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