Optimizing fishbone aisles for dual‐command operations in a warehouse

Unit‐load warehouses store and retrieve unit‐loads, typically pallets. When storage and retrieval operations are not coordinated, travel is from a pickup and deposit (P&D) point to a pallet location and back again. In some facilities, workers interleave storage and retrieval operations to form a dual‐command cycle. Two new aisle designs proposed by Gue and Meller (“Improving the unit‐load warehouse.” In Progress in Material Handling Research: 2006. Material Handling Industry of America, Charlotte, NC, 2006) use diagonal aisles to reduce the travel distance to a single pallet location by approximately 10 and 20[percnt] for the two designs, respectively. We develop analytical expressions for travel between pallet locations for one of these—the fishbone design. We then compare fishbone warehouses that have been optimized for dual‐command to traditional warehouses that have been optimized in the same manner, and show that an optimal fishbone design reduces dual‐command travel by 10–15%. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 54: 389–403, 2009     

The assignment of storage locations to containers for a container stack

Assigning storage locations to incoming or reshuffled containers is a fundamental problem essential to the operations efficiency of container terminals. The problem is notoriously hard for its combinatorial and dynamic nature. In this article, we minimize the number of reshuffles in assigning storage locations for incoming and reshuffled export containers. For the static problem to empty a given stack without any new container arrival, the optimum reshuffle sequence is identified by an integer program (IP). The integer program captures the evolution of stack configurations as a function of decisions and is of interest by itself. Heuristics based on the integer program are then derived. Their competitiveness in accuracy and time are established by extensive numerical runs comparing them with existing heuristics in literature and in practice as well as with extensions of the existing heuristics. Variants of the IP‐based heuristics are then applied to the dynamic problem with continual retrievals and arrivals of containers. Again, numerical runs confirm that the IP‐based heuristic is competitive. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

The solution to an open problem for a caching game

In a caching game introduced by Alpern et al. (Alpern et al., Lecture notes in computer science (2010) 220–233) a Hider who can dig to a total fixed depth normalized to 1 buries a fixed number of objects among n discrete locations. A Searcher who can dig to a total depth of h searches the locations with the aim of finding all of the hidden objects. If he does so, he wins, otherwise the Hider wins. This zero‐sum game is complicated to analyze even for small values of its parameters, and for the case of 2 hidden objects has been completely solved only when the game is played in up to 3 locations. For some values of h the solution of the game with 2 objects hidden in 4 locations is known, but the solution in the remaining cases was an open question recently highlighted by Fokkink et al. (Fokkink et al., Search theory: A game theoretic perspective (2014) 85–104). Here we solve the remaining cases of the game with 2 objects hidden in 4 locations. We also give some more general results for the game, in particular using a geometrical argument to show that when there are 2 objects hidden in n locations and n→∞, the value of the game is asymptotically equal to h/n for h≥n/2. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 23–31, 2016     

Exact algorithms and bounds for the dynamic assignment interdiction problem

We study a multi‐stage dynamic assignment interdiction (DAI) game in which two agents, a user and an attacker, compete in the underlying bipartite assignment graph. The user wishes to assign a set of tasks at the minimum cost, and the attacker seeks to interdict a subset of arcs to maximize the user's objective. The user assigns exactly one task per stage, and the assignment costs and interdiction impacts vary across stages. Before any stage commences in the game, the attacker can interdict arcs subject to a cardinality constraint. An interdicted arc can still be used by the user, but at an increased assignment cost. The goal is to find an optimal sequence of assignments, coupled with the attacker's optimal interdiction strategy. We prove that this problem is strongly NP‐hard, even when the attacker can interdict only one arc. We propose an exact exponential‐state dynamic‐programming algorithm for this problem as well as lower and upper bounds on the optimal objective function value. Our bounds are based on classical interdiction and robust optimization models, and on variations of the DAI game. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 373–387, 2017     

Competitive location and capacity decisions for firms serving time‐sensitive customers

