Showing papers in "Naval Research Logistics in 2011"
TL;DR: This work considers the single-server constant retrial queue with a Poisson arrival process and exponential service and retrial times, and examines the customers' behavior, and identifies the Nash equilibrium joining strategies.
Abstract: We consider the single-server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are forced to abandon the system, but they can leave their contact details. Hence, after a service completion, the server seeks for a customer among those that have unsuccessfully applied for service but left their contact details, at a constant retrial rate. We assume that the arriving customers that find the server busy decide whether to leave their contact details or to balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine the customers' behavior, and we identify the Nash equilibrium joining strategies. We also study the corresponding social and profit maximization problems. We consider separately the observable case where the customers get informed about the number of customers waiting for service and the unobservable case where they do not receive this information. Several extensions of the model are also discussed. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
82 citations
TL;DR: In this article, a tree search-based heuristic algorithm is proposed to solve the quay crane scheduling problem, where the availability of cranes at a vessel is restricted to certain time windows.
Abstract: The quay crane scheduling problem consists of scheduling tasks for loading and unloading containers on cranes that are assigned to a vessel for its service. This article introduces a new approach for quay crane scheduling, where the availability of cranes at a vessel is restricted to certain time windows. The problem is of practical relevance, because container terminal operators frequently redeploy cranes among vessels to speed up the service of high-priority vessels while serving low-priority vessels casually. This article provides a mathematical formulation of the problem and a tree-search-based heuristic solution method. A computational investigation on a large set of test instances is used to evaluate the performance of the heuristic and to identify the impact of differently structured crane time windows on the achievable vessel handling time. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
67 citations
TL;DR: In this article, the authors consider a supplier with finite production capacity and stochastic production times and formulate the production control problem as a continuous-time Markov decision process and prove there is an optimal state-dependent base-stock policy, where the base stock levels depend upon the number of orders at various stages of update.
Abstract: We consider a supplier with finite production capacity and stochastic production times. Customers provide advance demand information (ADI) to the supplier by announcing orders ahead of their due dates. However, this information is not perfect, and customers may request an order be fulfilled prior to or later than the expected due date. Customers update the status of their orders, but the time between consecutive updates is random. We formulate the production-control problem as a continuous-time Markov decision process and prove there is an optimal state-dependent base-stock policy, where the base-stock levels depend upon the numbers of orders at various stages of update. In addition, we derive results on the sensitivity of the state-dependent base-stock levels to the number of orders in each stage of update. In a numerical study, we examine the benefit of ADI, and find that it is most valuable to the supplier when the time between updates is moderate. We also consider the impact of holding and backorder costs, numbers of updates, and the fraction of customers that provide ADI. In addition, we find that while ADI is always beneficial to the supplier, this may not be the case for the customers who provide the ADI. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 88-106, 2011
54 citations
TL;DR: This article analyses a divergent supply chain consisting of a central warehouse and N nonidentical retailers and derivation of an exact recursive procedure for determining the expected inventory holding and backorder costs for the system, under the assumption of Poisson demand.
Abstract: This article analyses a divergent supply chain consisting of a central warehouse and N nonidentical retailers. The focus is on joint evaluation of inventory replenishment and shipment consolidation effects. A time-based dispatching and shipment consolidation policy is used at the warehouse in conjunction with real-time point-of-sale data and centralized inventory information. This represents a common situation, for example, in various types of vendor managed inventory systems. The main contribution is the derivation of an exact recursive procedure for determining the expected inventory holding and backorder costs for the system, under the assumption of Poisson demand. Two heuristics for determining near optimal shipment intervals are also presented. The results are applicable both for single-item and multiitem systems. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 59-71, 2011 (Less)
45 citations
TL;DR: In this paper, the reliability properties of m-consecutive-k-out-of-n:f systems with exchangeable components were investigated and closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics were established.
Abstract: In this article, we study reliability properties of m-consecutive-k-out-of-n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature-based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m-consecutive-k-out-of-n: F systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
45 citations
TL;DR: In this paper, the authors study properties of the lifetimes of coherent systems obtained using SOS and obtain a mixture representation based on the signature of the system, which is used to obtain stochastic comparisons.
