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