In this article we explore how two competing firms locate and set capacities to serve time‐sensitive customers. Because customers are time‐sensitive, they may decline to place an order from either competitor if their expected waiting time is large. We develop a two‐stage game where firms set capacities and then locations, and show that three types of subgame perfect equilibria are possible: local monopoly (in which each customer is served by a single firm, but some customers may be left unserved), constrained local monopoly (in which firms serve the entire interval of customers but do not compete with each other), and constrained competition (in which firms also serve the entire interval of customers, but now compete for some customers). We perform a comparative statics analysis to illustrate differences in the equilibrium behavior of a duopolist and a coordinated monopolist. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

Analytic solution for the nucleolus of a three‐player cooperative game

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large‐scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed‐form) for a three‐player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A multi‐objective model for bank ATM networks

In this paper we present an application of the core solution concepts for multi‐objective games to a bank ATM network model. In these games, the worth of a coalition is given by a subset of vectors of the k‐dimensional space rather than by a scalar. The paper investigates how an ATM network model based on multi‐objective cooperative game theory could be used as an alternative way of setting interchange fees paid by the customer's bank to the one that owns the ATM. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Capacity allocation to sales agents in a decentralized logistics network

Many logistics systems operate in a decentralized way, while most optimization models assume a centralized planner. One example of a decentralized system is in some sea cargo companies: sales agents, who share ship capacity on a network, independently accept cargo from their location and contribute to the revenue of the system. The central headquarters does not directly control the agents' decisions but can influence them through system design and incentives. In this paper, we model the firm's problem to determine the best capacity allocation to the agents such that system revenue is maximized. In the special case of a single‐route, we formulate the problem as a mixed integer program incorporating the optimal agent behavior. For the NP‐hard multiple‐route case, we propose several heuristics for the problem. Computational experiments show that the decentralized system generally performs worse when network capacity is tight and that the heuristics perform reasonably well. We show that the decentralized system may perform arbitrarily worse than the centralized system when the number of locations goes to infinity, although the choice of sales incentive impacts the performance. We develop an upper bound for the decentralized system, where the bound gives insight on the performance of the heuristics in large systems. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Duality in constrained multi‐facility location models

We consider the ??_p‐norm multi‐facility minisum location problem with linear and distance constraints, and develop the Lagrangian dual formulation for this problem. The model that we consider represents the most general location model in which the dual formulation is not found in the literature. We find that, because of its linear objective function and less number of variables, the Lagrangian dual is more useful. Additionally, the dual formulation eliminates the differentiability problem in the primal formulation. We also provide the Lagrangian dual formulation of the multi‐facility minisum location problem with the ??_pb‐norm. Finally, we provide a numerical example for solving the Lagrangian dual formulation and obtaining the optimum facility locations from the solution of the dual formulation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 410–421, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10010     

Robust tower location for code division multiple access networks

Designing Code Division Multiple Access networks includes determining optimal locations of radio towers and assigning customer markets to the towers. In this paper, we describe a deterministic model for tower location and a stochastic model to optimize revenue given a set of constructed towers. We integrate these models in a stochastic integer programming problem with simple recourse that optimizes the location of towers under demand uncertainty. We develop algorithms using Benders' reformulation, and we provide computational results. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The minmax multidimensional knapsack problem with application to a chance‐constrained problem

In this paper we present a new combinatorial problem, called minmax multidimensional knapsack problem (MKP), motivated by a military logistics problem. The logistics problem is a two‐period, two‐level, chance‐constrained problem with recourse. We show that the MKP is NP‐hard and develop a practically efficient combinatorial algorithm for solving it. We also show that under some reasonable assumptions regarding the operational setting of the logistics problem, the chance‐constrained optimization problem is decomposable into a series of MKPs that are solved separately. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Continuous accumulation games on discrete locations

