on the same machinedepends on the delivery date. It applies to all operations forall products. Equation (7) determines that the sequence ofoperations is fixed for each product. It further increases thecomplexity of the problem. Only one alternative plan can beused for each product, which is shown in equation (8). Thetechnological process with the highest priority is used as theinitial plan. Choosing only one possible plan automaticallymeans that only one machine is designated for theperformance of a single operation because the machine ishidden in the plan. Equations (8) and (9) determineproduct's throughput time according to the way ofoperations performance. The algorithm also takes accountof the fact that some operations take place consecutivelyand others simultaneously. Equation (10) determines thateach operation's throughput time and all product costsshould equal or exceed 0.

Tournament-type selection was used. For this selectiontype, a certain number of chromosomes is selected, whichthen take part in the tournament. Two individuums arematched and the chromosome with the best value isselected. If the number of chromosomes to be matchedincreases in an algorithm, the pressure on the selection isincreased. Inferior chromosomes are not selected and thusdo not take part in the creation of the next generation whileat the same time good individuums also do not dominate thereproduction process.

Two-point crossover was chosen as the crossoveroperator. Selected from the population are two parents whoform two offsprings. Two random points are selected in thechromosome, as shown in Fig. 6. The material between bothpoints is exchanged between the parents. This alwayscreates feasible solutions. The crossover operator is

5.3Genetic operators

5.3.1Selection

5.3.2Crossover

Genetski operatori

Odabir

Prijelaz

Figure 6Slika 6.

Crossover operatorOperator prijelaza

subjected to the probability that determines the use of thecrossover chromosome.

Amutation is about introducing new genetic material inthe existing chromosome. It introduces variety in thepopulation and broadens the search area. A mutation as wellas crossover is subjected to some probability. For theexisting problem, the uniform mutation was selected. Thismutation is about each gene in a chromosome beingattributed a random number, which is then matched with theprobability of mutation. If the random number is smaller,the gene is subjected to a mutation. This is shown in Fig. 7.

5.3.3MutationMutacija

Genetic operators were selected on the basis of asystematic comparison between the results of optimisingand the necessary calculating time.

During the development of genetic algorithm, severalset-ups and approaches were systematically tested. Testsshowed that with roughly 1000 evaluations it is possible tofind a satisfactory solution for a plan. The size of thepopulation was limited to 60. Larger population extends thecalculation time while there are no significant savings withthe population sizes of 80 and 120 (Fig. 8).

The optimum selection was determined aftercomparing selections without the use of crossover andmutation operators. The roulette and tournament selectionsproved to be the best.

Two-point crossover with one-point mutation quicklyconverges towards a good solution but it also calms down

6Experimental resultsRezultati eksperimenta

Figure 7Slika 7.

MutationMutacija



35.000

37.000

39.000

41.000

43.000

45.000

47.000

49.000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Generation

Influence by size of population on convergence

POPSIZE = 20 POPSIZE = 40

POPSIZE = 60 POPSIZE = 80

POPSIZE = 120

Ca

pa

bil

ity

of

po

pu

lati

on

/EU

R

Figure 8Slika 8.

Influence by size of population on convergenceUtjecaj veličine populacije na konvergenciju

Table 1Tabela 1.

Processing time of all operations for a job with alternative plansObradno vrijeme svih operacija za posao s alternativnim planovima

Processing time/h

Operation 1Jobs

Plan 1 Plan 2 Plan 3Operation 2 Operation 3 Operation 4

J130,3

(M13)/ /

0,8

(M19)

2,8

(M27)

J235,1

(M10)

33,6

(M8)

33,6

(M15)

1,21

(M19)

1,04

(M22)

17,42

(M26)

J392,1

(M13)/ /

1,3

(M19)

11,1

(M27)

J410,8

(M10)

8,9

(M12)/

0,3

(M19)

0,3

(M27)

J59,6

(M10)

8,7

(M12)/

0,3

(M19)

0,4

(M27)

Tabela 2Table 2.

Rezultati inicijalnog planaResults from the initial plan

Total

costs/EURThroughput time/h Makespan/h

Sum of

delays/day

Maximum utilisation

of all machines/%

Combined

weighted

function/EUR

Initial plan 146 269,6. 4 386,27. 1 257,58. 83 23 452 567,5.

quickly and is unable to look further for better solutions. Arandom mutation is looking for solutions to a larger extentand the convergence of the population towards bettersolutions is slower but the final solution is very good. Forthese reasons, two-point crossover with random mutation isused in the final version. The crossover probability is set at0,9 and the mutation probability at 0,01.

For the purpose of determining the optimum solutionfor the production of a product or a product range, severalalternative plans were used for each product. These plansare entered in the information system and their numbers ofoperations and designated machines for each operation arealready specified. Thirty products were scheduled ontoeighteen CNC machines in the case study. There are thirtymachines and ninety-five operations all together. There canbe up to four operations on a particular product and up tothree alternative plans. Planned time in hours and machinesfor particular operations is shown in Tab. 1. In the case ofalternative plans additional machines are specified as atproducts J2, J4 and J5.

For each target function almost optimal solution wasfound with genetic algorithms. Solutions are good enough –satisfactory for production scheduling. There exist betteroptimal solutions but with no significant difference whichdoes not pay additional calculation time. The objective is to

find the almost optimum or satisfactory manufacturing planout of the alternative plans in order to achieve a good resultof the fitness function.

