Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

A note on integer linear fractional programming

This note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.     

On a search for a moving target

We consider the problem of searching for a target that moves in discrete time and space according to some Markovian process. At each time, a searcher attempts to detect the target. If the searcher's action at each time is such as to maximize his chances of immediate detection, we call his strategy “myopic.” We provide a computationally useful necessary condition for optimality, and use it to provide an example wherein the myopic strategy is not optimal.     

Optimality conditions for convex semi-infinite programming problems

This paper gives characterization of optimal Solutions for convex semiinfinite programming problems. These characterizations are free of a constraint qualification assumption. Thus they overcome the deficiencies of the semiinfinite versions of the Fritz John and the Kuhn-Tucker theories, which give only necessary or sufficient conditions for optimality, but not both.     

A class of continuous nonlinear programming problems with time-delayed constraints

A general class of continuous time nonlinear problems is considered. Necessary and sufficient conditions for the existence of solutions are established and optimal solutions are characterized in terms of a duality theorem. The theory is illustrated by means of an example.     

The bilinear programming problem

The paper deals with bilinear programming problems and develops a finite algorithm using the “piecewise strategy” for large-scale systems. It consists of systematically generating a sequence of expanding polytopes with the global optimum within each polytope being known. The procedure then stops when the final polytope contains the feasible region.     

A survey of maintenance models: The control and surveillance of deteriorating systems

The literature on maintenance models is surveyed. The focus is on work appearing since the 1965 survey, “Maintenance Policies for Stochastically Failing Equipment: A Survey” by John McCall and the 1965 book, The Mathematical Theory of Reliability, by Richard Barlow and Frank Proschan. The survey includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.     

Armor configurations via dynamic programming

The problem of selecting materials, their thicknesses and order for armor designed for the defeat of shaped charge threats, has been formulated as a constrained optimization problem. The mathematical model provides an optimal order and thickness of each layer of material such that the resulting armor configuration will be of minimum mass per unit area subject to constraints on total thickness and shaped charge jet tip exit velocity.     

On a new approach to the analysis of stationary inventory problems

The intent of this paper is to demonstrate that the theory of stationary point processes is a useful tool for the analysis of stationary inventory systems. In conventional inventory theory, the equilibrium distributions for a specified inventory policy are obtained, whenever possible, by recursive or limiting procedures, or both. A different and more direct approach, based on stationary point processes, is proposed here. The time instants at which stock delivery is effected are viewed as points of the stationary point process, which possesses uniform statistical properties on the entire real axis; hence the equilibrium statistics of the inventory process can be calculated directly. In order to best illustrate this approach, various examples are given, including some that constitute new results.