Sequencing many jobs on a multi-purpose facility

Suppose a given set of jobs has to be processed on a multi-purpose facility which has various settings or states. There is a choice of states in which to process a job and the cost of processing depends on the state. In addition, there is also a sequence-dependent changeover cost between states. The problem is then to schedule the jobs, and pick an optimum setting for each job, so as to minimize the overall operating costs. A dynamic programming model is developed for obtaining an optimal solution to the problem. The model is then extended using the method of successive approximations with a view to handling large-dimensioned problems. This extension yields good (but not necessarily optimal) solutions at a significant computational saving over the direct dynamic programming approach.     

On a sequential rule for estimating the location parameter of an exponential distribution

Let us assume that observations are obtained at random and sequentially from a population with density function In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions Where δ(X_I,…,X_N) is a suitable estimator of μ based on the random sample (X₁,…, X_N), N is a stopping variable, and A and p are given constants. To study the performance of the rule it is compared with corresponding “optimum fixed sample procedures” with known σ by comparing expected sample sizes and expected costs. It is shown that the rule is “asymptotically efficient” when absolute loss (p=-1) is used whereas the one based on squared error (p = 2) is not. A table is provided to show that in small samples similar conclusions are also true.     

Inventory allocation among an assembly and its repairable subassemblies

In this paper we consider a major assembly composed of two or more subassemblies. The failure of any subassembly causes the major assembly to not function. Every failed subassembly is repaired or replaced. A total investment in stocks of spare components is to be distributed among the various subassemblies and the major assembly so as to provide the best possible customer service. This is a complicated problem: relevant factors are the failure rates, unit costs, and repair times of the various components. For the case of Poisson failures, a heuristic solution is developed which is a compromise between theoretical optimality and practical usefulness.     

Properties of a multifacility location problem involving euclidian distances

This paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem.     

Heuristic solution to a discrete collection model

A discrete time Collection Model is formulated, involving the completion of a touring objective on a network with stochastic node states. Heuristic touring strategies are constructed, there being as yet inadequate analytic results for its optimal solution. Effectiveness of the heuristics is assessed by comparing expected tour times under the heuristics with expected tour times given perfect information. A branch and bound algorithm is presented for computing the perfect information tour times.     

Expectation of contract incentives

The application of statistical expectation to risk density functions and fee/incentive-element relationships is shown to be useful in structuring contract incentives. A mathematical procedure for calculating the expected value of fee for a given risk/incentive arrangement is described along with cost examples and related sensitivity analyses. The structuring of equivalent incentives is demonstrated by the use of the contracting procedure used for procuring the C-5A aircraft.     

A mathematical programming approach to identification and optimization of a class of unknown systems

There exists a class of decision problems for which: (1) models of input-output response functions are not available in a closed-form, functional representation; (2) informational costs associated with learning about the response function are significant. For these problems, combining identification with optimization using mathematical programming is potentially attractive. Three approaches to the identification-optimization problem are proposed: an outer-linearized approximation using relaxation (OLR); an inner-linearized approximation using restriction (ILR); and a sequential combination of inner- and outer-linearized subproblems (SIO). Algorithms based on each approach are developed and computational experience reported.     

On the set of (perfect) equilibria of a bimatrix game

This article provides a new approach to the set of (perfect) equilibria. With the help of an equivalence relation on the strategy space of each player. Nash sets and Selten sets are introduced. The number of these sets is finite and each of these sets is a polytope. As a consequence the set of (perfect) equilibria is a finite union of polytopes. © 1994 John Wiley & Sons. Inc.