A robustness index for scheduling problems based on sensitivity analysis

1
A robustness index for scheduling problems based
on sensitivity analysis

• M. Emin Aydin
• London South Bank University, London, UK

2
Overview

• Introduction
• Sensitivity analysis
• Robustness in job shop scheduling
• Robustness based sensitivity analysis
• Conclusion

3
Introduction

• Job shop scheduling is the most representative
  production scheduling problems
• On the other hand, it is quite restricted, which
  abstract the problems from the real life
• solutions remain not applicable and very fragile
  even it is well optimised.
• The main issue here is to produce solutions as
  robust as possible so that they can be applied to
  real problems.
• re-scheduling approaches have arisen whereas most
  of them remain expensive to apply
• A sensitivity analysis based approach is
  discussed in this presentation

4
Sensitivity Analysis (SA)
Examined Model
Original Model
Subject to
Subject to
5
SA for JSS

• Issues to consider
• Staff shortage
• Changing priorities
• Machine failure

• Types of operations to examine
• Critical operations
• Non-critical operation
• Any operation

6
Robustness in JSS

• Simultaneously, meeting as many performance
  measures as possible
• Ease of move to altering neighbours without
  incurring too much extra cost
• Provision of similar solutions on changes

7
Robustness based on SA

• Robustness to be measure based on SA
• A level of sensitivity against changing
  conditions
• the more the cost brought up by changing
  conditions the poorer the solution to the model
• the stronger the model the less the cost on
  changing conditions

8
Measuring robustness

• Where
• R is the calculated overall robustness measure,
• k is the number of issues examined for
  sensitivity,
• wi is the weight assigned to the ith issue
• ri is the level of sensitivity calculated for ith
  issue

• Robustness can be measured based on SA as the
  total level of sensitivity will constitute a
  robustness
• The robustness can be an index of weighted
  assessed robustness for each examined issue for
  sensitivity
• The index can be any other function that suits
  the contextual background
• Left is given a particular index measuring the
  robustness based on a weighted summation function

9
Conclusion

• Sensitivity analysis for job shop scheduling
  provides very good information to assess the
  robustness
• Robustness is directly proportional to the
  overall level of sensitivity
• An appropriate function is needed to be selected
  for measuring robustness more healthy