Presentation - SCHEDULING Techniques

8/12/2019 Presentation - SCHEDULING Techniques

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SCHEDULING TECHNIQUES

A.C.S.I.Mumthas


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The representation of the precedence constraints as a graph job-on-arc job-on-node

job j

job j

job k

job k

(a) Job-on-arc format

(b)Job-on-node format

Job Description Duration ( p j )12345678

Design production toolingPrepare manufacturing drawingsPrepare production facility for new tools and partsProcure toolingProcure production partsKit partsInstall toolsTesting

46

101210

242

weeksweeksweeksweeksweeksweeksweeksweeks

Immediate Immediate Job Predecessors Successors12345678

12

3, 4, 53, 46, 7

45

6, 76, 7

688

(a) Job-on-node format (b) Job-on-arc format

1 4 7 2 5

3 81

2 5 6

4 7 80

6

3


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a job can start its processing onlywhen all its predecessors havebeen completed.

determines the earliest possible startingtimes and completion times as well as theminimum makespan.

Backward Procedure latest possible starting times andcompletion times of all the jobs, assuming

the makespan is kept at its minimumstarts out with the minimum makespan and computes the

latest starting times and latest completion times, such thatthe minimum makespan still can be achieved.

Jobs 1 2 3 4 5 6 7 8 9 10 11 12 13 14Processing times 5 6 9 12 7 12 10 6 10 9 7 8 7 5

Jobs 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Processingtimes 5 6 9 12 7 12 10 6 10 9 7 8 7 5

Forward 11 14 23 21 26 33 32 36 42 43 51 50 56

Backward 5 12 14 24 30 26 34 36 43 43 51 51 51 56

2 4

9

7

3 11

1

5

6 1412

8

10

13


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t o = the optimistic (shortest) processing time of job jt m = most likely time (estimated best time) of job jt p = the pessimistic (longest) processing time of job jt e = mean (expected) time of job j

t e = (t o+4t m +t p)/6An estimate of the expected makespan is then obtained by summing the estimates forthe expected processing times of all jobs on a critical path.

Compute an estimate for the variance of the processing time of job j by taking; 2 =[ (t p - t o)/6] 2

Since the jobs on the critical path have to be processed one after another, the varianceof the total processing time of all jobs on the critical path can be an estimate for the variance of the makespan The distribution of the makespan is assumed to be normal, i.e., Gaussian, withmean t e and variance of the makespan .

If there are several critical paths, then the actual makespan is the maximum of the total realized processing times ofeach one of the critical paths.

Second, the total amount of processing on the critical path is assumed to be normally distributed. If the numberof jobs on the critical path is very large, then this assumption may be reasonable (because of the Central Limit

Theorem).


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Assumptions:There is a budget that can be used for allocating additional funds to the various

jobs.processing time of a job is a linear function of the amount allocated.

In order to determine the minimum cost of the entire project it is necessary todetermine the most appropriate processing time for each one of the n jobs.

It is very effective to solve in heuristic methods. because:it s usually the way the problem is dealt with in practiceit can also be used when costs are non-linear

while reducing the processing times to a minimumparticular minimum cut set may be not relevant any more.another path may become criticalIf it happens a new collection of minimum cut sets has to be determined.It does not make sense to reduce the makespan to a value that is less than the committed due

date, since this would only increase the cost and wouldnot result in any benet .

Cut set

Minimal cut set Sink

Source


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(a) Cost of reducing processing time (b) Overhead cost function co (t )

Processing time

Resourceallocated

Overheadcostfunctionco (t )

time

TIME/COST TRADE-OffS : NON-LINEAR COSTS

It is very important to reduce the processing times in a cut set in each iteration by just onetime unit . In this case it is not advisable to have a larger step size in the reduction of theprocessing times since the shape of the cost functions may affect the step size.

