1. General Purpose Procedures Applied 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

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-optimal solutions) at a reasonable cost without being able to guarantee optimality.

4. Dispatching Rules
A dispatching rule prioritises all the jobs that are waiting for processing 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

6. Local Search Step. 1. Initialisation k=0
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 Sk+1N(Sk) If the choice criteria cannot be satisfied by any member of N(Sk), then the algorithm stops
if F(Sk+1) < best_cost then Sbest = Sk+1 and best_cost = F(Sk+1)
Step 3. Termination
If termination conditions apply
then the algorithm stops
else k = k+1 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, k)
(i, j)
machine i
schedule after interchange of (h, l) and (h, k)
(h, k)
(h, l)
machine h
(i, k)
(i, j)
machine i

11. 3. Search process
select schedules randomly
select first schedules that appear promising for example, swap jobs that affect the objective the most
4. Acceptance-rejection criterion
probabilistic: simulated annealing
deterministic: tabu-search