Estimation for dirichlet mixed models

Dirichlet mixed models find wide application. Estimation is usually achieved through the method of moments. Here we present an iterative hybrid algorithm for obtaining the maximum likelihood estimate employing both modified Newton-Raphson and E-M methods. This successful MLE algorithm enables calculation of a jack-knife MLE. Simulation comparison of the three estimates is provided. The MLE substantially improves upon the moments estimator particularly with increasing dimension. The jack-knife MLE in turn offers dramatic improvement over the MLE.     

Multilinear extensions and quotients of simple games

Studied here is the problem of evaluating the formation of coalitions in cooperative games by considering its internal and external effects. Our analysis is based upon a formal theory of the quotient game and the use of multilinear extensions to compute the Shapley value and the coalitional value. When it applies to simple games, a series of interesting results is obtained. © 1996 John Wiley & Sons, Inc.     

Compound poisson approximation in systems reliability

The compound Poisson “local” formulation of the Stein-Chen method is applied to problems in reliability theory. Bounds for the accuracy of the approximation of the reliability by an appropriate compound Poisson distribution are derived under fairly general conditions, and are applied to consecutive-2 and connected-s systems, and the 2-dimensional consecutive-k-out-ofn system, together with a pipeline model. The approximations are usually better than the Poisson “local” approach would give. © 1996 John Wiley & Sons, Inc.     

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.     

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.     

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.     

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.     

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.     

Scheduling about a large common due date with tolerance to minimize mean absolute deviation of completion times

In this article the problem of minimizing the mean absolute deviation (MAD) of job completion times about an unrestricted given common due date with tolerance in the n-job, single-machine scheduling environment is considered. We describe some optimality conditions and show that the unrestricted version of the MAD problem with an arbitrary due date tolerance is polynomial by proposing a polynomial-time algorithm for identifying an optimal schedule. © 1994 John Wiley & Sons, Inc.