Showing papers in "Naval Research Logistics in 2006"

A branch-and-cut algorithm for the quay crane scheduling problem in a container terminal

Abstract: The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch-and-cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Optimal pricing and inventory control policy in periodic-review systems with fixed ordering cost and lost sales

Abstract: This paper studies a periodic-review pricing and inventory control problem for a retailer, which faces stochastic price-sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s,S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Reliability Inference for Field Conditions from Accelerated Degradation Testing

Abstract: Accelerated degradation testing (ADT) is usually conducted under deterministic stresses such as constant-stress, step-stress, and cyclic-stress. Based on ADT data, an ADT model is developed to predict reliability under normal (field) operating conditions. In engineering applications, the “standard” approach for reliability prediction assumes that the normal operating conditions are deterministic or simply uses the mean values of the stresses while ignoring their variability. Such an approach may lead to significant prediction errors. In this paper, we extend an ADT model obtained from constant-stress ADT experiments to predict field reliability by considering the stress variations. A case study is provided to demonstrate the proposed statistical inference procedure. The accuracy of the procedure is verified by simulation using various distributions of field stresses. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.

Quay crane scheduling at container terminals to minimize the maximum relative tardiness of vessel departures

Abstract: In this paper, we study the problem of scheduling quay cranes (QCs) at container terminals where incoming vessels have different ready times. The objective is to minimize the maximum relative tardiness of vessel departures. The problem can be formulated as a mixed integer linear programming (MILP) model of large size that is difficult to solve directly. We propose a heuristic decomposition approach to breakdown the problem into two smaller, linked models, the vessel-level and the berth-level models. With the same berth-level model, two heuristic methods are developed using different vessel-level models. Computational experiments show that the proposed approach is effective and efficient. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Optimization and mediated bartering models for ground delay programs

Abstract: 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

Vulnerable options in supply chains: Effects of supplier competition

Abstract: Concerned with the risk of supplier default, a firm may choose to diversify its orders among multiple suppliers. Furthermore, the discrepancy in production lead-times among suppliers furnishes a firm with a valuable option to defer ordering decisions until uncertainty has been partially resolved. The suppliers also have an option: to defer their pricing decisions. Using a single-period, multi-stage model of a two-echelon supply chain with competing risky suppliers and a single manufacturer, this paper investigates how the supplier default risk and default co-dependence affect manufacturer procurement and production decisions, supplier pricing decisions, firms profits, and the deferment option value and how the introduction of the deferment option alters supplier competition. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006

Hedging Quantity Risks with Standard Power Options in a Competitive Wholesale Electricity Market

Abstract: This paper addresses quantity risk in the electricity market and explores several ways of managing such risk. The paper also addresses the hedging problem of a load-serving entity, which provides electricity service at a regulated price in electricity markets with price and quantity risk. Exploiting the correlation between consumption volume and spot price of electricity, an optimal zero-cost hedging function characterized by payoff as a function of spot price is derived. It is then illustrated how such a hedging strategy can be implemented through a portfolio of forward contracts and call and put options. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 53: 697-712, 2006

A Logistic Regression/Markov Chain Model for NCAA Basketball

Abstract: Each year, more than $3 billion is wagered on the NCAA Division 1 men's basketball tournament. Most of that money is wagered in pools where the object is to correctly predict winners of each game, with emphasis on the last four teams remaining (the Final Four). In this paper, we present a combined logistic regression/Markov chain model for predicting the outcome of NCAA tournament games given only basic input data. Over the past 6 years, our model has been significantly more successful than the other common methods such as tournament seedings, the AP and ESPN/USA Today polls, the RPI, and the Sagarin and Massey ratings. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.

The α‐reliable mean‐excess regret model for stochastic facility location modeling

Abstract: In this paper, we study a strategic facility location problem under uncertainty. The uncertainty associated with future events is modeled by defining alternative future scenarios with probabilities. We present a new model called the α-reliable mean- excess model that minimizes the expected regret with respect to an endogenously selected subset of worst-case scenarios whose collective probability of occurrence is no more than 1 − α. Our mean-excess risk measure is coherent and computationally efficient. Computational experiments also show that the α-reliable mean-excess criterion matches the α-reliable minimax criterion closely.