Abstract: The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k-out-of-n systems. In particular, we show that they are not necessarily hazard rate ordered. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
43 citations
TL;DR: Three discrete time Bayesian state‐space models with Poisson measurements aiming to address different issues in call center arrival modeling are introduced and their Bayesian inference is developed.
Abstract: In this article, we introduce three discrete time Bayesian state-space models with Poisson measurements, each aiming to address different issues in call center arrival modeling. We present the properties of the models and develop their Bayesian inference. In so doing, we provide sequential updating and smoothing for call arrival rates and discuss how the models can be used for intra-day, inter-day, and inter-week forecasts. We illustrate the implementation of the models by using actual arrival data from a US commercial bank's call center and provide forecasting comparisons. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 28–42, 2011
39 citations
TL;DR: In this article, a mixed integer programming model is formulated for the problem and a Lagrangian relaxation model is then obtained through relaxing the order assignment con- straints, a combined algorithm that contains nested double loops.
Abstract: This article considers the order batching problem in steelmaking and continuous-casting production. The problem is to jointly specify the slabs needed to satisfy each customer order and group all the slabs of different customer orders into production batches. A novel mixed integer programming model is formulated for the problem. Through relaxing the order assignment con- straints, a Lagrangian relaxation model is then obtained. By exploiting the relationship between Lagrangian relaxation and column generation, we develop a combined algorithm that contains nested double loops. At the inner loop, the subgradient method is applied for approximating the Lagrangian dual problem and pricing out columns of the master problem corresponding to the linear dual form of the Lagrangian dual problem. At the outer loop, column generation is employed to solve the master problem exactly and adjust Lagrangian multipliers. Computational experiments are carried out using real data collected from a large steel company, as well as on large-scaled problem instances randomly generated. The results demonstrate that the combined algorithm can obtain tighter lower bound and higher quality solution within an acceptable computation time as compared to the conventional Lagrangian relaxation algorithm. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 370-388, 2011
35 citations
TL;DR: The proposed GA with neighborhood search works well regarding solution quality and computational time compared with existing algorithms in the RCPSP literature, especially for the instances with a large number of activities.
Abstract: The resource-constrained project scheduling problem (RCPSP) consists of a set of non-preemptive activities that follow precedence relationship and consume resources. Under the limited amount of the resources, the objective of RCPSP is to find a schedule of the activities to minimize the project makespan. This article presents a new genetic algorithm (GA) by incorporating a local search strategy in GA operators. The local search strategy improves the efficiency of searching the solution space while keeping the randomness of the GA approach. Extensive numerical experiments show that the proposed GA with neighborhood search works well regarding solution quality and computational time compared with existing algorithms in the RCPSP literature, especially for the instances with a large number of activities. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
35 citations
TL;DR: New insight is obtained—not easily obtained using simply geometric calculations—into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate.
Abstract: Given a number of patrollers that are required to detect an intruder in a channel, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximized the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn-rate constraints, and that the intruder travels straight down a channel with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large-scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests for one, two, and three underwater patrollers, an underwater intruder, different trajectory constraints, several intruder speeds and other specific parameter choices, we obtain new insight—not easily obtained using simply geometric calculations—into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 804-820, 2011
34 citations
TL;DR: This article applies the methods of adversarial risk analysis to the problem of selecting a route through a network in which an opponent chooses vertices for ambush to help convoy routing across a road network.
Abstract: Problems in counterterrorism and corporate competition have prompted research that attempts to combine statistical risk analysis with game theory in ways that support practical decision making. This article applies these methods of adversarial risk analysis to the problem of selecting a route through a network in which an opponent chooses vertices for ambush. The motivating application is convoy routing across a road network when there may be improvised explosive devices and imperfect intelligence about their locations. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: In this paper, the authors give necessary and sufficient conditions based on signatures to obtain distribution-free stochastic ordering properties for coherent systems with exchangeable components, and apply these results to all the coherent systems having five or less components.
