New inequalities for finite and infinite group problems from approximate lifting

In this paper, we derive new families of facet‐defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem include two‐ and three‐slope facet‐defining inequalities as well as the first family of four‐slope facet‐defining inequalities. The new valid inequalities for the infinite group problem include families of two‐ and three‐slope extreme inequalities. These new inequalities not only illustrate the diversity of strong inequalities for the finite and infinite group problems, but also provide a large variety of new cutting planes for solving integer and mixed‐integer programming problems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A poissonian binomial model with constrained parameters

The article examines ways of computing cumulative probabilities for a constrained Poissonian binomial distribution arising from a model of a weapon defense system.     

Suppression of enemy air defenses (SEAD) as an information duel

Blue strike aircraft enter region ? to attack Red targets. In Case 1, Blue conducts (preplanned) SEAD to establish air superiority. In the (reactive) SEAD scenario, which is Case 2, such superiority is already in place, but is jeopardized by prohibitive interference from Red, which threatens Blue's ability to conduct missions. We utilize both deterministic and stochastic models to explore optimal tactics for Red in such engagements. Policies are developed which will guide both Red's determination of the modes of operation of his engagement radar, and his choice of Blue opponent to target next. An index in the form of a simple transaction kill ratio plays a major role throughout. Published 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 723–742, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10046     

A model for step‐stress accelerated life testing

Modern technology is producing high reliability products. Life testing for such products under normal use condition takes a lot of time to obtain a reasonable number of failures. In this situation a step‐stress procedure is preferred for accelerated life testing. In this paper we assume a Weibull and Lognormal model whose scale parameter depends upon the present level as well as the age at the entry in the present stress level. On the basis of that we propose a parametric model to the life distribution for step‐stress testing and suggest a suitable design to estimate the parameters involved in the model. A simulation study has been done by the proposed model based on maximum likelihood estimation. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Optimal retail assortments for substitutable items purchased in sets

We consider the problem of optimizing assortments in a multi‐item retail inventory system. In addition to the usual holding and stockout costs, there is a fixed cost for including any item in the assortment. Customers' preferences for items include both probabilistic substitution patterns and the desire to purchase sets of complementary items. We develop a demand model to capture this behavior, and derive tractable approximations that allow us to formulate the optimization problem as a 0–1 mixed integer linear program. Numerical examples are solved to illustrate key insights into how both complementary and substitute items affect the optimal assortment and the expected profit. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 793–822, 2003.     

Optimal stocking policies for low usage items in multi-echelon inventory systems

Multi-echelon logistic systems are essential parts of the service support function of high technology firms. The combination of technological developments and competitive pressures has led to the development of services systems with a unique set of characteristics. These characteristics include (1) low demand probabilities: (2) high cost items; (3) complex echelon structures; (4) existence of pooling mechanisms among stocking locations at the same echelon level; (5) high priority for service, which is often expressed in terms of response time service levels for product groups of items: (6) scrapping of failed parts; and (7) recycling of issued stock due to diagnostic use. This article develops a comprehensive model of a stochastic, multi-echelon inventory system that takes account of the above characteristics. Solutions to the constrained optimization problem are found using a branch and bound procedure. The results of applying this procedure to a spare parts inventory system for a computer manufacturer have led to a number of important policy conclusions.     

A branch and bound algorithm for solving a class of nonlinear integer programming problems

This article presents a branch and bound method for solving the problem of minimizing a separable concave function over a convex polyhedral set where the variables are restricted to be integer valued. Computational results are reported.     

Rescheduling to minimize makespan on a changing number of identical processors

We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.