Optimal power control in a wireless network using a model with stochastic link coefficients

This paper addresses optimal power allocation in a wireless communication network under uncertainty. The paper introduces a framework for optimal transmit power allocation in a wireless network where both the useful and interference coefficients are random. The new approach to power control is based on a stochastic programming formulation with probabilistic SIR constraints. This allows to state the power allocation problem as a convex optimization problem assuming normally or log‐normally distributed communication link coefficients. Numerical examples illustrate the performance of the optimal stochastic power allocation. A distributed algorithm for the decentralized solution of the stochastic power allocation problem is discussed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Minimizing makespan on a single batch processing machine with nonidentical job sizes

We deal with the problem of minimizing makespan on a single batch processing machine. In this problem, each job has both processing time and size (capacity requirement). The batch processing machine can process a number of jobs simultaneously as long as the total size of these jobs being processed does not exceed the machine capacity. The processing time of a batch is just the processing time of the longest job in the batch. An approximation algorithm with worst‐case ratio 3/2 is given for the version where the processing times of large jobs (with sizes greater than 1/2) are not less than those of small jobs (with sizes not greater than 1/2). This result is the best possible unless P = NP. For the general case, we propose an approximation algorithm with worst‐case ratio 7/4. A number of heuristics by Uzosy are also analyzed and compared. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 226–240, 2001     

Opportunistic retooling of a flexible machine subject to failure

A set of jobs can be processed without interruption by a flexible machine only if the set of tools required by all jobs can be loaded in the tool magazine. However, in practice the total number of tools required by a job set would exceed the tool magazine capacity. In such situations, the job set has to be carefully partitioned at the start of the production run such that each partition can be processed without interruption. During the production run, if there are unscheduled machine downtimes due to machine failure, this provides an additional opportunity to optimally retool the magazine for a smaller job set consisting of just the unprocessed jobs. In this paper, we study job sequencing rules that allow us to minimize the total expected cost of machine down time due to machine failures and magazine retooling, assuming a dynamic re‐sequencing of the unprocessed jobs after each machine failure. Using these rules, we develop a branch‐and‐bound heuristic that allows us to solve problems of reasonable size. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 79–97, 2001     

Analysis of a new vehicle scheduling and location problem

We consider a container terminal discharging containers from a ship and locating them in the terminal yard. Each container has a number of potential locations in the yard where it can be stored. Containers are moved from the ship to the yard using a fleet of vehicles, each of which can carry one container at a time. The problem is to assign each container to a yard location and dispatch vehicles to the containers so as to minimize the time it takes to download all the containers from the ship. We show that the problem is NP‐hard and develop a heuristic algorithm based on formulating the problem as an assignment problem. The effectiveness of the heuristic is analyzed from both worst‐case and computational points of view. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 363–385, 2001     

On the classification gap in mathematical programming-based approaches to the discriminant problem

This article proposes a mathematical-programming-based approach to solve the classification problem in discriminant analysis which explicitly considers the classification gap. The procedure consists of two distinct phases and initially treats the classification gap as a fuzzy set in which the classification rule is not yet established. The nature of the classification gap is examined and a variety of methods are discussed which can be applied to identify the most appropriate classification rule over the fuzzy set. The proposed methodology has several potential advantages. First, it offers a more refined approach to the classification problem, facilitating careful analysis of the fuzzy region where the classification decision may not be obvious. Secondly, the two-phase approach enables the analysis of larger data sets when using computer-intensive procedures such as mixed-integer programming. Finally, because of the restricted choice of separating hyperplanes in phase 2, the approach appears to be more robust than other classification techniques with respect to outlier-contaminated data conditions. The robustness issue and computational advantage of our proposed methodology are illustrated using a limited simulation experiment.     

Inference for the maximum cell probability under multinomial sampling

This article investigates inference for p_max, the largest cell probability in multinomial trials for the case of a small to moderate number of trials. Emphasis focuses on point and interval estimation. Both frequentist and Bayesian approaches are developed. The results of extensive simulation investigation are included as well as the analysis of a set of crime data for the city of New Orleans taken from the National Crime Survey.     

The shortest queue model with jockeying

In this article we deal with the shortest queue model with jockeying. We assume that the arrivals are Poisson, each of the exponential servers has his own queue, and jockeying among the queues is permitted. Explicit solutions of the equilibrium probabilities, the expected customers, and the expected waiting time of a customer in the system are given, which only depend on the traffic intensity. Numerical results can be easily obtained from our solutions. Several examples are provided in the article.     

Some two-on-two homogeneous stochastic combats

In this article we consider two versions of two-on-two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.