A solution for this problem is reached either; when no minimum cut sets with reducible processing times remain,

or,in case there are such cut sets, the marginal cost of reducing such a cut set is higher

than the savings obtained due to the reduced overhead.

p max p min

c b

c aResourceallocated

Processing time


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The workforce may consist of various different pools and each pool has a xed number of operators with a specic skill. Each job requires for its execution a givennumber from each pool. If the processing of some jobs overlap in time, then the sumof their demands for operators from any given pool may not exceed the total

number in that pool


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MACHINE SCHEDULING AND JOB

SHOP SCHEDULING


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Job shop problems can be organized as follows;

Single Machine and Parallel Machine Models Job Shops and Mathematical ProgrammingJob Shops and the Shifting Bottleneck HeuristicLEKIN: A Generic Job Shop Scheduling System

A exible job shop ; consists of a collection of work-centers and each work-center consists of a numberof identical machines in parallel. Each job follows a predetermined route visiting anumber of work-centers; when a job visits a work-center, it may be processedon any one of the machines at that work-center.

If a job shop is subject to recirculation a job may visit each machine more than once.


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Apparent Tardiness Cost rst (ATC) rule . If the machine is freed at time t, the ATC ruleselects among the remaining jobs the job with the highest value of

where K is a so-called scaling parameter and p is the average of the processingtimes of the jobs that remain to be scheduled

ATC priority rule is actually a weighted mixture of the WSPT and MS priority rulesNonpre-emptive single machine scheduling problem in which the jobs have different

release dates and the maximum lateness (Lmax) has to be minimized. This problem isknown as NP-Hard, which implies that, unfortunately, no efficient (polynomial time)algorithm exists for this problem. The problem can be solved either by branch-and-boundor by dynamic programming.

Longest Processing Time rst (LPT) rule is used when the loads of the various machineshave to be balanced

According to this rule, whenever one of the machines is freed, the longest job amongthose waiting for processing is selected to go next. unfortunately, this does not guaranteean optimal solution

Ij (t ) = wj pj exp

max(dj pj t,0)

Kp


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Constraint programming is a technique that originated in the Articial

Intelligence (AI) community. In recent years, it has often been implemented inconjunction with Operations Research (OR) techniques in order to improve itsoverall effectiveness .

Constraint programming, in its original design, only tries to nd a good solutionthat is feasible and satises all the given constraints.

For each operation a computation is done to determine its earliest possiblestarting time and latest possible completion time on the machine inquestion.

After all the time windows have been computed, the time windows of allthe operations on each machine are compared with one another.

When the time windows of two operations on any given machine do not overlap,a precedence relationship between the two operations can be imposed; in anyfeasible schedule the operation with the earlier time window must precedethe operation with the later time window


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Originally, this system was designed as a tool for teaching and research.The LEKIN system can accomodate various machine environments, namely:

(i) single machine(ii) parallel machines(iii) ow shop(iv) exible ow shop(v) job shop(vi) exible job shop

Furthermore, it is capable of dealing with sequence dependent setup times in all theenvironments listed above.

In the main menu the user can select a machine environment. After the user hasselected an environment, he has to enter all the necessary machine data and job datamanually.After all the data have been entered four windows appear simultaneously, namely,

(i) the machine park window,(ii) the job pool window,(iii) the sequence window, and(iv) the Gantt chart window,


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The system contains a number of algorithms for several of the machine environmentsand objective functions. These algorithms include

(i) dispatching rules (include EDD and WSPT),(ii) heuristics of the shifting bottleneck type,

(iii) local search techniques, and(iv) a heuristic for the exible ow shop with the total weighted tardiness

Logbook and comparison of different schedules done in LEIKIN system is shown below;


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A flexible manufacturing system (FMS) is a manufacturingsystem in which there is some amount of flexibility that allowsthe system to react in the case of changes, whether predictedor unpredicted.

Flexibility Machine Flexibility - ability to change product types, order

of operations executed on a part. Routing Flexibility - ability to use multiple machines to

perform the same operation on a part, and the system'sability to absorb large-scale changes, such as in volume,capacity, or capability.

In most FMSs the work machines which are often automatedare connected by a material handling system to optimize parts

flow.