Abstract: We give necessary and sufficient conditions based on signatures to obtain distribution-free stochastic ordering properties for coherent systems with exchangeable components. Specifically, we consider the stochastic, the hazard (failure) rate, the reversed hazard rate, and the likelihood ratio orders. We apply these results to obtain stochastic ordering properties for all the coherent systems with five or less exchangeable components. Our results extend some preceding results. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: Deterministic generalized Lanchester models are fitted to daily sortie and loss data from the Battle of Britain to find days with higher sortie numbers on average favored the Luftwaffe, whereas the loss‐ratio was not significantly dependent on the force ratio.
Abstract: We fit deterministic generalized Lanchester models to daily sortie and loss data from the Battle of Britain. The best fit for the period 14th August to 30th October 1940 is δB ∼ G1.2, δG ∼ G0.9, where B and G are RAF Fighter Command and Luftwaffe sortie numbers, and δB and δG are daily loss numbers, respectively. The data naturally divide into two phases, with losses (as a proportion of overall sortie numbers) much reduced after 15th September. Fits were generally better for the first phase than for the second, and for British losses than for German; in every case the dependence on G is stronger than that on B. Days with higher sortie numbers on average favored the Luftwaffe, whereas the loss-ratio was not significantly dependent on the force ratio. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 58: 210–222, 2011
TL;DR: A new formulation for the air defense problem of warships in a naval task group and a solution method is presented and efficient heuristic procedures for solving the problem are proposed.
Abstract: In this study, we present a new formulation for the air defense problem of warships in a naval task group and propose a solution method. We define the missile allocation problem (MAP) as the optimal allocation of a set of surface-to-air missiles (SAMs) of a naval task group to a set of attacking air targets. MAP is a new treatment of an emerging problem fostered by the rapid increase in the capabilities of anti-ship missiles (ASMs), the different levels of air defense capabilities of the warships against the ASM threat, and new technology that enables a fully coordinated and collective defense. In addition to allocating SAMs to ASMs, MAP also schedules launching of SAM rounds according to shoot-look-shoot engagement policy or its variations, considering multiple SAM systems and ASM types. MAP can be used for air defense planning under a given scenario. As thorough scenario analysis would require repetitive use of MAP, we propose efficient heuristic procedures for solving the problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: In this article, the authors consider a class of facility location problems with a time dimension, which requires assigning every customer to a supply facility in each of a finite number of periods.
Abstract: We consider a class of facility location problems with a time dimension, which requires assigning every customer to a supply facility in each of a finite number of periods. Each facility must meet all assigned customer demand in every period at a minimum cost via its production and inventory decisions. We provide exact branch-and-price algorithms for this class of problems and several important variants. The corresponding pricing problem takes the form of an interesting class of production planning and order selection problems. This problem class requires selecting a set of orders that maximizes profit, defined as the revenue from selected orders minus production-planning-related costs incurred in fulfilling the selected orders. We provide polynomial-time dynamic programming algorithms for this class of pricing problems, as well as for generalizations thereof. Computational testing indicates the advantage of our branch-and-price algorithm over various approaches that use commercial software packages. These tests also highlight the significant cost savings possible from integrating location with production and inventory decisions and demonstrate that the problem is rather insensitive to forecast errors associated with the demand streams. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 419-436, 2011
TL;DR: In this article, the authors study a stochastic inventory model of a firm that periodically orders a product from a make-to-order manufacturer, where orders can be shipped by a combination of two freight modes that differ in lead-times and costs.
Abstract: We study a stochastic inventory model of a firm that periodically orders a product from a make-to-order manufacturer. Orders can be shipped by a combination of two freight modes that differ in lead-times and costs, although orders are not allowed to cross. Placing an order as well as each use of each freight mode has a fixed and a quantity proportional cost. The decision of how to allocate units between the two freight modes utilizes information about demand during the completion of manufacturing. We derive the optimal freight mode allocation policy, and show that the optimal policy for placing orders is not an (s,S) policy in general. We provide tight bounds for the optimal policy that can be calculated by solving single period problems. Our analysis enables insights into the structure of the optimal policy specifying the conditions under which it simplifies to an (s,S) policy. We characterize the best (s,S) policy for our model, and through extensive numerical investigation show that its performance is comparable with the optimal policy in most cases. Our numerical study also sheds light on the benefits of the dual freight model over the single freight models.
