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Using Simulated Annealing and Evolution Strategy scheduling capital products with complex product structure. By: Dongping SONG Supervisors: Dr. Chris Hicks and Prof. Chris F. Earl Department of MMM Engineering University of Newcastle, Oct., 2000. Contents. Introduction

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slide1

Using Simulated Annealing and Evolution Strategy schedulingcapital products with complex product structure

By: Dongping SONG

Supervisors: Dr. Chris Hicks and

Prof. Chris F. Earl

Department of MMM Engineering

University of Newcastle, Oct., 2000.

contents
Contents
  • Introduction
  • Problem formulation
  • A discrete event-driven model
  • Simulated Annealing
  • Evolution Strategy
  • Case studies
  • Conclusions
introduction
Introduction

Production scheduling -- the allocation of resources over time to perform a collection of tasks (Baker, 1974).

Two important points in scheduling:

Sequencing -- in which order to perform tasks on resources

Timing -- when to start and complete tasks

introduction4
Introduction
  • The importance of sequencing has been well recognised, because
  • the optimal schedule can only be characterised by the sequences for performance measures such as mean flow-time, percentage of jobs tardy, mean tardiness, etc.
  • However, timing scheduling is necessary
  • for performance measures such as earliness and tardiness costs, total discrepancy from the due dates, etc.
introduction effect of timing
Introduction - effect of timing

Example 1. One machine with three independent jobs.

Due dates

Schedule A:

Schedule B:

Schedule C:

introduction effect of timing6
Introduction - effect of timing

Example 2. Two machines four jobs s.t. job 1 becomes job 4 and job 2 becomes job 3 after completion.

Schedule A:

Schedule B:

introduction a capital product
Introduction - a capital product

Complex product structure

slide8

product

Waiting time

Time period

Gantt chart -- with 113 operations (13 assemblies).

slide9

Work-load

Machine

Time period

Resource chart -- work-load on 13 machines.

introduction10
Introduction
  • Constraints in our scheduling problem:
    • Operation precedence constraints
    • Resource capacity constraints
    • Due date constraints
    • Assembly co-ordination requirements
  • Scheduling problem: to find optimal operation sequences and timings to meet above constraints and minimise total cost.
problem formulation
Problem formulation
  • Notation: si -- planned start time for operation i;N -- total operation number.
  • Solution space of schedules := RN´{sequences on resources}.
  • Solution space can be simplified to RN, because operations on the same resource have different start times (i.e. timings imply sequences).
problem formulation12
Problem formulation
  • The schedule problem can be formulated as a numerical optimisation problem.
  • Find the optimal {si, i=1,..,N} to minimise the total cost

J(s) = å (Work-in-progress holding costs + product earliness costs + product tardiness costs)

problem formulation13
Problem formulation
  • Questions:

(1) How to execute a schedule that is characterised by {si} ?

(2) How to evaluate the cost function for a given schedule ?

discrete event driven model
Discrete event-driven model
  • Two types of events :
    • the start of an operation
    • the completion of an operation.
  • Two constraints to trigger the start events :
    • Physical constraints : an event cannot occur before all preceding events are completed.
    • Planning constraints : an operation cannot be started before its planned start time si.
discrete event driven model15
Discrete event-driven model

The evolution of the system for a given schedule {si} can be described by:

  • If a resource is idle, an operation will be processed as soon as the physical and planning constraints are satisfied.
  • If there is a queue of operations ready for processing, the operation with the earliest siwill be processed first.
simulated annealing
Simulated Annealing
  • Neighbourhood of a solution -- by adding a random number to each si.
  • Outer loop -- cooling the temperature T until T=0.
  • Inner loop -- perform Metropolis simulation with fixed T to find equilibrium state.
simulated annealing17
Simulated Annealing
  • Adjust the solution :
    • shift the whole schedule (optional)
    • impose precedence constraints (optional)
    • make non-negative
  • Evaluate cost function :
    • run the DED model
evolution strategy
Evolution Strategy
  • Similarity of Genetic Algorithms and ES:
    • model organic evolution.
    • iterative scheme including “selection”, “crossover” and “mutation”.
  • Difference of GA and ES:
    • GA uses binary or string representations, suitable for combinatorial optimisation problem.
    • ES uses continuous variable, suitable for numerical optimisation problem.
evolution strategy20
Evolution Strategy
  • Crossover -- randomly copy elements from parents column by column.
evolution strategy21
Evolution Strategy
  • Mutation -- add a random number from a Normal distribution to each element.
evolution strategy22
Evolution Strategy
  • Adjust the solution :
    • shift the whole schedule (optional)
    • impose precedence constraints (optional)
    • make non-negative
  • Evaluate cost function -- run the DED model.
  • Selection -- choose a set of best offspring as parents for the next generation
case studies
Case studies

Characteristics of scheduling problems

case study 1
Case study 1

MRP -- material requirement planning

FIFO -- first in first out

EDD -- earliest due date first

SPT -- shortest processing time first

Cost is reduced by 50% for SA and ES.

case study 1 cost v s cpu
Case study 1 -- cost v.s cpu

Cost

SA

ES

CPU(s)

Total cost v.s. CPU time for SA and ES

case study 1 es method
Case study 1 -- ES method

Cost

Maximum cost at each generation

Maximum cost in all parents

CPU(s)

Minimum cost at each generation

case study 2
Case study 2

Cost is reduced by 50% for SA and ES.

case study 2 cost v s cpu
Case study 2 -- cost v.s. cpu

Cost

SA

ES

CPU(s)

Total cost v.s CPU time for SA and ES

case study 2 es method
Case study 2 -- ES method

Cost

Maximum cost at each generation

Maximum cost in all parents

CPU(s)

Minimum cost at each generation

conclusions
Conclusions
  • SA and ES can reduce total cost by 50% compared with MRP+dispatching rules.
  • ES is generally better than SA in both cost and CPU time.
  • ES is more robust to its initial parameter selection than SA.
conclusions32
Conclusions
  • Suggestions for SA initial parameters:
    • T0 and step-size is taken from [d/N, 20*d/N];
    • Temperature cooling rate > 0.5 and step-size reduction factors > 0.70;
    • No-improvement number at inner loop > N/2;
  • Suggestions for ES initial parameters:
    • Offspring population is from [N/2, 2*N];
    • Parent population is 1/10 to 1/5 of offspring;
    • Initial standard deviation is from [d/N, 5*d/N].
further work
Further work
  • Compare our methods with GA (Pongcharoen, et al.) for the same cost function.
  • Develop hybrid optimisation methods by combining SA, ES with Perturbation Analysis or heuristics.
  • Extend to stochastic situations such as dynamic customer demand arrivals and processing uncertainties.
sa effect of parameters
SA -- effect of parameters

T0=1

T0=40

T0=20

T0=10

Initial temperature and temperature cooling factor

es effect of parameters
ES -- effect of parameters

Solid-line : ON/GN=80/250

dashed-line: ON/GN=100/400

dotted-line: ON/GN=160/250

dash-dotted: ON/GN=200/200

Offspring Number(ON)/Generation Number(GN) and Standard deviation reduction factor