Mean-variance trade-offs in supply contracts

Abstract: We study the trade-offs faced by a manufacturer signing a portfolio of long-term contracts with its suppliers and having access to a spot market. The manufacturer incurs inventory risk when purchasing too many contracts and spot price risk when buying too few. We quantify these risks for a single selling period by studying the profit mean and variance for a given portfolio of option contracts. We characterize the set of efficient portfolios that the manufacturer must hold in order to obtain dominating mean-variance pairs. Among these, we emphasize the maximum expectation portfolio, obtained by solving the classical newsvendor problem, and the corresponding minimum variance portfolio. We show that the upper-level sets of a mean-variance utility function are connected. Hence, a greedy method will find the portfolios on the efficient frontier. Finally, we provide a comparison with standard hedging strategies and show that the approximation associated with financial hedging can be relatively inaccurate. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006

Aircraft routing under the risk of detection

Abstract: The deterministic problem for finding an aircraft's optimal risk trajectory in a threat environment has been formulated. The threat is associated with the risk of aircraft detection by radars or similar sensors. The model considers an aircraft's trajectory in three-dimensional (3-D) space and represents the aircraft by a symmetrical ellipsoid with the axis of symmetry directing the trajectory. Analytical and discrete optimization approaches for routing an aircraft with variable radar cross-section (RCS) subject to a constraint on the trajectory length have been developed. Through techniques of Calculus of Variations, the analytical approach reduces the original risk optimization problem to a vectorial nonlinear differential equation. In the case of a single detecting installation, a solution to this equation is expressed by a quadrature. A network optimization approach reduces the original problem to the Constrained Shortest Path Problem (CSPP) for a 3-D network. The CSPP has been solved for various ellipsoid shapes and different length constraints in cases with several radars. The impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact of variable RCS on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Emergency transshipment in decentralized dealer networks: When to send and accept transshipment requests

Abstract: While there has been significant previous literature on inventory transshipment, most research has focused on the dealers' demand filling decision (when to fill transshipment requests from other dealers), ignoring the requesting decision (when to send transshipment requests to other dealers). In this paper we develop optimal inventory transshipment policies that incorporate both types of decisions. We consider a decentralized system in which the dealers are independent of the manufacturer and of each other. We first study a network consisting of a very large number of dealers. We prove that the optimal inventory and transshipment decisions for an individual dealer are controlled by threshold rationing and requesting levels. Then, in order to study the impact of transshipment among independent dealers in a smaller dealer network, we consider a decentralized two-dealer network and use a game theoretic approach to characterize the equilibrium inventory strategies of the individual dealers. An extensive numerical study highlights the impact of the requesting decision on the dealers' equilibrium behavior in a decentralized setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

A multilevel passenger screening problem for aviation security

Abstract: Passenger prescreening is a critical component of aviation security systems. This paper introduces the Multilevel Allocation Problem (MAP), which models the screening of passengers and baggage in a multilevel aviation security system. A passenger is screened by one of several classes, each of which corresponds to a set of procedures using security screening devices, where passengers are differentiated by their perceived risk levels. Each class is defined in terms of its fixed cost (the overhead costs), its marginal cost (the additional cost to screen a passenger), and its security level. The objective of MAP is to assign each passenger to a class such that the total security is maximized subject to passenger assignments and budget constraints. This paper shows that MAP is NP-hard and introduces a Greedy heuristic that obtains approximate solutions to MAP that use no more than two classes. Examples are constructed using data extracted from the Official Airline Guide. Analysis of the examples suggests that fewer security classes for passenger screening may be more effective and that using passenger risk information can lead to more effective security screening strategies. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Equity valuation, production, and financial planning: A stochastic programming approach

Abstract: Most of the operations management literature assumes that a firm can always finance production decisions at an optimal level or borrow at a constant interest rate; however, operational decisions are constrained by limited capital and often critically depend on external financing. This paper proposes an integrated corporate planning model, which extends the forecasting-based discount dividend pricing method into an optimization-based valuation framework to make production and financial decisions simultaneously for a firm facing marker uncertainty. We also develop an efficient algorithm to solve the resulting integer stochastic programming model with nonlinear constraints. Compared with traditional valuation and planning models, our method yields higher equity valuations, indicating that valuation without considering contingent decisions is inherently inaccurate. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Fully Sequential Indifference-Zone Selection Procedures with Variance-Dependent Sampling

Abstract: Fully sequential indifference-zone selection procedures have been proposed in the simulation literature to select the system with the best mean performance from a group of simulated systems. However, the existing sequential indifference-zone procedures allocate an equal number of samples to the two systems in comparison even if their variances are drastically different. In this paper we propose new fully sequential indifference-zone procedures that allocate samples according to the variances. We show that the procedures work better than several existing sequential indifference-zone procedures when variances of the systems are different. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 53: 464-476, 2006

Financial Engineering of the Integration of Global Supply Chain Networks and Social Networks with Risk Management

