tailieunhanh - A two-phase linear programming approach for redundancy allocation problems

Provision of redundant components in parallel is an efficient way to increase the system reliability, however, the weight, volume and cost of the system will increase simultaneously. This paper proposes a new two-phase linear programming approach for solving the nonlinear redundancy allocation problems subject to multiple linear constraints. | Yugoslav Journal of Operations Research 12 (2002), Number 2, 227-236 A TWO-PHASE LINEAR PROGRAMMING APPROACH FOR REDUNDANCY ALLOCATION PROBLEMS Yi-Chih HSIEH Department of Industrial Management National Huwei Institute of Technology Taiwan, . yhsieh@ Abstract: Provision of redundant components in parallel is an efficient way to increase the system reliability, however, the weight, volume and cost of the system will increase simultaneously. This paper proposes a new two-phase linear programming approach for solving the nonlinear redundancy allocation problems subject to multiple linear constraints. The first phase is used to approximately allocate the resource by using a general linear programming, while the second phase is used to re-allocate the slacks of resource by using a 0-1 integer linear programming. Numerical results demonstrate the effectiveness and efficiency of the proposed approach. Keywords: Two-phase linear programming, redundancy allocation. 1. INTRODUCTION Highly reliable systems can reduce loss of money and time in the real world. Two approaches are generally available to enhance the system reliability, ., (i) using highly reliable components constituting the system, and/or (ii) using redundant components in various subsystems in the system (Misra and Sharma [24]). For the former approach, although system reliability can be enhanced, it is occasionally beyond our requirement even the highest reliable elements are used. Although using the latter approach enhances system reliability directly, the cost, weight, and volume of the system increase simultaneously. The redundancy allocation problem is to maximize system reliability subject to specific constraints, . cost, weight and volume etc. The general formulation of this problem can be expressed as: 228 . Hsieh / A Two-Phase Linear Programming Approach max Rs ( x1 , x2 ,., xn ) n st ∑ gi, j ( xi ) ≤ bi , i = 1, 2,., m (P) j =1 xi ∈ positive .