A note on the two machine job shop with exponential processing times

Consider two machines, labeled 1 and 2. A set of tasks has to be processed first on machine 1 and after that on machine 2. A second set of tasks has to be processed first on machine 2 and after that on machine 1. All the processing times are exponentially distributed. We present a policy which minimizes the expected completion time of all tasks.     

Scheduling coupled tasks

Consider a set of task pairs coupled in time: a first (initial) and second (completion) tasks of known durations with a specified time between them. If the operator or machine performing these tasks is able to process only one at a time, scheduling is necessary to insure that no overlap occurs. This problem has a particular application to production scheduling, transportation, and radar operations (send-receive pulses are ideal examples of time-linked tasks requiring scheduling). This article discusses several candidate techniques for schedule determination, and these are evaluated in a specific radar scheduling application.     

Estimating reliability growth (or deterioration) using time series analysis

In this paper we propose a method for estimating reliability growth (or deterioration) using time series analysis. Our method does not call for the specification of a particular model, and estimates the growth in the presence of periodicity. We illustrate our procedure by considering some binomial failure data generated during the testing of a large system of the U.S. Navy.     

Some comparative & design aspects of fixed cycle production systems

A serial production line is defined wherein a unit is produced if, and only if, all machines are functioning. A single buffer stock with finite capacity is to be placed immediately after one of the first N-1 machines in the N machine line. When all machines have equal probability of failure it is shown that the optimal buffer position is exactly in the middle of the line. This result is synthesized with the earlier work of Koenigsberg and Buzacott including an analysis of the covariance between transition states. An alternative model formulation is presented and integrated with previous results. Finally, a sufficient condition and solution procedure is derived for the installation of a buffer where there is a possible trade-off between increasing the reliability of the line versus adding a buffer stock.     

Zero-sum games with multiple goals

This paper investigates a class of two-person zero-sum multiple payoff games in which each component is deterministic. The problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem. Applications are discussed and illustrative examples are presented.     

Joint pricing and ordering policy for exponentially decaying inventory with known demand

This paper is concerned with the problem of simultaneously setting price and production levels for an exponentially decaying product. Such products suffer a loss in utility which is proportional to the total quantity of stock on hand. A continuous review, deterministic demand model is considered. The optimal ordering decision quantity is derived and its sensitivity to changes in perishability and product price is considered. The joint ordering pricing decision is also computed and consideration of parametric changes of these decisions indicates a non-monotonic response for optimal price to changes in product decay. Issues of market entry and extensions to a model with shortages are also analyzed.     

An attack-defense game with matrix strategies

This paper presents the results and the method of analysis for an attack-defense game involving allocation of resources. Each player is assumed to have several different types of resources to be divided in optimal fashion among a fixed set of targets. The payoff function of the game is convex. The “No Soft-Spot” principle of M. Dresher, and the concept of the generalized inverse of a matrix are used to determine optimal strategies for each player and the value of the game.