scheduling hand out

8/2/2019 Scheduling Hand Out

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SHORT TERM SCHEDULING

Scheduling involve assigning specific dates to

job . It involves the allocation of resources

over time to accomplish tasks . As such , it is

the determination of the order in which jobs

need to be processed and the time to start

each job


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TYPES OF FLOW SYSTEMS

PRODUCT LAYOUT

ASSEMBLY LINES

TRANSFER LINES

PROCESS LAYOUT

FLOW SHOP (jobs go through same sequence)

JOB SHOP (each job has its own route)


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PROCESS LAYOUT FLOW SYSTEMS

PRODUCTS ARE RELEASED TO THE

PRODUCTION SYSTEM IN BATCHES

IF BATCHES VISIT SAME SEQUENCE OF

STATIONS --> FLOW SHOP

IF DIFFERENT BATCHES HAVE THEIR OWN

ROUTE --> JOB SHOP


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http://www.baskent.edu.tr/~kilter 4

Scheduling in Low-Volume Systems

Job-shop scheduling


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FEATURES OF JOB SHOPS

WIDE VARIETY OF PRODUCT REQUIREMENTS

MUST BE DESIGNED FOR MAXIMUM

FLEXIBILITY

INDIVIDUAL STATIONS MUST BE CAPABLE OF

WIDE VARIETY OF TASKS


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FEATURES OF JOB SHOPS

EXPERTISE IS PROCESS RELATED

ORGANIZED BY PROCESSING FUNCTION

UP TO 95% OF JOB TIME SPENT IN NON-PRODUCTIVE ACTIVITY

REMAINING 5% SPLIT BETWEEN LOT SETUP

AND PROCESSING


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KEY QUESTIONS

WHEN TO RELEASE ORDERS TO THE

PRODUCTION FACILITY?

HOW TO SEQUENCE JOBS AT A SINGLE

WORKSTATION?

HOW TO SCHEDULE JOBS THROUGH THE

ENTIRE FACILITY?


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NEED FOR SCHEDULING

For effective utilization of resource ( machine

time , operator time etc)

To determine the realistic delivery time of

spare part / finished goods

Advise the customer in case of delays

Determine bottle neck operations so thatcorrective action could be taken


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Scheduling methods and models

SEQUENCING: PROCESS OF DEFINING THEORDER IN WHICH JOBS ARE TO BE RUN ON A

MACHINE SCHEDULING: PROCESS OF ADDING START AND

FINISH TIME TO THE PROCESS DICTATED BY THESEQUENCE

Gantt Chart : it is a graphical tool whichrepresent a production schedule


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SCHEDULING:

Effective scheduling means faster movement of

goods and services through a facility . This means

greater use of assets and hence greater capacity

per every rupee invested which in turn lower cost Added capacity , faster throughput and the

related facility means better customer service

through faster delivery Good scheduling also contribute to realistic

commitment and hence dependable delivery


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SCHEDULING

Scheduling involves assigning due dates to specific job butmany jobs compete simultaneously for the same resources.Two type of scheduling techniques:

Forward schedulingstart the schedule as soon as jobrequirements are known . It is designed to produceschedule that can be accomplished even if it mean notmeeting the due date.

Backward scheduling begin with the due date , schedulingthe final operation first .Step in the job are then scheduledone at a time in reverse order . By subtracting the leadtime for each job, the start time is obtained . Note thenecessary resources may not be available


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SCHEDULING CRITERIA

The correct scheduling technique depend on

the volume of orders, the nature of the

operation and the overall complexity of the

jobs and the importance placed on each of the

four criteria :

(a) Minimise completion timeThis criterion is

evaluated by determining the averagecompletion time per job


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SCHEDULING CRITERIA

Maximize utilization this is evaluated by

determining the per cent of time that the

facility is utilized

Minimize work in progress inventory the

average number of job in the system.

