Nonlinear Binary Programming Research Articles

Optimal replacement policies for k-out-of-n systems

The authors study a discrete-time, infinite-horizon, dynamic programming model for the replacement of components in a binary k-out-of-n:F system. The goal is to trade off the component replacement and system failure costs. Under the criterion of minimizing the long-run average cost per period, it is optimal to follow a critical component policy (CCP), viz., a policy specified by a critical component set and the rule: replace a component if and only if it is failed and is in the critical component set. Computing an optimal CCP is a binary nonlinear programming problem, which can be solved by searching through a set with O(n/sup k-1/) points. This approach to finding an optimal CCP is practical when k is small. In particular, assuming s-independent components, it requires O(n/sup 2k-1/) calculations. The authors analyze in detail the two most important cases with small k: the series (1-out-of-n:F) system and the 2-out-of-n:F system. >

A dynamic production planning and scheduling algorithm for two products processed on one line

This paper presents a dynamic production planning and scheduling algorithm for two products processed on one line over a fixed time horizon. Production rates are assumed fixed, and restrictions are placed or inventory levels and production run lengths. The resulting problem is a nonlinear binary program, which is solved using an implicit enumeration strategy. The algorithm focuses on the run changeover period while developing tighter bounds on the length of the upcoming run to improve computational efficiency. About 99% pf 297 randomly generated problems with varying demand patterns are solved in less than 15 seconds of CPU time on a CDC Cyber 172 Computer. A mixed integer programming formulation of the generalized multi-product case under no-backlogging of demand is also given.

A New Technique to Optimize System Reliability

This paper describes an algorithm for solving reliability optimization problems formulated as nonlinear binary programming problems with multiple-choice constraints. These constraints stand for restrictions in which only one variable is assigned to each subset making up the set; thus, they are expressed by equations whose r.h.s. is unity. Different types of methods for achieving high reliability (an increase in component reliability, parallel redundancy, standby redundancy, etc.) can be easily used simultaneously as design alternatives for each subsystem. In order to solve the problem effectively, the Lawler & Bell algorithm is improved by introducing a new lexicographic enumeration order which always satisfies the multiple-choice constraints. The function for obtaining feasible solutions which give first ~ L-th minimum values of the objective function is added to the algorithm in order to make it more useful for decision making. After a numerical example assists in understanding the algorithm, the computational efficiency is compared with that of the Lawler & Bell algorithm.

Data and reports: Contents design and users allocation

When a common information system should supply data in a batch processing mode to many various users, the systems analyst is faced with the problem of allocating data among various reports and reports among different users. The traditional approach to that problem is very unstructured. Such a problem is formulated here in a nonlinear binary programming model. Four alternative techniques of solving the model are presented, followed by an example. The main contribution is a systematic and analytic approach toward a major problem in information systems design.