Optimization and mediated bartering models for ground delay programs

The Federal Aviation Administration (FAA) and the airline community within the United States have adopted a new paradigm for air traffic flow management, called Collaborative Decision Making (CDM). A principal goal of CDM is shared decision‐making responsibility between the FAA and airlines, so as to increase airline control over decisions that involve economic tradeoffs. So far, CDM has primarily led to enhancements in the implementation of Ground Delay Programs, by changing procedures for allocating slots to airlines and exchanging slots between airlines. In this paper, we discuss how these procedures may be formalized through appropriately defined optimization models. In addition, we describe how inter‐airline slot exchanges may be viewed as a bartering process, in which each “round” of bartering requires the solution of an optimization problem. We compare the resulting optimization problem with the current procedure for exchanging slots and discuss possibilities for increased decision‐making capabilities by the airlines. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

An application of yield management for Internet Service Providers

In this paper we study strategies for better utilizing the network capacity of Internet Service Providers (ISPs) when they are faced with stochastic and dynamic arrivals and departures of customers attempting to log‐on or log‐off, respectively. We propose a method in which, depending on the number of modems available, and the arrival and departure rates of different classes of customers, a decision is made whether to accept or reject a log‐on request. The problem is formulated as a continuous time Markov Decision Process for which optimal policies can be readily derived using techniques such as value iteration. This decision maximizes the discounted value to ISPs while improving service levels for higher class customers. The methodology is similar to yield management techniques successfully used in airlines, hotels, etc. However, there are sufficient differences, such as no predefined time horizon or reservations, that make this model interesting to pursue and challenging. This work was completed in collaboration with one of the largest ISPs in Connecticut. The problem is topical, and approaches such as those proposed here are sought by users. © 2001 John Wiley & Sons, Inc., Naval Research Logistics 48:348–362, 2001     

Heuristics for the multi‐resource generalized assignment problem

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001     

Statistical decision analysis of stochastic linear programming problems

This paper presents a statistical decision analysis of a one-stage linear programming problem with deterministic constraints and stochastic criterion function. Procedures for obtaining numerical results are given which are applicable to any problem having this general form. We begin by stating the statistical decision problems to be considered, and then discuss the expected value of perfect information and the expected value of sample information. In obtaining these quantities, use is made of the distribution of the optimal value of the linear programming problem with stochastic criterion function, and so we discuss Monte Carlo and numerical integration procedures for estimating the mean of this distribution. The case in which the random criterion vector has a multivariate Normal distribution is discussed separately, and more detailed methods are offered. We discuss dual problems, including some relationships of this work with other work in probabilistic linear programming. An example is given in Appendix A showing application of the methods to a sample problem. In Appendix B we consider the accuracy of a procedure for approximating the expected value of information.     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.     

Managing components for assemble‐to‐order products with lead‐time‐dependent pricing: The full‐shipment model

We study a component inventory planning problem in an assemble‐to‐order environment faced by many contract manufacturers in which both quick delivery and efficient management of component inventory are crucial for the manufacturers to achieve profitability in a highly competitive market. Extending a recent study in a similar problem setting by the same authors, we analyze an optimization model for determining the optimal component stocking decision for a contract manufacturer facing an uncertain future demand, where product price depends on the delivery times. In contrast to our earlier work, this paper considers the situation where the contract manufacturer needs to deliver the full order quantity in one single shipment. This delivery requirement is appropriate for many industries, such as the garment and toy industries, where the economies of scale in transportation is essential. We develop efficient solution procedures for solving this optimization problem. We use our model results to illustrate how the different model parameters affect the optimal solution. We also compare the results under this full‐shipment model with those from our earlier work that allows for multiple partial shipments. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Aircraft weapon budgeting

This article considers the problem of allocating a fixed budget among alternative air-to-ground weapons. The weapon-budgeting problem is high-dimensional, involving all feasible combinations of aircraft, weapons, and targets. The decision maker's utility function is defined over kills of the various target types, but it is unrealistic to expect him to write down the mathematical formula for this function. The article suggests two procedures for reducing the dimension of the maximization problem and operating without exact knowledge of the utility function. The first procedure uses successive linear approximations to generate the set of “efficient” or undominated weapon allocations. The second procedure applies separability restrictions to the utility function, thereby reducing the overall maximization problem to a sequence of low-dimensional subproblems.     

Sequential and systematic sampling plans for the Markov‐dependent production process

Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov‐dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and, in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called “systematic sampling plans.” The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 451–467, 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     

The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options

This article generalizes the dynamic and stochastic knapsack problem by allowing the decision‐maker to postpone the accept/reject decision for an item and maintain a queue of waiting items to be considered later. Postponed decisions are penalized with delay costs, while idle capacity incurs a holding cost. This generalization addresses applications where requests of scarce resources can be delayed, for example, dispatching in logistics and allocation of funding to investments. We model the problem as a Markov decision process and analyze it through dynamic programming. We show that the optimal policy with homogeneous‐sized items possesses a bithreshold structure, despite the high dimensionality of the decision space. Finally, the value (or price) of postponement is illustrated through numerical examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 267–292, 2015     

The resource constrained project scheduling problem with multiple crashable modes: An exact solution method

We introduce a formulation and an exact solution method for a nonpreemptive resource constrained project scheduling problem in which the duration/cost of an activity is determined by the mode selection and the duration reduction (crashing) within the mode. This problem is a natural combination of the time/cost tradeoff problem and the resource constrained project scheduling problem. It involves the determination, for each activity, of its resource requirements, the extent of crashing, and its start time so that the total project cost is minimized. We present a branch and bound procedure and report computational results with a set of 160 problems. Computational results demonstrate the effectiveness of our procedure. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 107–127, 2001     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