Minimize customer waiting timethe average

number of late days


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SCHEDULING CRITERIA

A good scheduling approach should be simple

, clear , easily understood , easy to carry out ,

flexible and realistic

Conclusion : The overall objectives of

scheduling is to optimise the use of resources

so that production objectives could be met


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Loading

Loading means the assignment of job to work

or processing centres . Operation managers

assign jobs to work centre so that cost , idle

time or completion times are kept to aminimum . Loading work centres take two

forms : capacity oriented and assigning

specific jobs to work centres


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INPUT OUTPUT CONTROL

Input/Output Control


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Loading Gantt Chart

Gantt charts are visual aids that are useful in

loading It shows the loading and idle times of

work centres


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Gantt chart (load)

Gantt Charts


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Gantt chart


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Assignment

The assignment method involve assigning

tasks or job to resourcesone job to one

machine

Objective minimize cost


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Assignment Method of Linear Programming


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The Assignment Problem

In many business situations, management needs toassign - personnel to jobs, - jobs to machines, -machines to job locations, or - salespersons toterritories.

Consider the situation of assigning n jobs to nmachines.

When a job i (=1,2,....,n) is assigned to machine j

(=1,2, .....n) that incurs a cost Cij. The objective is to assign the jobs to machines at the

least possible total cost.


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This situation is a special case of the

Transportation Model And it is known as the

assignment problem.

Here, jobs represent sources and machines

represent destinations.

The supply available at each source is 1 unit

And demand at each destination is 1 unit.


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The assignment model can be expressed

mathematically as follows:

Xij= 0, if the job j is not assigned to machine i

1, if the job j is assigned to machine i


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The Assignment Problem Example

Ballston Electronics manufactures small electricaldevices.

Products are manufactured on five differentassembly lines (1,2,3,4,5).

When manufacturing is finished, products aretransported from the assembly lines to one of thefive different inspection areas (A,B,C,D,E).

Transporting products from five assembly lines tofive inspection areas requires different times (inminutes)


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Under current arrangement, assignment of

inspection areas to the assembly lines are 1 to A, 2

to B, 3 to C, 4 to D, and 5 to E.This arrangement requires 10+7+12+17+19 = 65 man

minutes.


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Management would like to determine whethersome other assignment of production lines toinspection areas may result in less cost.

This is a typical assignment problem. n = 5 Andeach assembly line is assigned to each inspectionarea.

It would be easy to solve such a problem when n

is 5, but when n is large all possible alternativesolutions are n!, this becomes a hard problem.


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Assignment problem can be either formulated

as a linear programming model, or it can be

formulated as a transportation model.

However, An algorithm known as Hungarian

Methodhas proven to be a quick and efficient

way to solve such problems.

This technique is programmed into many

computer modules


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Hungarian Method Example

Step 1: Select the smallest value in each row.

Subtract this value from each value in that row

Step 2: Do the same for the columns that do not

have any zero value.


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If not finished, continue

with other columns.


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Step 3: Assignments are made at zero values.

Therefore, we assign job 1 to machine 1; job 2

to machine 3, and job 3 to machine 2.

Total cost is 5+12+13 = 30.

It is not always possible to obtain a feasible

assignment as in here.


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Hungarian Method Example 2

A feasible assignment is not possible at this

moment.

In such a case, The procedure is to draw a

minimum number oflines through some of

the rows and columns, Such that all zero

values are crossed out.


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The next step is to select the smallest uncrossed out element. This

element is subtracted from every uncrossed out elementand added

to every element at the intersection of two lines.


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We can now easily assign to the zero values.

Solution is to assign (1 to 1), (2 to 3), (3 to 2)

and (4 to 4).

If drawing lines do not provide an easy

solution, then we should perform the task of

drwaing lines one more time.

Actually, we should continue drawing lines

until a feasible assignment is possible.


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Sequencing

Possible priority rules:

First come, first served (FCFS): Jobs are processed in the order in which they arrive ata machine or work center.

Shortest processing time (SPT): Jobs are processed according to processing time at amachine or work center, shortest job first.

Earliest due date (EDD): Jobs are processed according to due date, earliest due datefirst.

Critical ratio (CR): Jobs are processed according to smallest ratio of time remaininguntil due date to processing time remaining.

Slack per operation (S/O): Jobs are processed according to average slack time (time

until due date minus remaining time to process). Compute by dividing slack timeby number of remaining operations, including the current one.

Rush: Emergency or preferred customers first.

LPT : longest processing timethe longer, bigger job are often more important andthey are selected first


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Sequencing

Assumptions of priority rules:

The set of jobs is known; no new jobs arrive after processing begins; and no jobs are

canceled.

Setup time is independent of processing sequence.

Setup time is deterministic.

Processing times are deterministic rather than variable.