TL;DR: This article proposes an algorithm that complements prior work by sampling solutions from a sequence of surrogate distributions that iteratively approximate the target Boltzmann distributions, and establishes a novel connection between MARS and the well‐known Stochastic Approximation method.
Abstract: The Annealing Adaptive Search (AAS) algorithm for global optimization searches the solution space by sampling from a sequence of Boltzmann distributions. For a class of optimization problems, it has been shown that the complexity of AAS increases at most linearly in the problem dimension. However, despite its desirable property, sampling from a Boltzmann distribution at each iteration of the algorithm remains a practical challenge. Prior work to address this issue has focused on embedding Markov chain-based sampling techniques within the AAS framework. In this article, based on ideas from the recent Cross-Entropy method and Model Reference Adaptive Search, we propose an algorithm, called Model-based Annealing Random Search (MARS), that complements prior work by sampling solutions from a sequence of surrogate distributions that iteratively approximate the target Boltzmann distributions. We establish a novel connection between MARS and the well-known Stochastic Approximation method. By exploiting this connection, we prove the global convergence of MARS and characterize its asymptotic convergence rate behavior. Our empirical results indicate promising performance of the algorithm in comparison with some of the existing methods. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: In this paper, the authors developed a mathematical model for advantageously positioning these vessels, and possibly shore-based radar too, to minimize the probability that an intelligent adversary in one or more speedboats will evade detection while mounting an attack.
Abstract: The U.S. Coast Guard, Customs and Border Patrol, Marine Corps, and Navy have deployed several hundred port patrol vessels to protect waterways, U.S. Navy ships and other high-value assets in ports world-wide. Each vessel has an armed crew of four, is relatively fast, and features a surface search radar, radios, and a machine gun. These vessels coordinate surveillance patrols in groups of two or four. We developed a mathematical model for advantageously positioning these vessels, and possibly shore-based radar too, to minimize the probability that an intelligent adversary in one or more speedboats will evade detection while mounting an attack. Attackers can use elevated obstructions to evade radar detection in their attack paths, and ports feature many such restrictions to navigation and observation. A key, but realistic assumption complicates planning: the attackers will be aware of defensive positions and capabilities in advance of mounting their attack. The defender-attacker optimization suggests plans here for a fictitious port, the port of Hong Kong, and the U.S. Navy Fifth Fleet Headquarters in Bahrain. In these cases, the defender can almost certainly detect any attack, even though the attacker, observing defender prepositioning, plans clever, and evasive attack tracks. Published 2011 Wiley Periodicals, Inc.† Naval Research Logistics, 2011
TL;DR: This article introduces the use of Benders' cuts to guide a large neighborhood search to solve the traveling umpire problem, a sports scheduling problem inspired by the real‐life needs of the officials of a sports league.
Abstract: This article introduces the use of Benders' cuts to guide a large neighborhood search to solve the traveling umpire problem, a sports scheduling problem inspired by the real-life needs of the officials of a sports league. At each time slot, a greedy matching heuristic is used to construct a schedule. When an infeasibility is recognized first a single step backtracking is tried to resolve the infeasibility. If unsuccessful, Benders' cuts are generated to guide a large neighborhood search to ensure feasibility and to improve the solution. Realizing the inherent symmetry present in the problem, a large family of cuts are generated and their effectiveness is tested. The resulting approach is able to find better solutions to many instances of this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: A novel three-layer commodity-flow location routing formulation that distributes multiple products, respects hard time windows, allows demand points to be supplied by more than one vehicle or depot, and locates facilities at two different layers is proposed.
Abstract: Ammunition, whether it be an arrow in the middle ages, a lead bullet in the 1800s, or a laser guided smart bomb today, has been the most prominent factor in determining the outcome of combat. Failing to supply the required amount of ammunition properly may lead to defeat. Our main objective in this study is to provide a decision support tool that can help plan ammunition distribution on the battlefield. We demonstrate through an extensive literature review that the existing models are not capable of handling the specifics of the problem in this study. To this end, we propose a novel three-layer commodity-flow location routing formulation that distributes multiple products, respects hard time windows, allows demand points to be supplied by more than one vehicle or depot, and locates facilities at two different layers. We derive several valid inequalities to speed up the solution time of our model, illustrate the performance of the model in several realistically sized scenarios, and report encouraging results. Finally, we introduce a dynamic model that designs the distribution system in consecutive time periods for the entire combat duration. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 58: 188–209, 2011
TL;DR: A stochastic approximation algorithm to find good bid price policies for the joint capacity allocation and overbooking problem over an airline network is developed based on visualizing the total expected profit as a function of the bid prices and searching for a good set of bid prices by using the stochastically gradients of thetotal expected profit function.
