Waypoint analysis for command and control

Command and Control (C2) in a military setting can be epitomized in battles‐of‐old when commanders would seek high ground to gain superior spatial‐temporal information; from this vantage point, decisions were made and relayed to units in the field. Although the fundamentals remain, technology has changed the practice of C2; for example, enemy units may be observed remotely, with instruments of varying positional accuracy. A basic problem in C2 is the ability to track an enemy object in the battlespace and to forecast its future position; the (extended) Kalman filter provides a straightforward solution. The problem changes fundamentally if one assumes that the moving object is headed for an (unknown) location, or waypoint. This article is concerned with the new problem of estimation of such a waypoint, for which we use Bayesian statistical prediction. The computational burden is greater than an ad hoc regression‐based estimate, which we also develop, but the Bayesian approach has a big advantage in that it yields both a predictor and a measure of its variability. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Approximating nondominated sets in continuous multiobjective optimization problems

Many important problems in Operations Research and Statistics require the computation of nondominated (or Pareto or efficient) sets. This task may be currently undertaken efficiently for discrete sets of alternatives or for continuous sets under special and fairly tight structural conditions. Under more general continuous settings, parametric characterisations of the nondominated set, for example through convex combinations of the objective functions or ε‐constrained problems, or discretizations‐based approaches, pose several problems. In this paper, the lack of a general approach to approximate the nondominated set in continuous multiobjective problems is addressed. Our simulation‐based procedure only requires to sample from the set of alternatives and check whether an alternative dominates another. Stopping rules, efficient sampling schemes, and procedures to check for dominance are proposed. A continuous approximation to the nondominated set is obtained by fitting a surface through the points of a discrete approximation, using a local (robust) regression method. Other actions like clustering and projecting points onto the frontier are required in nonconvex feasible regions and nonconnected Pareto sets. In a sense, our method may be seen as an evolutionary algorithm with a variable population size. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

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     

Average-case analysis of the bin-packing problem with general cost structures

We consider a version of the famous bin-packing problem where the cost of a bin is a concave function of the number of items in the bin. We analyze the problem from an average-case point of view and develop techniques to determine the asymptotic optimal solution value for a variety of functions. We also describe heuristic techniques that are asymptotically optimal. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 673–686, 1997     

Inventory models of future supply uncertainty with single and multiple suppliers

We consider order-quantity/reorder-point inventory models where the availability of supply is subject to random fluctuations. We use concepts from renewal reward processes to develop average cost objective function models for single, two, and multiple suppliers. Identifying the regenerative cycle for each problem aids the development of the cost function. In the case of two suppliers, spectral theory is used to derive explicit expressions for the transient probabilities of a four-state continuous-time Markov chain representing the status of the system. These probabilities are used to compute the exact form of the average cost expression. For the multiple-supplier problem, assuming that all the suppliers have similar availability characteristics, we develop a simple model and show that as the number of suppliers becomes large, the model reduces to the classical EOQ model. © 1996 John Wiley & Sons, Inc.     

Optimal base stock policies and truck capacity in a two-echelon system

With the recent trend toward just-in-time deliveries and reduction of inventories, many firms are reexamining their inventory and logistics policies. Some firms have dramatically altered their inventory, production, and shipping policies with the goal of reducing costs and improving service. Part of this restructuring may involve a specific contract with a trucking company, or it may entail establishing in-house shipping capabilities. This restructuring, however, raises new questions regarding the choice of optimal trucking capacity, shipping frequency, and inventory levels. In this study, we examine a two-level distribution system composed of a warehouse and a retailer. We assume that demand at the retailer is random. Since the warehouse has no advance notice of the size of the retailer order, inventory must be held there as well as at the retailer. We examine inventory policies at both the warehouse and the retailer, and we explicitly consider the trucking capacity, and the frequency of deliveries from the warehouse to the retailer. Both linear and concave fixed transportation costs are examined. We find the optimal base stock policies at both locations, the optimal in-house or contracted regular truck capacity, and the optimal review period (or, equivalently, delivery frequency). For the case of normally distributed demand we provide analytical results and numerical examples that yield insight into systems of this type. Some of our results are counterintuitive. For instance, we find some cases in which the optimal truck capacity decreases as the variability of demand increases. In other cases the truck capacity increases with variability of demand. © 1993 John Wiley & Sons, Inc.     

Vehicle fleet refueling strategies to maximize operational range

The focus of this research is on self-contained missions requiring round-trip vehicle travel from a common origin. For a single vehicle the maximal distance that can be reached without refueling is defined as its operational range. Operational range is a function of a vehicle's fuel capacity and fuel consumption characteristics. In order to increase a vehicle's range beyond its operational range replenishment from a secondary fuel source is necessary. In this article, the problem of maximizing the range of any single vehicle from a fleet of n vehicles is investigated. This is done for four types of fleet configurations: (1) identical vehicles, (2) vehicles with identical fuel consumption rates but different fuel capacities, (3) vehicles which have the same fuel capacity but different fuel consumption rates, and (4) vehicles with both different fuel capacities and different consumption rates. For each of the first three configurations the optimal refueling policy that provides the maximal range is determined for a sequential refueling chain strategy. In such a strategy the last vehicle to be refueled is the next vehicle to transfer its fuel. Several mathematical programming formulations are given and their solutions determined in closed form. One of the major conclusions is that for an identical fleet the range of the farthest vehicle can be increased by at most 50% more than the operational range of a single vehicle. Moreover, this limit is reached very quickly with small values of n. The performance of the identical fleet configuration is further investigated for a refueling strategy involving a multiple-transfer refueling chain, stochastic vehicle failures, finite refueling times, and prepositioned fleets. No simple refueling ordering rules were found for the most general case (configuration 4). In addition, the case of vehicles with different fuel capacities is investigated under a budget constraint. The analysis provides several benchmarks or bounds for which more realistic structures may be compared. Some of the more complex structures left for future study are described.