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General Purpose ProceduresApplied to Scheduling

Contents

Constructive approach

1. Dispatching Rules

Local search

1. Simulated Annealing

2. Tabu-Search

3. Genetic Algorithms

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Literature

1. Operations Scheduling with Applications in Manufacturingand Services, Michael Pinedo and Xiuli Chao, McGraw Hill, 2000,Chapter 3.1 and 3.2.

or

Scheduling, Theory, Algorithms, and Systems, Second Addition,Michael Pinedo, Prentice Hall, 2002, Chapter 14.1

2. Modern Heuristic Techniques for Combinatorial Problems, (Ed) C.Reeves 1995, McGraw-Hill. Chapter 2.2.1.

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Constructive procedures:

1. Dispatching Rules

2. Composite Dispatching Rules3. Dynamic Programming4. Integer Programming5. Branch and Bound6. Beam Search

Local Search

1. Simulated Annealing2. Tabu-Search3. Genetic Algorithms

Heuristic technique is a method which seeks good (i.e. near-optimalsolutions) at a reasonable cost without being able to guaranteeoptimality.

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Dispatching Rules

A dispatching rule prioritises all the jobs that are waiting forprocessing on a machine.

Classification

• Static: not time-dependent• Dynamic: time dependent

• Local: uses information about the queue where the job is waiting or machine where the job is queued

• Global: uses information about other machines(e.g. processing time of the jobs on the next machine on its route, orthe current queue length

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Rule Data ObjectivesService in random orderSIRO

ease of implementation

Earliest release date firstERD

rj minimise variation of thewaiting times of jobs at amachine

Earliest due date first EDD dj minimise latenessMinimum slack firstmax(dj-pj-t, 0)

dj, pj minimise due daterelated objectives

Weighted shortestprocessing time firstWSPTwj / pj

wj, pj minimise weighted sum ofcompletion times

Longest processing timefirst LPT

pj load balancing overparallel machines

Shortest setup time firstSST

sjk makespan

Least flexible job first LFJ Mj makespanCritical path CP pj, precedence makespanLargest number ofsucessors LNS

pj, precedence makespan

Shortest queue at the nextmachine SQNO

machine idleness

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Local Search

Step. 1. Initialisationk=0Select a starting solution S0SRecord the current best-known solution by setting Sbest = S0

and best_cost = F(Sbest)

Step 2. Choice and UpdateChoose a Solution Sk+1N(Sk)If the choice criteria cannot be satisfied by any member of N(Sk), then the algorithm stopsif F(Sk+1) < best_cost then Sbest = Sk+1 and best_cost = F(Sk+1)

Step 3. TerminationIf termination conditions applythen the algorithm stops

else k = k+1 and go to Step 2.

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• Global Optimum: better than all other solutions

• Local Optimum: better than all solutions in a certain neighbourhood

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1. Schedule representation2. Neighbourhood design3. Search process4. Acceptance-rejection criterion

1. Schedule representation

Nonpreemptive single machine schedule• permutation of n jobs

Nonpreemptive job shop schedule• m consecutive strings, each representing a permutation of

n operations on a machine

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2. Neighbourhood design

Single machine: • adjacent pairwise interchange• take an arbitrary job in the schedule and insert it in another positions

Job shop:• interchange a pair of adjacent operations on the critical path

of the schedule• one-step look-back interchange

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(h, l)(h, k)machine h

(i, j)(i, k)machine i

(h, l) (h, k)machine h

(i, j)(i, k)machine i

(h, l) (h, k)machine h

(i, j) (i, k)machine i

• current schedule

• schedule after interchange of (i, j) and (i, k)

• schedule after interchange of (h, l) and (h, k)

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3. Search process

• select schedules randomly• select first schedules that appear promisingfor example, swap jobs that affect the objective the most

4. Acceptance-rejection criterion

probabilistic: simulated annealingdeterministic: tabu-search