Abstract: In this article, we develop a stochastic approximation algorithm to find good bid price policies for the joint capacity allocation and overbooking problem over an airline network. Our approach is based on visualizing the total expected profit as a function of the bid prices and searching for a good set of bid prices by using the stochastic gradients of the total expected profit function. We show that the total expected profit function that we use is differentiable with respect to the bid prices and derive a simple expression that can be used to compute its stochastic gradients. We show that the iterates of our stochastic approximation algorithm converge to a stationary point of the total expected profit function with probability 1. Our computational experiments indicate that the bid prices computed by our approach perform significantly better than those computed by standard benchmark strategies and the performance of our approach is relatively insensitive to the frequency with which we recompute the bid prices over the planning horizon.
TL;DR: This article deals with the optimal allocation of mine clearance resources to a network of roads that is continually being mined by an opponent, IED warfare as practiced in Iraq and Afghanistan.
Abstract: This article deals with the optimal allocation of mine clearance resources to a network of roads that is continually being mined by an opponent. The motivating application is IED warfare as practiced in Iraq and Afghanistan. The situation differs from most mine warfare analyses in being protracted indefinitely in time, with the processes of mine placement by Red and mine clearance by Blue being intermixed. Each incident involving a Blue convoy and a Red mine removes the mine and possibly causes some damage to the convoy. Blue's object is to minimize the total damage rate by optimally deploying mine clearance forces to road segments. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 58: 180–187, 2011
TL;DR: This article adapts a policy which is optimal for a related problem and proves that this policy is indeed also optimal forA restricted class of instances of the authors' problem and is both effective and efficiently computable.
Abstract: The problem we consider is a stochastic shortest path problem in the presence of a dynamic learning capability. Specif- ically, a spatial arrangement of possible obstacles needs to be traversed as swiftly as possible, and the status of the obstacles may be disambiguated (at a cost) en route. No efficiently computable optimal policy is known, and many similar problems have been proven intractable. In this article, we adapt a policy which is optimal for a related problem and prove that this policy is indeed also optimal for a restricted class of instances of our problem. Otherwise, this policy is generally suboptimal but, nonetheless, it is both effective and efficiently computable. Examples/simulations are provided in a mine countermeasures application. Of central use is the Tangent Arc Graph, a polynomially sized topological superimposition of exponentially many visibility graphs. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 389-399, 2011
TL;DR: In this paper, the optimal number of retail outlets and transshipment locations for an infinite horizon periodic stochastic inventory system is investigated in the context of an inventory-location model.
Abstract: We study an infinite horizon periodic stochastic inventory system consisting of retail outlets and customers located on a homogenous line segment. In each period, the total demand, generated by the customers on the line, is normally distributed. To better match supply and demand, we incorporate lateral transshipments. We propose a compact model in which the strategic decisions—the number and locations of retail outlets—are determined simultaneously with the operational decisions—the inventory replenishment and transshipment quantities. We find the optimal balance between the risk-pooling considerations, which drive down the optimal number of retail outlets, and lateral transshipments, which drive up the optimal number of retail outlets. We also explore the sensitivity of the optimal number of retail outlets to various problem parameters. This article presents a novel way of integrating lateral transshipments in the context of an inventory-location model. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: In this paper, the optimal ordering policy is a state-dependent base stock policy characterized by a base-stock level that is a function of advance capacity information (ACI), which can reduce the uncertainty of future supply if a company is able to obtain ACI about future supply/production capacity availability from its supplier.
Abstract: An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic-review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state-dependent base-stock policy characterized by a base-stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: In this article, the optimal control of a periodic-review make-to-stock system with limited production capacity and multiple demand classes is studied, and a heuristic algorithm is proposed to approximate the optimal policy.
