presentation - scheduling techniques
TRANSCRIPT
-
8/12/2019 Presentation - SCHEDULING Techniques
1/40
SCHEDULING TECHNIQUES
A.C.S.I.Mumthas
-
8/12/2019 Presentation - SCHEDULING Techniques
2/40
-
8/12/2019 Presentation - SCHEDULING Techniques
3/40
-
8/12/2019 Presentation - SCHEDULING Techniques
4/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
5/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
6/40
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).
-
8/12/2019 Presentation - SCHEDULING Techniques
7/40
-
8/12/2019 Presentation - SCHEDULING Techniques
8/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
9/40
(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
-
8/12/2019 Presentation - SCHEDULING Techniques
10/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
11/40
MACHINE SCHEDULING AND JOB
SHOP SCHEDULING
-
8/12/2019 Presentation - SCHEDULING Techniques
12/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
13/40
-
8/12/2019 Presentation - SCHEDULING Techniques
14/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
15/40
-
8/12/2019 Presentation - SCHEDULING Techniques
16/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
17/40
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,
-
8/12/2019 Presentation - SCHEDULING Techniques
18/40
-
8/12/2019 Presentation - SCHEDULING Techniques
19/40
-
8/12/2019 Presentation - SCHEDULING Techniques
20/40
-
8/12/2019 Presentation - SCHEDULING Techniques
21/40
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;
-
8/12/2019 Presentation - SCHEDULING Techniques
22/40
-
8/12/2019 Presentation - SCHEDULING Techniques
23/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
24/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
25/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
26/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
27/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
28/40
-
8/12/2019 Presentation - SCHEDULING Techniques
29/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
30/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
31/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
32/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
33/40
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.
-
8/12/2019 Presentation - SCHEDULING Techniques
34/40
34
-
8/12/2019 Presentation - SCHEDULING Techniques
35/40
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)
-
8/12/2019 Presentation - SCHEDULING Techniques
36/40
The main objective in a supply chain is to produce anddeliver finished products to end consumers in themost cost effective and timely manner.
-
8/12/2019 Presentation - SCHEDULING Techniques
37/40
Information flow between planning and scheduling systems
-
8/12/2019 Presentation - SCHEDULING Techniques
38/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
39/40
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
-
8/12/2019 Presentation - SCHEDULING Techniques
40/40