Abstract: In this paper, we focus on the financial engineering of integrated global supply chain networks and social networks. Through a multilevel, dynamic supernetwork framework consisting of the global supply chain network with electronic commerce and the social network, we capture the multicriteria decision-making behavior of the various decision-makers (manufacturers, retailers, and consumers), which includes the maximization of profit, the maximization of relationship values, and the minimization of risk. Relationship levels in our framework are assumed to influence transaction costs as well as risk and to have value for the decision-makers. We explore the dynamic co-evolution of the global product transactions, the associated product prices, and the relationship levels on the supernetwork until an equilibrium pattern is achieved. The pricing mechanism guarantees that optimality for each decision-maker is achieved in the financially engineered multitiered, multilevel supernetwork. We provide some qualitative properties of the dynamic trajectories, under suitable assumptions, and propose a discrete-time algorithm, which yields explicit closed form expressions at each iteration for the tracking of the evolution of the global product transactions, relationship levels, and prices until an equilibrium is attained. We illustrate the model and computational procedure with several numerical examples.

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

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

Resale price maintenance contracts with retailer sales effort: Effect of flexibility and competition

Abstract: In Resale Price Maintenance (RPM) contracts, the manufacturer specifies the resale price that retailers must charge to consumers. We study the role of using a RPM contract in a market where demand is influenced by retailer sales effort. First, it is well known that RPM alone does not provide incentive for the retailer to use adequate sales effort and some form of quantity fixing may be needed to achieve channel coordination. However, when the market potential of the product is uncertain, RPM with quantity fixing is a rigid contract form. We propose and study a variety of RPM contracts with quantity fixing that offer different forms of flexibility including pricing flexibility and quantity flexibility. Second, we address a long-time debate in both academia and practice on whether RPM is anti-competitive in a market when two retailers compete on both price and sales effort. We show that depending on the relative intensity of price competition and sales effort competition, RPM may lead to higher or lower retail prices compared to a two-part tariff contract, which specifies a wholesale price and a fixed fee. Further, the impact of RPM on price competition and sales effort competition is always opposite to each other. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

Abstract: We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single-period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function. For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win–win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor-managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor-managed delivery arrangement that potentially improves the centralized solution. Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single-period setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

A general strategic capacity planning model under demand uncertainty

Abstract: Capacity planning decisions affect a significant portion of future revenue. In equipment intensive industries, these decisions usually need to be made in the presence of both highly volatile demand and long capacity installation lead times. For a multiple product case, we present a continuous-time capacity planning model that addresses problems of realistic size and complexity found in current practice. Each product requires specific operations that can be performed by one or more tool groups. We consider a number of capacity allocation policies. We allow tool retirements in addition to purchases because the stochastic demand forecast for each product can be decreasing. We present a cluster-based heuristic algorithm that can incorporate both variance reduction techniques from the simulation literature and the principles of a generalized maximum flow algorithm from the network optimization literature. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Approximate dynamic programming methods for an inventory allocation problem under uncertainty

Abstract: We propose two approximate dynamic programming methods to optimize the distribution operations of a company manufacturing a certain product at multiple production plants and shipping it to different customer locations for sale. We begin by formulating the problem as a dynamic program. Our first approximate dynamic programming method uses a linear approximation of the value function and computes the parameters of this approximation by using the linear programming representation of the dynamic program. Our second method relaxes the constraints that link the decisions for different production plants. Consequently, the dynamic program decomposes by the production plants. Computational experiments show that the proposed methods are computationally attractive, and in particular, the second method performs significantly better than standard benchmarks.

An EOQ model with multiple suppliers and random capacity

Abstract: We consider an EOQ model with multiple suppliers that have random capacities, which leads to uncertain yield in orders. A given order is fully received from a supplier if the order quantity is less than the supplier's capacity; otherwise, the quantity received is equal to the available capacity. The optimal order quantities for the suppliers can be obtained as the unique solution of an implicit set of equations in which the expected unsatisfied order is the same for each supplier. Further characterizations and properties are obtained for the uniform and exponential capacity cases with discussions on the issues related to diversification among suppliers. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

A misclassification cost-minimizing evolutionary-neural classification approach

Abstract: Machine learning algorithms that incorporate misclassification costs have recently received considerable attention. In this paper, we use the principles of evolution to develop and test an evolutionary/genetic algorithm (GA)-based neural approach that incorporates asymmetric Type I and Type II error costs. Using simulated, real-world medical and financial data sets, we compare the results of the proposed approach with other statistical, mathematical, and machine learning approaches, which include statistical linear discriminant analysis, back-propagation artificial neural network, integrated cost preference-based linear mathematical programming-based minimize squared deviations, linear integrated cost preference-based GA, decision trees (C 5.0, and CART), and inexpensive classification with expensive tests algorithm. Our results indicate that the proposed approach incorporating asymmetric error costs results in equal or lower holdout sample misclassification cost when compared with the other statistical, mathematical, and machine learning misclassification cost-minimizing approaches. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.