There will be no interruptions in processing such as machine breakdowns, accidents,

or worker illness.


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Performance Measures:


Job flow time. This is the length of time a job is at a particular workstation or work

center.

Job lateness. This is the length of time the job completion date is expected to exceed

the date the job was due or promised to a customer.

Makespan.Makespan is the total time needed to complete a group of jobs. It is the

length of time between the start of the first job in the group and the completion of

the last job in the group.

Average number of jobs. Jobs that are in a shop are considered to be work-in-process

inventory.Average number of jobs = Total flow time Makespan


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Average completion time = Sum of flowtime/number of jobs

Utilization=Total job work(processing) time/

sum of flow time Average number of jobs in the system =Sum of

total flow time /Total job work(processing)time

Average job lateness=Total late days/numberof jobs


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Example

Processing times (including setup times) and due dates for six jobs waiting to be

processed at a work center are given in the following table. Determine the

sequence of jobs, the average flow time, average tardiness, and average number

of jobs at the work center, for each of these rules:

FCFS

SPTEDD

CR


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FCFSThe FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see

table):1. Average flow time: 1206 = 20 days.

2. Average tardiness: 546 = 9 days.

3. The makespan is 41 days.

Average number of jobs at the work center: 12041 = 2.93.


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SPTUsing the SPT rule, the job sequence is A-C-E-B-D-F (see the following table). The resulting

values for the three measures of effectiveness are1. Average flow time: 1086 = 18 days.

2. Average tardiness: 406 = 6.67 days.

3. Average number of jobs at the work center: 10841 = 2.63.


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EDDUsing earliest due date as the selection criterion, the job sequence is C-A-E-B-D-F. The

measures of effectiveness are as follows (see table):1. Average flow time: 1106 = 18.33 days.



Using the critical ratio we find


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At day 4 [C completed], the critical ratios are

At day 16 [C and F completed], the critical ratios are

At day 18 [C, F, and A completed], the critical ratios are


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At day 23 [C, F, A, and E completed], the critical ratios are

At day 18 [C, F, and A completed], the critical ratios are


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At day 23 [C, F, A, and E completed], the critical ratios are

The job sequence is C-F-A-E-B-D, and the resulting values for the measures of effectiveness are


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as follows:

1. Average flow time: 1336 = 22.17 days.




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Performance


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Example

Use the S/O rule to schedule the following jobs. Note that processing time includes

the time remaining for the current and subsequent operations. In addition, you

will need to know the number of operations remaining, including the current one.


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Determine the difference between the due date and the processing time for each

operation. Divide the difference by the number of remaining operations, and rank

them from low to high. This yields the sequence of jobs:

Sequencing Jobs through Two Work


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Sequencing Jobs through Two WorkCenters

For the technique to work, several conditions must be satisfied:

Job time (including setup and processing) must be known and constant for each job at

each work center.

Job times must be independent of the job sequence.

All jobs must follow the same two-step work sequence.

Job priorities cannot be used.

All units in a job must be completed at the first work center before the job moves on

to the second work center.


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Johnson rule

The next step in complexity is the case in which N jobs (where N is2 or more) must go

through two different machines or job centres in the same owner

Determination of the optimum sequence involves these steps:

List the jobs and their times at each work center.

Select the job with the shortest time. If the shortest time is at the first work center,

schedule that job first; if the time is at the second work center, schedule the job

last. Break ties arbitrarily.

Eliminate the job and its time from further consideration.

Repeat steps 2 and 3, working toward the center of the sequence, until all jobs havebeen scheduled.


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Example

A group of six jobs is to be processed through a two-machine flow shop. The first

operation involves cleaning and the second involves painting. Determine a

sequence that will minimize the total completion time for this group of jobs.

Processing times are as follows:


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Select the job with the shortest processing time. It is job D, with a time of two hours.

Since the time is at the first center, schedule job D first. Eliminate job D from further

consideration.

Job B has the next shortest time. Since it is at the second work center, schedule it last

and eliminate job B from further consideration. We now have

The remaining jobs and their times are


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The shortest remaining time is six hours for job E at work center 1. Thus, schedule that

job toward the beginning of the sequence (after job D). Thus,

Job C has the shortest time of the remaining two jobs. Since it is for the first work

center, place it third in the sequence. Finally, assign the remaining job (F) to thefourth position and the result is

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