The results of different target functions are summarizedin Tab. 3. Size of population was set to sixty and number ofgenerations to fifty. Calculation time on a middle classpersonal computer was 280 seconds for each target functionfrom table 3. The almost optimal solutions for particulartarget functions are marked with shadow. Other values inthe same line are given for comparison between differenttarget functions. Each target function achieves the bestresult in the colon – it is according to expectations. Specialattention was given to deliver products on due dates and tocontrol costs at the same time. We have made a combinedweighted function that considers both criteria: due date andcosts. In the comparison between the first and the secondtarget function it can be seen that the results are very similar.Because of the bigger makespan the function Throughputtime has more delays and bigger additional costs. In thatcase products are not well scheduled on the machines.

According to the minimum of delay criteria the fourthtarget function is the best choice. Products enlarge thethroughput time in this case and total costs althoughcombined costs are at acceptable level. The delays are only6 days. The last one of the target functions is a combined



weighted function. It represents the compromise betweentotal costs and delays. The value of this target function from

3 is not optimal, but it represents a good solutionacceptable for the practice.

Attention was also paid to the busiest machines on theshop floor and utilization of the machines. At the maximum

Tab.

Tabela 3Table 3.

Usporedba vrijednosti ciljnih funkcijaComparison between the values of target functions

Target functionTotal

costs/EUR

Throughput

time/hMakespan/h

Sum of

delays/day

Maximum

utilisation of

all

machines/%

Combined

weighted

function/EUR

Total costs/EUR 116 849,2 3 565,60 421,55 29 51 161 489,5

Throughput time/h 125 131,9 3 533,68 461,08 36 49 193 800,8

Makespan/h 126 840,1 3 753,66 421,55 33 52 180 927,5

Sum of delays/day 138 955,9 4 001,91 443,98 6 53 146 468,9

Non-utilization of all machines/% 153 241,1 4 139,53 443,98 48 58 259 471,8

Combined weighted function/EUR 124 658,7 3 816,34 439,98 7 51 134 035,1

Figure 9Slika 9.

Influence by target function total costsUtjecaj ciljne funkcije ukupni troškovi

Figure 10Slika 10.

Influence by target function combined weighted functionUtjecaj ciljne funkcije kombinirana ponderirana funkcija

Figure 11Slika 11.

Influence by target function throughput timeUtjecaj ciljne funkcije vrijeme proizvodnosti

utilization target function, where the result is 58 %, the orderof products on machines gives the biggest delay. The reasonis probably in the order of the products on the machines. Allproducts together give very good utilization, but someproducts will be delayed because of this.

Figs 9 to 11 show the comparison between three target



functions. The conditions stabilize after 30 generation.From the other researchers it is known that 1200 evaluationswith genetic algorithm represent a good enough solutionthat could be put into practice. In our case there have beenmade 3000 evaluations. Beside the target function presentedare also the results from the other two target functions inFigs 9 to 11. This means, in Fig. 9 are beside the Total costsof target function also given the total costs from the targetfunction Throughput time and Combined weightedfunction.

After all these results the specific solution for the turnedparts' production has been made. We decided that thecombined weighted function gives the satisfactory solution.From the sale department's point of view the minimumdelays are the top priority, while from the productiondepartment and the management's one the minimum costsare the top priority. The combined weighted target functioncould satisfy both.

On the example of the production of turned parts, thearticle has shown how to combine process planning andscheduling into an integrated and thus more efficientsystem. Each criterion or target function works veryconvincing, which could take us on a blind road. The need istherefore to check some combinations of different targetfunction, like in the combined weighted function. Theproposed criterion for turned parts' production includestotal costs and delays. For the lowest common costs,additional delays will have to be accepted.

At the end we could compare the results from thechosen target function and the initial plan given in Table 2. Ithas been put on the machine in the same order they cameinto our company and for each product or job, firstalternative plan was chosen. The costs of combinedweighted function drop by 69,1 %. 15,6 % are the total costs,the rest is because of the right choice of the machines. Themakespan moves from 1257,58 hours to 439,98 hours. Theamount of the saving is because we have a big emphasis ondelays. For that reason the special weight has beendeveloped.

Besides planning and scheduling of manufacturingactivities, the presented model also allows optimisation ofmanufacturing plans and machines. In this case the solutionarea is much larger due to the fact that all available machinesare varied within each operation of the plan. It is possible totake account also of the machines that are not yet present inthe existing plans or exist only in investment plans.Calculation time is by a factor of ten or more.

Further researches will focus on the introduction ofgroup turning technology on CNC machines. Geometricallysimilar products require minimum machine set-up time forthe transition from one product to another. The introductionof the group technology principle in the presented planningmodel will be made possible on the basis of geneticalgorithms. First, it will be necessary to provide reliableinformation on the association with a group for each productand enter it in the information system.

.

7ConclusionZaključak

Acknowledegment

8References

Zahvala

Literatura

These researches are supported by the Ministry ofHigher Education, Science and Technology under theproject P-MR-08/88. Operation part is financed by theEuropean Union, European Social Fund.

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Authors' addressesAdrese autora

Aleš Slak

Jože Duhovnik

Iskra ISD-Strugarstvo d.o.o.Savska loka 4

4000 Kranj, Sloveniae-mail: [email protected]

Iskra MehanizmiLipnica 8SI 4245 Kropa, Sloveniae-mail: [email protected]: [email protected]

University of LjubljanaFaculty of Mechanical Engineering

, Sloveniae-mail: [email protected]

SI-

Jože Tavčar

-

Aškerčeva 6SI-1000 Ljubljana

dynamic planning and multicriteria scheduling of … · master production schedule (mps) and...

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