Minimal forecast horizon procedures for dynamic lot size models

This article presents new results which should be useful in finding production decisions while solving the dynamic lot sizing problem of Wagner–Whitin on a rolling horizon basis. In a rolling horizon environment, managers obtain decisions for the first period (or the first few periods) by looking at the forecasts for several periods. This article develops procedures to find optimal decisions for any specified number of initial periods (called planning horizon in the article) by using the forecast data for the minimum possible number of future periods. Computational results comparing these procedures with the other procedures reported in the literature are very encouraging.     

A forward network simplex algorithm for solving multiperiod network flow problems

An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.     

Present practices and future plans for MIL-STD-781

MIL-STD-781 specifies reliability acceptance test procedures based on both fixed-length tests and probability ratio sequential tests. The assumption underlying MIL-STD-781 is a constant mean time between failures (MTBF) and typical practice applies MIL-STD-781 to electrical, electronic, and mechanical equipment. This article discusses some of the difficulties that have prompted the C and D revisions of MIL-STD-781. In addition, it discusses the relationship of MIL-STD-781 with MIL-STD-1635(EC) which deals with reliability growth testing. The article concludes with a discussion of needed research in reliability growth testing, in support of MIL-STD-781, and in the area of stress and its impact of MTBF.     

Sandwich approximation of univariate convex functions with an application to separable convex programming

In this article an algorithm for computing upper and lower ? approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ? the number of iterations is bounded by