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.     

A penalty for concave minimization derived from the tuy cutting plane

A wide variety of optimization problems have been approached with branch-and-bound methodology, most notably integer programming and continuous nonconvex programming. Penalty calculations provide a means to reduce the number of subproblems solved during the branch-and-bound search. We develop a new penalty based on the Tuy cutting plane for the nonconvex problem of globally minimizing a concave function over linear constraints and continuous variables. Computational testing with a branch-and-bound algorithm for concave minimization indicates that, for the problems solved, the penalty reduces solution time by a factor ranging from 1.2 to 7.2. © 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.     

Printed circuit board family grouping and component allocation for a multimachine,open-shop assembly cell

This article considers a particular printed circuit board (PCB) assembly system employing surface mount technology. Multiple, identical automatic placement machines, a variety of board types, and a large number of component types characterize the environment studied. The problem addressed is that of minimizing the makespan for assembling a batch of boards with a secondary objective of reducing the mean flow time. The approach adopted is that of grouping boards into production families, allocating component types to placement machines for each family, dividing of families into board groups with similar processing times, and the scheduling of groups. A complete setup is incurred only when changing over between board families. For the environment studied, precedence constraints on the order of component placement do not exist, and placement times are independent of feeder location. Heuristic solution procedures are proposed to create board subfamilies (groups) for which the component mounting times are nearly identical within a subfamily. Assignment of the same component type to multiple machines is avoided. The procedures use results from the theory of open-shop scheduling and parallel processor scheduling to sequence boards on machines. Note that we do not impose an open-shop environment but rather model the problem in the context of an open shop, because the order of component mountings is immaterial. Three procedures are proposed for allocating components to machines and subsequently scheduling boards on the machines. The first two procedures assign components to machines to balance total work load. For scheduling purposes, the first method groups boards into subfamilies to adhere to the assumptions of the open-shop model, and the second procedure assumes that each board is a subfamily and these are scheduled in order of shortest total processing time. The third procedure starts by forming board subfamilies based on total component similarity and then assigns components to validate the open-shop model. We compare the performance of the three procedures using estimated daily, two-day, and weekly production requirements by averaging quarterly production data for an actual cell consisting of five decoupled machines. © 1994 John Wiley & Sons, Inc.     

On the design of a tandem queue with blocking: Modeling,analysis, and gradient estimation

We demonstrate here how recent advances in the study of discrete-event stochastic systems provide fruitful results for the modeling, analysis, and design of manufacturing systems. We consider a multistage make-to-stock system where outputs from the final stage are used to satisfy customer demands. We address the problem of finding the appropriate trade-off between reduced order waiting time and increased process speeds. Using the idea of infinitesimal perturbation analysis (IPA), we establish a simple procedure where sample-path derivatives can be obtained along an arbitrary sample path. Under suitable conditions, we demonstrate that these derivative estimators are unbiased and strongly consistent and can be used in a classical stochastic optimization scheme to solve the problem. The role of continuity and convexity on the validity of the estimator is also addressed. Although the focus of this article is not to solve for the optimal solution, we provide a theoretical justification for such a pursuit. The approach is appealing as it is numerically stable, easy to implement, and can be extended to other system performance measures. © 1994 John Wiley & Sons, Inc.     

Minimax resource allocation problems with ordering constraints

Resource allocation problems consider the allocation of limited resources among numerous competing activities. We address an allocation problem with multiple knapsack resource constraints. The activities are grouped into disjoint sets. Ordering constraints are imposed on the activities within each set, so that the level of one activity cannot exceed the level of another activity in the same set. The objective function is of the minimax type and each performance function is a nonlinear, strictly decreasing and continuous function of a single variable. Applications for such resource allocation problems are found, for example, in high-tech industries confronted with large-scale and complex production planning problems. We present two algorithms to solve the allocation problem with ordering constraints. The first one uses characterization of the optimal decision variables to apply a search method. The second algorithm solves a sequence of problems, each in the format of the original problem without ordering constraints. Whereas the computational effort of the first algorithm depends on the desired degree of accuracy even for linear performance functions, the effort of the latter algorithm is polynomial for certain classes of performance functions. © 1994 John Wiley & Sons, Inc.