In an accumulation game, a HIDER attempts to accumulate a certain number of objects or a certain quantity of material before a certain time, and a SEEKER attempts to prevent this. In a continuous accumulation game the HIDER can pile material either at locations $1, 2, …, n, or over a region in space. The HIDER will win (payoff 1) it if accumulates N units of material before a given time, and the goal of the SEEKER will win (payoff 0) otherwise. We assume the HIDER can place continuous material such as fuel at discrete locations i = 1, 2, …, n, and the game is played in discrete time. At each time k > 0 the HIDER acquires h units of material and can distribute it among all of the locations. At the same time, k, the SEEKER can search a certain number s < n of the locations, and will confiscate (or destroy) all material found. After explicitly describing what we mean by a continuous accumulation game on discrete locations, we prove a theorem that gives a condition under which the HIDER can always win by using a uniform distribution at each stage of the game. When this condition does not hold, special cases and examples show that the resulting game becomes complicated even when played only for a single stage. We reduce the single stage game to an optimization problem, and also obtain some partial results on its solution. We also consider accumulation games where the locations are arranged in either a circle or in a line segment and the SEEKER must search a series of adjacent locations. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 60–77, 2002; DOI 10.1002/nav.1048     

Interchange fee rate,merchant discount rate,and retail price in a credit card network: A game‐theoretic analysis

We consider two game‐theoretic settings to determine the optimal values of an issuer's interchange fee rate, an acquirer's merchant discount rate, and a merchant's retail price in a credit card network. In the first setting, we investigate a two‐stage game problem in which the issuer and the acquirer first negotiate the interchange fee rate, and the acquirer and the retailer then determine their merchant discount rate and retail price, respectively. In the second setting, motivated by the recent US bill “H.R. 2695,” we develop a three‐player cooperative game in which the issuer, the acquirer, and the merchant form a grand coalition and bargain over the interchange fee rate and the merchant discount rate. Following the cooperative game, the retailer makes its retail pricing decision. We derive both the Shapley value‐ and the nucleolus‐characterized, and globally‐optimal unique rates for the grand coalition. Comparing the two game settings, we find that the participation of the merchant in the negotiation process can result in the reduction of both rates. Moreover, the stability of the grand coalition in the cooperative game setting may require that the merchant should delegate the credit card business only to the issuer and the acquirer with sufficiently low operation costs. We also show that the grand coalition is more likely to be stable and the U.S. bill “H.R. 2695” is thus more effective, if the degree of division of labor in the credit card network is higher as the merchant, acquirer, and issuer are more specialized in the retailing, acquiring, and issuing operations, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

A branch‐and‐price algorithm for a targeting problem

In this paper, we consider a new weapon‐target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model, but it can be transformed into a linear integer programming model. We present a branch‐and‐price algorithm for the problem employing the disaggregated formulation, which has exponentially many columns denoting the feasible allocations of weapon systems to each target. A greedy‐style heuristic is used to get some initial columns to start the column generation. A branching strategy compatible with the pricing problem is also proposed. Computational results using randomly generated data show this approach is promising for the targeting problem. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Probabilistic resource pooling games

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player‐specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non‐empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm‐Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.     

Rendez‐vous search on a rectangular lattice

In a rendez‐vous search two or more teams called seekers try to minimize the time needed to find each other. In this paper, we consider s seekers in a rectangular lattice of locations where each knows the configuration of the lattice, the distribution of the seekers at time 0, and its own location, but not the location of any other. We measure time discretely, in turns. A meeting takes place when the two seekers reach the same point or adjacent points. The main result is that for any dimension of lattice, any initial distribution of seekers there are optimal strategies for the seekers that converge (in a way we shall make clear) to a center. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Flow shop scheduling with earliness,tardiness, and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding), and intermediate (work‐in‐process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two different, but closely related, Dantzig‐Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig‐Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two different lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near‐optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with different types of strongly ????‐hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near‐optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

A decomposition heuristic for the twin robots scheduling problem

This article provides an efficient heuristic based on decomposition for the twin robots scheduling problem (TRSP). TRSP concerns two moving robots executing storage and retrieval requests in parallel along a shared pathway. The depots are located at both ends of the line and a dedicated robot is assigned to each of them. While moving goods between their respective depots and some storage locations on the line, noncrossing constraints among robots need to be considered. Our heuristic uses a dynamic programming framework to determine the schedule of one robot while keeping the other one's fixed. It finds near‐optimal solutions even for large problem instances with hundreds of jobs in a short time span. © 2014 Wiley Periodicals, Inc. 62:16–22, 2015     

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