General Purpose Procedures Applied to Scheduling

1
General Purpose ProceduresApplied to Scheduling
Contents Constructive approach 1. Dispatching
Rules Local search 1. Simulated
Annealing 2. Tabu-Search 3. Genetic Algorithms
2
Literature 1. Operations Scheduling with
Applications in Manufacturing and 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.
3
Constructive procedures 1. Dispatching Rules 2.
Composite Dispatching Rules 3. Dynamic
Programming 4. Integer Programming 5. Branch and
Bound 6. Beam Search Local Search 1. Simulated
Annealing 2. Tabu-Search 3. Genetic
Algorithms Heuristic technique is a method which
seeks good (i.e. near-optimalsolutions) at a
reasonable cost without being able to
guaranteeoptimality.
4
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, or the current
  queue length

5
(No Transcript)
6
Local Search
Step. 1. Initialisation k0 Select a starting
solution S0?S Record the current best-known
solution by setting Sbest S0 and best_cost
F(Sbest) Step 2. Choice and Update Choose a
Solution Sk1?N(Sk) If the choice criteria
cannot be satisfied by any member of N(Sk),
then the algorithm stops if F(Sk1) lt
best_cost then Sbest Sk1 and best_cost
F(Sk1) Step 3. Termination If termination
conditions apply then the algorithm stops else
k k1 and go to Step 2.
7

• Global Optimum better than all other solutions
• Local Optimum better than all solutions in a
  certain neighbourhood

8

• 1. Schedule representation
• 2. Neighbourhood design
• 3. Search process
• 4. 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

9

• 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

10

• current schedule

(h, l)
(h, k)
machine h
(i, j)
(i, k)
machine i

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

(h, l)
(h, k)
machine h
(i, j)
(i, k)
machine i

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

(h, l)
(h, k)
machine h
(i, j)
(i, k)
machine i
11

• 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 annealing
• deterministic tabu-search