The stochastic joint replenishment problem: A new policy, analysis, and insights

Abstract: In this study, we propose a new parsimonious policy for the stochastic joint replenishment problem in a single-location, N-item setting. The replenishment decisions are based on both group reorder point-group order quantity and the time since the last decision epoch. We derive the expressions for the key operating characteristics of the inventory system for both unit and compound Poisson demands. In a comprehensive numerical study, we compare the performance of the proposed policy with that of existing ones over a standard test bed. Our numerical results indicate that the proposed policy dominates the existing ones in 100 of 139 instances with comparably significant savings for unit demands. With batch demands, the savings increase as the stochasticity of demand size gets larger. We also observe that it performs well in environments with low demand diversity across items. The inventory system herein also models a two-echelon setting with a single item, multiple retailers, and cross docking at the upper echelon. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Inducing coordination in supply chains through linear reward schemes

Abstract: Decentralized decision-making in supply chain management is quite common, and often inevitable, due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision-making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi-agent operations management settings. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Bin-packing problem with concave costs of bin utilization

Abstract: We consider a generalized one-dimensional bin-packing model where the cost of a bin is a nondecreasing concave function of the utilization of the bin. Four popular heuristics from the literature of the classical bin-packing problem are studied: First Fit (FF), Best Fit (BF), First Fit Decreasing (FFD), and Best Fit Decreasing (BFD). We analyze their worst-case performances when they are applied to our model. The absolute worst-case performance ratio of FF and BF is shown to be exactly 2, and that of FFD and BFD is shown to be exactly 1.5. Computational experiments are also conducted to test the performance of these heuristics. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

A branch-and-price algorithm for parallel machine scheduling with time windows and job priorities

Abstract: This paper presents a branch-and-price algorithm for scheduling n jobs on m nonhomogeneous parallel machines with multiple time windows. An additional feature of the problem is that each job falls into one of ρ priority classes and may require two operations. The objective is to maximize the weighted number of jobs scheduled, where a job in a higher priority class has "infinitely" more weight or value than a job in a lower priority class. The methodology makes use of a greedy randomized adaptive search procedure (GRASP) to find feasible solutions during implicit enumeration and a two-cycle elimination heuristic when solving the pricing subproblems. Extensive computational results are presented based on data from an application involving the use of communications relay satellites. Many 100-job instances that were believed to be beyond the capability of exact methods, were solved within minutes. © 2005 Wiley Periodicals, Inc. Naval Research Logistics 53: 24-44, 2006.

Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

Abstract: We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP-hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two-phase heuristics and dynamic two-phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Optimal production and maintenance policy for imperfect production systems

Abstract: A joint optimization of the production run length and preventive maintenance (PM) policy is studied for a deteriorating production system where the in-control period follows a general probability distribution with non-decreasing failure rate. In the literature, the sufficient conditions for the optimality of the equal-interval PM schedule is explored to derive an optimal production run length and an optimal number of PM actions. Nevertheless, an exhaustive search may arise. In this study, based on the assumption that the conditions for the optimality of the equal-interval PM schedule hold, we derive some structural properties for the optimal production/PM policy, which increases the efficiency of the solution procedure. These analyses have implications for the practical application of the production/PM model to be more available in practice. A numerical example of gamma shift distribution with non-decreasing failure rates is used to illustrate the solution procedure, leading to some insight into the management process. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Relaxed sequencing games have a nonempty core

Abstract: We study sequencing situations with a fixed initial order and linear cost functions. Cost savings can be obtained by rearranging jobs. Next to finding an optimal order, an additional issue is formed by the division of these savings. Cooperative game theory studies this issue. A common assumption states that cooperation between players is restricted to groups that are connected according to the initial order. The value of disconnected groups is defined additively over their connected components. In this paper we allow players in disconnected coalitions to switch places as long as they do not hurt the players not in the coalition under consideration. The resulting games are called relaxed sequencing games. Although they have been studied before, no general results on stable profit divisions have been derived so far. In this paper we prove that relaxed sequencing games have a nonempty core, i.e., they all have stable profit divisions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006