Abstract: This article studies the optimal control of a periodic-review make-to-stock system with limited production capacity and multiple demand classes. In this system, a single product is produced to fulfill several classes of demands. The manager has to make the production and inventory allocation decisions. His objective is to minimize the expected total discounted cost. The production decision is made at the beginning of each period and determines the amount of products to be produced. The inventory allocation decision is made after receiving the random demands and determines the amount of demands to be satisfied. A modified base stock policy is shown to be optimal for production, and a multi-level rationing policy is shown to be optimal for inventory allocation. Then a heuristic algorithm is proposed to approximate the optimal policy. The numerical studies show that the heuristic algorithm is very effective. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 43–58, 2011
TL;DR: A port of entry inspection sequencing task as a problem of finding an optimal binary decision tree for an appropriate Boolean decision function is formulated and new algorithms for finding such optimal trees that are more efficient computationally are reported on.
Abstract: 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
TL;DR: In this article, the effect of competition on prices, profits, and consumers' surplus in multi-period, finite horizon, dynamic pricing settings was studied, where a single myopic consumer visits two competing retailers, who offer identical goods, in a (first order Markovian) probabilistic fashion.
Abstract: We evaluate the effect of competition on prices, profits, and consumers' surplus in multiperiod, finite horizon, dynamic pricing settings. In our base model, a single myopic consumer visits two competing retailers, who offer identical goods, in a (first order Markovian) probabilistic fashion—if the posted price exceeds the consumer's valuation for the good, he returns to the same store in the following period with a certain probability. We find that even a small reduction in the return probability from one—which corresponds to the monopoly case at which prices decline linearly—is sufficient to revert the price decline from a linear into an exponential shape. Each retailer's profit is particularly sensitive to changes in his return probability when it is relatively high, and is maximized under complete loyalty behavior (i.e., return probability is one). On the other hand, consumer surplus is maximized under complete switching behavior (i.e., return probability is zero). In the presence of many similar consumers, the insights remain valid. We further focus on the extreme scenario where all consumers follow a complete switching behavior, to derive sharp bounds, and also consider the instance where, in this setting, myopic consumers are replaced with strategic consumers. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: A multi‐period tree network maintenance scheduling model is introduced and the effect of maintenance capacity restrictions on traffic/information flow interruptions is investigated and the intuitions gained from the uniform flow case continue to hold in general settings.
Abstract: We introduce a multi-period tree network maintenance scheduling model and investigate the effect of maintenance capacity restrictions on traffic/information flow interruptions. Network maintenance refers to activities that are performed to keep a network operational. For linear networks with uniform flow between every pair of nodes, we devise a polynomial-time combinatorial algorithm that minimizes flow disruption. The spiral structure of the optimal maintenance schedule sheds insights into general network maintenance scheduling. The maintenance problem on linear networks with a general flow structure is strongly NP-hard. We formulate this problem as a linear integer program, derive strong valid inequalities, and conduct a polyhedral study of the formulation. Polyhedral analysis shows that the relaxation of our linear network formulation is tight when capacities and flows are uniform. The linear network formulation is then extended to an integer program for solving the tree network maintenance scheduling problem. Preliminary computations indicate that the strengthened formulations can solve reasonably sized problems on tree networks and that the intuitions gained from the uniform flow case continue to hold in general settings. Finally, we extend the approach to directed networks and to maintenance of network nodes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
TL;DR: In this paper, an equity model between groups of demand points is proposed to provide equal service to the different groups by minimizing the deviation from equality among groups, and the objective function is the sum of squares of differences between all pairs of service distances between demand points in different groups.
Abstract: An equity model between groups of demand points is proposed. The set of demand points is divided into two or more groups. For example, rich and poor neighborhoods and urban and rural neighborhoods. We wish to provide equal service to the different groups by minimizing the deviation from equality among groups. The distance to the closest facility is a measure of the quality of service. Once the facilities are located, each demand point has a service distance. The objective function, to be minimized, is the sum of squares of differences between all pairs of service distances between demand points in different groups. The problem is analyzed and solution techniques are proposed for the location of a single facility in the plane. Computational experiments for problems with up to 10,000 demand points and rectilinear, Euclidean, or general lp distances illustrate the efficiency of the proposed algorithm. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011