On mixed integer quadratic programs

This paper provides a method for solving mixed integer quadratic programs with the help of cutting-plane technique.     

On nash subsets of bimatrix games

This work considers a class of bimatrix games to which some well-known structure theorems of 0-sum matrix games can be made to generalize. It is additionally shown how to construct such games and how to generate the equilibrium points defining a given game as a member of that class.     

Inventory models with a mixture of backorders and lost sales

This article presents several single-echelon, single-item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 - b is lost forever. Both deterministic and stochastic demand are considered. although the case of stochastic demand is treated heuristically. In each situation, a mathematical model representing the average annual cost of operating the inventory system is developed. and an optimum operating policy derived. At the extremes b=1 and b=0 the models presented reduce to the usual backorders and lost sales cases, respectively.     

Estimation of a hidden service distribution of an M/G/∞ system

The maximum likelihood estimator of the service distribution function of an M/G/∞ service system is obtained based on output time observations. This estimator is useful when observation of the service time of each customer could introduce bias or may be impossible. The maximum likelihood estimator is compared to the estimator proposed by Mark Brown, [2]. Relative to each other, Brown's estimator is useful in light traffic while the maximum likelihood estimator is applicble in heavy trafic. Both estimators are compared to the empirical distribution function based on a sample of service times and are found to have drawbacks although each estimator may have applications in special circumstances.     

On nash subsets and mobility chains in bimatrix games

This work is concerned with constructing, analyzing, and finding “mobility chains” for bimatrix games, sequences of equilibrium points along which it is possible for the two players to progress, one equilibrium point at a time, to an equilibrium point that is preferred by both players. The relationship between mobility chains and Nash subsets is established, and some properties of maximal Nash subsets are proved.     

Multiperiod capacity expansion and shipment planning with linear costs

In this paper we consider a multiperiod deterministic capacity expansion and shipment planning problem for a single product. The product can be manufactured in several producing regions and is required in a number of markets. The demands for each of the markets are non-decreasing over time and must be met exactly during each time period (i.e., no backlogging or inventorying for future periods is permitted). Each region is assumed to have an initial production capacity, which may be increased at a given cost in any period. The demand in a market can be satisfied by production and shipment from any of the regions. The problem is to find a schedule of capacity expansions for the regions and a schedule of shipments from the regions to the markets so as to minimize the discounted capacity expansion and shipment costs. The problem is formulated as a linear programming model, and solved by an efficient algorithm using the operator theory of parametric programming for the transporation problem. Extensions to the infinite horizon case are also provided.     

A class of distributions generated from distributions of exponential type

A class of exponential type distributions with special exponential parameters is defined. It is assumed that the exponential parameters vary according to some (known) probability law. It has been shown in this paper that the compound distribution can be easily represented in form involving moment generating function of the mixing distribution. The results obtained in this paper provide an efficient and simple method of obtaining compound failure time distribution with known mixing distributions (uniform, exponential, gamma).     

Longitudinal manpower planning models

A manpower planning model is presented that exploits the longitudinal stability of manpower cohorts. The manpower planning process is described. An infinite horizon linear program for calculating minimum cost manpower input plans is presented and found to have a straightforward solution in a great many cases and to yield an easily implemented approximation technique in other cases.     

Toward optimal bidding strategies

In this paper we investigate a form of rational behavior in response to an oligopoly pricing problem where only one buyer is involved. We investigate the problem from the standpoint of the seller who wants to maximize his gain from the transaction. In particular, we deal with the problem of one seller's response to an invitation to submit a sealed (i. e., noncooperative) bid to a government or other dominant purchasing agency for supplying a specified bundle of goods and services for which either (1) no other demand exists, or (2) the terms or quantities involved cannot, at least in the short run, be obtained from another source. Although treated from a normative standpoint, i. e., what bid the supplier should make, the paper also has implications for the buyer's behavior and oligopoly-monopsony pricing in a more general sense.     

Queueing models for spares provisioning

A population of items which break down at random times and require repair is studied (the classic “machine repair problem with spares”). It is desired to determine the number of repair channels and spares required over a multiyear planning horizon in which population size and component reliability varies, and a service level constraint is imposed. When an item fails, a spare (if available) is immediately dispatched to replace the failed item. The failed item is removed, transported to the repair depot, repaired, and then placed in the spares pool (which is constrained to be empty not more than 10% of the time) unless there is a backlog of requests for spares, in which case it is dispatched immediately. The first model considered treats removal, transportation, and repair as one service operation. The second model is a series queue which allows for the separate treatment of removal, transportation, and repair. Breakdowns are assumed Poisson and repair times exponential.