Applying Lanchester's linear law to model the Ardennes campaign

In modern warfare, many believe the decisive factor in winning a battle is seizing the right moment to shift from defense to attack, or vice versa. This paper attempts to bring that perspective to Lanchester's differential equations of warfare, and continues the application of Lanchester's linear law to the analysis of the World War II battle of Ardennes, as reported in earlier issues of Naval Research Logistics by Bracken and by Fricker. A new variable, shift time, accounting for the timing of the shift between defense and attack is explicitly included in our version of the model, and it helps obtain improved goodness of fit to historical data. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:653–661, 2001     

Bayesian testing strategies for software with an operational profile

We consider a software reliability model where the failure rate of each fault depends on the specific operation performed. The software is tested in a given sequence of test cases for fixed durations of time to collect data on failure times. We present a Bayesian analysis of software failure data by treating the initial number of faults as a random variable. Our analysis relies on the Markov Chain Monte Carlo methods and is used for developing optimal testing strategies in an adaptive manner. Two different models involving individual and common faults are analyzed. We illustrate an implementation of our approach by using some simulated failure data. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:747–763, 2001     

Product commonality in multiple‐period,make‐to‐stock systems

It is well known that replacing several products by a single common product can reduce required safety stock levels due to the benefits of risk pooling. Recent research utilizing single‐period models has investigated the cost savings (or losses) from doing so. This paper uses a very general multiple‐period model, with general demand distributions, any number of products, and the objective of minimizing production, holding, and shortage costs. Two scenarios are considered—one that utilizes a common product and one that does not. Prior results utilizing single‐period models indicate that even if the common product is more expensive than the products it replaces, there are many circumstances under which it is still worthwhile to employ. Surprisingly, this paper will show that this is almost never the case in a multiple‐period model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 737–751, 1999     

Capacitated selection problem

Optimizing the selection of resources to accomplish a set of tasks involves evaluating the tradeoffs between the cost of maintaining the resources necessary to accomplish the tasks and the penalty cost associated with unfinished tasks. We consider the case where resources are categorized into types, and limits (capacity) are imposed on the number of each type that can be selected. The objective is to minimize the sum of penalty costs and resource costs. This problem has several practical applications including production planning, new product design, menu selection and inventory management. We develop a branch‐and‐bound algorithm to find exact solutions to the problem. To generate bounds, we utilize a dual ascent procedure which exploits the special structure of the problem. Information from the dual and recovered primal solutions are used to select branching variables. We generate strong valid inequalities and use them to fix other variables at each branching step. Results of tests performed on reasonably sized problems are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 19–37, 1999     

Optimal assignment of high multiplicity flight plans to dispatchers

This paper addresses the problem of finding a feasible schedule of n jobs on m parallel machines, where each job has a deadline and some jobs are preassigned to some machine. This problem arises in the daily assignment of workload to a set of flight dispatchers, and it is strongly characterized by the fact that the job lengths may assume one out of k different values, for small k. We prove the problem to be NP‐complete for k = 2 and propose an effective implicit enumeration algorithm which allows efficiently solution a set of real‐life instances. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 359–376, 2000     

Combat modeling of remotely targeted vehicles and a battery against a moving target

This paper considers a combined system composed of multiple stand-by remotely piloted vehicles (RPVs) and a single battery against a single passive enemy target, where the target, if not killed, is allowed to change its location after each attack. The RPV has the duty to report on target acquisition, to confirm a target kill, and to pass information on any change in target location after each battery attack. The battery has the duty to attack the target on the basis of the target location information provided to it by the RPV. We develop a closed-form expression for the time-dependent state probabilities of the system, which can be used to compute several important combat measures of effectiveness, including (a) the time-varying mean and variance of the number of the RPVs being alive and of the surviving enemy target, (b) the mission success, mission failure, and combat draw probabilities, and (c) the mean and variance of the combat duration time. Illustrative numerical examples are solved for these combat measures, and sensitivity analyses are performed with respect to target acquisition time and target kill probability. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 645–667, 1998     

Class scheduling algorithms for Navy training schools

The problem of developing good schedules for Navy C-Schools has been modeled as a combinatorial optimization problem. The only complicating feature of the problem is that classes must be grouped together into sequences known as pipelines. An ideal schedule will have all classes in a pipeline scheduled in consecutive weeks. The objective is to eliminate the nonproductive time spent by sailors at C-Schools who are waiting for the next class in a pipeline. In this investigation an implicit enumeration procedure for this problem was developed. The key component of our algorithm is a specialized greedy algorithm which is used to obtain a good initial incumbent. Often this initial incumbent is either an optimal schedule or a near optimal schedule. In an empirical analysis with the only other competing software system, our greedy heuristic found equivalent or better solutions in substantially less computer time. This greedy heuristic was extended and modified for the A-School scheduling problem and was found to be superior to its only competitor. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 533–551, 1998     

Interchange fees for bank ATM networks

Banks have found it advantageous to connect their Automated Teller Machines (ATMs) in networks so that customers of one bank may use the ATMs of any bank in the network. When this occurs, an interchange fee is paid by the customer's bank to the one that owns the ATM. These have been set by historic interbank negotiation. The paper investigates how a model based on n-player game theory concepts of Shapley value and nucleolus could be used as an alternative way of setting such fees. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 407–417, 1998     

On the inspection game

The Inspection Game is a multistage game between a customs inspector and a smuggler, first studied by Melvin Dresher and Michael Maschler in the 1960s. An extension allowing the smuggler to act more than once, treated by Sakaguchi in a special case, is solved. Also, a more natural version of Sakaguchi's problem is solved in the special case where the smuggler may act at each stage. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 327–334, 1998     

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

We consider a stochastic counterpart of the well-known earliness-tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow-time penalty. One of our main results is that an optimal sequence for the problem must be V-shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near-optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.