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Job Shops Flexible Assembly

each job has its own identityand may be different from all other jobs a limited number of different product typesand the system has to produce a givenquantity of each product type

Make to order, low volume environment Mass production

Possibly complicated route through system High degree of automation


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Number of machines in series No buffers Material handling system

When a job finishes moves to next station No bypassing ( First In First Out) Blocking

Not much used in Apparel industry since the efficiency

of the process goes down when blocking happens,However in the Textile industry since the product isbulky this type of assembly systems can be used whenno buffer can be maintained.


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Conveyor moves jobs at fixed speeds Fixed distance between jobs

Spacing proportional to processing time No bypass Unit cycle time

time between two successive jobs line balancing

Objectives Minimize total setup cost Meet due dates for make-to-order jobs Spacing of capacity constrained operations Regular rate of material consumption

Most of the Apparel Manufacturing facilities follow this type of Assembly systemssince most of the operations can be broken down into equal time operations andcan maintain a smooth work flow and high efficiency.


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Objectives Minimize work-in-process (WIP)

Reduces blocking probabilities Three phases:

Machine allocation phase assigns each job to a specific machine at station Basic idea: workload balancing

Sequencing phase orders in which jobs are released Basic idea: spread out jobs sent to the same machine and minimizing overload

Time release phase Step 1: Release all jobs as soon as possible Step 2: Delay all jobs upstream from bottleneck as much as possible Step 3: Move up all jobs downstream from the bottleneck as much as possible


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Why Lot Sizing large number of identical jobs setup time/cost significant setup may be sequence dependent

Objectives Minimize total cost

setup cost inventory holding cost

Trade-off Cyclic schedules

Scheduling Decisions Determine the length of runs

lot sizes Determine the order of the runs

sequence to minimize setup cost


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Time horizon usually a few months (short range planning)

Optimal Cycle time through minimizing the total cost (Setup cost, Inventory holding cost)

Optimal lot size (Economic Order Quantity EOQ)through Total Production calculated according to OptimalCycle size (Unlimited Production capability is assumed)

This type of scheduling is not much used in Apparel orTextile industry since most of the factories produce morethan one type of products and requires more than onem/c to produce.


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Same method as followed for single item, now considern different items

In this method the total set up cost is independent ofthe sequence of operation

Scheduling Decision Only need to determine the cycle length (Cycle length

determines the run length for each item) Expression for total cost/time unit

As an example, this type of Scheduling can be used inscheduling bulk production of large machinery likedyeing m/c, finishing m/c in Textile industry and forembroidery m/c in Apparel Industry.


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Objective: minimize sum of setup times Equivalent to the Traveling Salesman Problem (TSP)

Item = city Travel time = setup time

Two Problems to solve Master problem

finds the best sequence Sub problem

finds the best production times, idle times, and cycle length There are many instances in both Textile and Apparel

Industry where a set up time is required beforeproduction, and therefor this type of Schedulingmethod can be used for such instances.


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Extensions to multiple machines

parallel machines flow shop flexible flow shop

Objective: assign items to machines to

balance the load Decision Variables

Same as previous multi-item problem Addition: assignment of items to machines

Must consider preferred cycle time machine balance setup times

This is the most common scheduling technique used in the Apparelindustry when scheduling sawing operations.


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These two major things should be taken in to account Continuous manufacturing industries (which include the

process industries) Main processing operations Finishing or converting operations,

Discrete manufacturing industries Primary converting operations (e.g., cutting and shaping of sheet

metal)

Main production operations (e.g., production of engines, PCBs,wafers) Assembly operations (e.g., cars, PCs)


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The main objective in a supply chain is to produce anddeliver finished products to end consumers in themost cost effective and timely manner.


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Information flow between planning and scheduling systems


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Medium term: 12 weeks Given demand and forecasts for products are

considered

Scheduling models optimize supply chains The costs that have to be minimized in this

optimization process include production costs, holding or storage costs,

transportation costs, tardiness costs, non-deliverycosts, handling costs, costs for increases


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Based on medium term schedule, short termscheduling plans the actual production for oneweek

More detailed model of resources (i.e., sequencedependent setup costs)

Uses genetic algorithm or constraint programming


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Presentation - SCHEDULING Techniques

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