A Two-Phase Linear programming Approach for Redundancy Problems

1
A Two-Phase Linear programming Approach for
Redundancy Problems

• by
• Yi-Chih HSIEH
• Department of Industrial Management National
  Huwei Institute of Technology Taiwan, R.O.C.

2
Outline

• Introduction
• PHASE I - APPROXIMATION STAGE
• PHASE II - IMPROVING STAGE
• Example
• Conclusion

3
Introduction

• Main advantages of highly reliable systems
• to reduce loss of money
• time in the real world
• Two available approaches to enhance the system
  reliability
• using highly reliable components
• using redundant components in various subsystems
  in the system

4
Introduction Second Approach

• SA Enhances system reliability directly
• Simultaneously impacted parameters
• System cost
• System volume
• System weight

5
Redundancy Allocation Problem

• The redundancy allocation problem is to maximize
  system reliability subject to specific
  constraints, e.g. cost, weight and volume etc.
• Numerous approaches for solving the redundancy
  allocation problem

6
Several Approaches

• Heuristics
• Artificial Algorithms
• genetic algorithms
• simulated annealing
• tabu search
• Exact Methods
• cutting plane
• branch-and-bound
• surrogate constraint method
• dynamic programming
• implicit search

7
Continuation

• Approximate Methods
• Lagrange multiplier
• geometric programming
• discrete maximum principle
• sequential simplex search
• random search
• boundary search
• differential dynamic programming

8
Two-Phase Linear Programming Approach

• Phase I (Approximation stage) Initially, with
  the linear approximation of the objective
  function and the relaxation of integer
  constraints, a general LP is solved for the
  approximate solution of problem (P1).
• Phase II (Improving stage) A 0-1 knapsack
  problem with m n linear constraints is then
  solved to improve the real solutions of Phase I
  to (feasible) integer solutions.

9

• Thanks