Optimal stopping in software testing

In this paper we address the problem of how to decide when to terminate the testing/modification process and to release the software during the development phase. We present a Bayesian decision theoretic approach by formulating the optimal release problem as a sequential decision problem. By using a non‐Gaussian Kalman filter type model, proposed by Chen and Singpurwalla (1994), to track software reliability, we are able to obtain tractable expressions for inference and determine a one‐stage look ahead stopping rule under reasonable conditions and a class of loss functions. © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Dynamic pricing and inventory control with learning

Optimal operating policies and corresponding managerial insight are developed for the decision problem of coordinating supply and demand when (i) both supply and demand can be influenced by the decision maker and (ii) learning is pursued. In particular, we determine optimal stocking and pricing policies over time when a given market parameter of the demand process, though fixed, initially is unknown. Because of the initially unknown market parameter, the decision maker begins the problem horizon with a subjective probability distribution associated with demand. Learning occurs as the firm monitors the market's response to its decisions and then updates its characterization of the demand function. Of primary interest is the effect of censored data since a firm's observations often are restricted to sales. We find that the first‐period optimal selling price increases with the length of the problem horizon. However, for a given problem horizon, prices can rise or fall over time, depending on how the scale parameter influences demand. Further results include the characterization of the optimal stocking quantity decision and a computationally viable algorithm. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 303–325, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10013     

A branch and bound algorithm for the minimum storage‐time sequencing problem

The minimum storage‐time sequencing problem generalizes many well‐known problems in combinatorial optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propose a new lower bound, based on a Lagrangian relaxation, which can be computed very efficiently. To improve upon this lower bound, we employ a bundle optimization algorithm. We also show that the best bound obtainable by this approach equals the one obtainable from the linear relaxation computed on a formulation whose first Chvàtal closure equals the convex hull of all the integer solutions of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 313–331, 2001     

Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets

We consider an integrated usage and maintenance optimization problem for a k‐out‐of‐n system pertaining to a moving asset. The k‐out‐of‐n systems are commonly utilized in practice to increase availability, where n denotes the total number of parallel and identical units and k the number of units required to be active for a functional system. Moving assets such as aircraft, ships, and submarines are subject to different operating modes. Operating modes can dictate not only the number of system units that are needed to be active, but also where the moving asset physically is, and under which environmental conditions it operates. We use the intrinsic age concept to model the degradation process. The intrinsic age is analogous to an intrinsic clock which ticks on a different pace in different operating modes. In our problem setting, the number of active units, degradation rates of active and standby units, maintenance costs, and type of economic dependencies are functions of operating modes. In each operating mode, the decision maker should decide on the set of units to activate (usage decision) and the set of units to maintain (maintenance decision). Since the degradation rate differs for active and standby units, the units to be maintained depend on the units that have been activated, and vice versa. In order to minimize maintenance costs, usage and maintenance decisions should be jointly optimized. We formulate this problem as a Markov decision process and provide some structural properties of the optimal policy. Moreover, we assess the performance of usage policies that are commonly implemented for maritime systems. We show that the cost increase resulting from these policies is up to 27% for realistic settings. Our numerical experiments demonstrate the cases in which joint usage and maintenance optimization is more valuable. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 418–434, 2017     

Planning horizon procedures for machine replacement models with several possible replacement alternatives

This paper develops a forward algorithm and planning horizon procedures for an important machine replacement model where it is assumed that the technological environment is improving over time and that the machine-in-use can be replaced by any of the several different kinds of machines available at that time. The set of replacement alternatives may include (i) new machines with different types of technologies such as labor- and capital- intensive, (ii) used machines, (iii) repairs and/or improvements which affect the performance characteristics of the existing machine, and so forth. The forward dynamic programming algorithm in the paper can be used to solve a finite horizon problem. The planning horizon results give a procedure to identify the forecast horizon T such that the optimal replacement decision for the first machine based on the forecast of machine technology until period T remains optimal for any problem with horizon longer than T and, for that matter, for the infinite horizon problem. A flow chart and a numerical example have been included to illustrate the algorithm.     

Structured maintenance policies on interior sample paths

We examine the problem of adaptively scheduling perfect observations and preventive replacements for a multi‐state, Markovian deterioration system with silent failures such that total expected discounted cost is minimized. We model this problem as a partially observed Markov decision process and show that the structural properties of the optimal policy hold for certain non‐extreme sample paths. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Safe distances

This work highlights the problem in military operations of setting safety limits for friendly forces, neutral forces, or civilians, to avoid sustaining unnecessary casualties both in wartime and in training. We present and investigate an analytic model which both enables the quantitative understanding of the inherent problems, and which furnishes a reasonably flexible tool in the hands of the analyst. Characteristic numerical results are displayed and analyzed: They show in particular that prevailing crude approximations are inadequate. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 259–269, 2001     

Efficient sequential decision‐making algorithms for container inspection operations

Following work of Stroud and Saeger (Proceedings of ISI, Springer Verlag, New York, 2006) and Anand et al. (Proceedings of Computer, Communication and Control Technologies, 2003), we formulate a port of entry inspection sequencing task as a problem of finding an optimal binary decision tree for an appropriate Boolean decision function. We report on new algorithms for finding such optimal trees that are more efficient computationally than those presented by Stroud and Saeger and Anand et al. We achieve these efficiencies through a combination of specific numerical methods for finding optimal thresholds for sensor functions and two novel binary decision tree search algorithms that operate on a space of potentially acceptable binary decision trees. The improvements enable us to analyze substantially larger applications than was previously possible. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011