A fast infiltration game on n arcs

Starting from a safe base, an Infiltrator tries to reach a sensitive zone within a given time limit without being detected by a Guard. The Infiltrator can move with speed at most u, while the Guard can only perform a restricted number of searches. A discrete variant of this zero-sum game played on a graph consisting of two vertices joined by n nonintersecting arcs is investigated. Optimal strategies and an explicit expression for its value are obtained. © 1996 John Wiley & Sons, Inc.     

Exploiting symmetry in the reliability analysis of coherent systems

Components in a complex system are usually not structurally identical. However, in many cases we may find components that are structurally symmetric, and one should make use of this additional information to simplify reliability analysis. The main purpose of this article is to define and study one such class of systems, namely, those having symmetric components, and to derive some reliability-related properties. © 1996 John Wiley & Sons, Inc.     

Multi-period airline overbooking with multiple fare classes

Consider a multi-period multi-fare class airline overbooking problem that relates to a single-leg flight. Passengers may cancel their reservations at any time, including being no-shows at flight-time. Canceling passengers receive a refund that depends on their fare class, e.g., supersaver, coach, etc. At flight-time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. A continuous state-space dynamic programming model is developed in which the state is the numbers of reservations currently on hand in each fare class. In each period, reservation requests occur in only one fare class and the fraction of reservations canceling in each class is independent of the number of reservations therein. A booking-limit policy is optimal, i.e., in each period the airline accepts reservation requests up to a booking limit if the number of initial reservations in the fare class is less than the booking limit, and declines reservation requests otherwise. The booking limits for each class depend on the numbers of reservations in the other classes. When there are two fare classes the optimal booking limits in each class decrease with the number of reservations in the other class. © 1996 John Wiley & Sons, Inc.     

Estimating negative binomial demand for retail inventory management with unobservable lost sales

The importance of effective inventory management has greatly increased for many major retailers because of more intense competition. Retail inventory management methods often use assumptions and demand distributions that were developed for application areas other than retailing. For example, it is often assumed that unmet demand is backordered and that demand is Poisson or normally distributed. In retailing, unmet demand is often lost and unobserved. Using sales data from a major retailing chain, our analysis found that the negative binomial fit significantly better than the Poisson or the normal distribution. A parameter estimation methodology that compensates for unobserved lost sales is developed for the negative binomial distribution. The method's effectiveness is demonstrated by comparing parameter estimates from the complete data set to estimates obtained by artificially truncating the data to simulate lost sales. © 1996 John Wiley & Sons, Inc.     

Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties

We examine the problem of scheduling n jobs with a common due date on a single machine. The processing time of each job is a random variable, which follows an arbitrary distribution with a known mean and a known variance. The machine is not reliable; it is subject to stochastic breakdowns. The objective is to minimize the expected sum of squared deviations of job completion times from the due date. Two versions of the problem are addressed. In the first one the due date is a given constant, whereas in the second one the due date is a decision variable. In each case, a general form of the deterministic equivalent of the stochastic scheduling problem is obtained when the counting process related to the machine uptime distribution is a generalized Poisson process. A sufficient condition is derived under which optimal sequences are V-shaped with respect to mean processing times. Other characterizations of optimal solutions are also established. Based on the optimality properties, algorithms with pseudopolynomial time complexity are proposed to solve both versions of the problem. © 1996 John Wiley & Sons, Inc.     

Scheduling target illuminators in naval battle-group anti-air warfare

We schedule a set of illuminators (homing devices) to strike a set of targets using surface-to-air missiles in a naval battle. The task is viewed as a production floor shop scheduling problem of minimizing the total weighted flow time, subject to time-window job availability and machine downtime side constraints. A simple algorithm based on solving assignment problems is developed for the case when all the job processing times are equal and the data are all integer. For the general case of scheduling jobs with unequal processing times, we develop two alternate formulations and analyze their relative strengths by comparing their respective linear programming relaxations. We select the better formulation in this comparison and exploit its special structures to develop several effective heuristic algorithms that provide good-quality solutions in real time; this is an essential element for use by the Navy. © 1995 John Wiley & Sons, Inc.     

The evolution of a selection system

The article is a case study. It describes the initialization and subsequent modifications of the selection process used for the annual Award for Excellence in Teaching at the Naval Postgraduate School (NPS). The method treats highly unbalanced data and utilizes some exploratory data analysis techniques in interesting ways. It leads to a defensible choice for a winner in a very messy setting. The award designates a faculty member as “teacher of the year” and includes a stipend of substantial value. The recipient is chosen by a committee which reviews objective information summarized from ballots submitted by franchised voters. The issues encountered have some general content and the handling of a number of them may have broader interest. ©John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Due-date assignment and early/tardy scheduling on identical parallel machines

This article examines the problem of simultaneously assigning a common due date to a set of independent jobs and scheduling them on identical parallel machines in such a way that the costs associated with the due date and with the earliness or tardiness of the jobs are minimized. We establish that, for certain values of the due-date cost, an optimal schedule for this problem is also optimal for an early/tardy scheduling problem studied by Emmons. We discuss the solution properties for the two problems, and show that both problems are NP-hard even for two machines. We further show that these problems become strongly NP-hard if the number of machines is allowed to be arbitrary. We provide a dynamic programming solution for the problems, the complexity of which indicates that the problems can be solved in pseudopolynomial time as long as the number of machines remains fixed. Finally, we present the results of a limited computational study. © 1994 John Wiley & Sons, Inc.     

On the timing of adoption of multiproduct technologies

This article examines a game of multiproduct technology adoption. We consider a duopoly model in which firms choose when to switch from a traditional single-product technology to a more flexible and more expensive multiproduct technology. The multiproduct technology allows a firm to invade the other firm's market, creating a more competitive environment and reducing profits. We analyze this investment decision as a game of timing using two different equilibrium concepts. First, we utilize the “silent” equilibrium concept, where firms commit at time zero to a switching time. This concept would be applicable to situations where firms cannot observe each other's actions, or when the implementation of the technology requires long lead times and the investment decision is private information. Using this notion we find that both firms adopt the multiproduct technology simultaneously within a certain time interval. We then characterize this time interval in terms of cost and demand conditions. We also derive conditions under which sequential adoption of the multiproduct technology occurs. The second concept used is that of noisy equilibrium, where firms cannot precommit themselves to an adoption time. This concept is appropriate when investment decisions are common knowledge. In this case a firm can credibly threaten to immediately follow suit if the other firm decides to adopt. This threat is sufficient to ensure the collusive outcome where neither firm adopts the flexible technology. © 1994 John Wiley & Sons, Inc.     

Simulating nonhomogeneous poisson processes with proportional intensities

The purpose of this research is to investigate simulation algorithms for nonhomogeneous Poisson processes with proportional intensities. Two algorithmic approaches are studied: inversion and thinning. Motivated by industrial practices, the covariate vector involved in the simulation is permitted to change after every event (or observation). The algorithms are extended to permit the simulation of general nonhomogeneous Poisson processes with possible discontinuities both in baseline intensity and covariate vector. This latter extension can be used to facilitate a wide range of failure situations that can arise with repairable systems. © 1994 John Wiley & Sons, Inc.