Showing papers in "Naval Research Logistics in 2004"

Crane scheduling with spatial constraints

Abstract: In this work, we examine port crane scheduling with spatial and separation constraints. Although common to most port operations, these constraints have not been previously studied. We assume that cranes cannot cross, there is a minimum distance between cranes and jobs cannot be done simultaneously. The objective is to find a crane-to-job matching which maximizes throughput under these constraints. We provide dynamic programming algorithms, a probabilistic tabu search, and a squeaky wheel optimization heuristic for solution. Experiments show the heuristics perform well compared with optimal solutions obtained by CPLEX for small scale instances where a squeaky wheel optimization with local search approach gives good results within short times. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Dynamic inventory and pricing models for competing retailers

Abstract: We address infinite-horizon models for oligopolies with competing retailers under demand uncertainty. We characterize the equilibrium behavior which arises under simple wholesale pricing schemes. More specifically, we consider a periodic review, infinite-horizon model for a two-echelon system with a single supplier servicing a network of competing retailers. In every period, each retailer faces a random demand volume, the distribution of which depends on his own retail price as well as those charged by possibly all competing retailers. We also derive various comparative statics results regarding the impact several exogenous system parameters (e.g., cost or distributional parameters) have on the equilibrium decisions of the retailers as well as their expected profits. We show that certain monotonicity properties, engrained in folklore as well as in known inventory models for centralized systems, may break down in decentralized chains under retailer competition. Our results can be used to optimize the aggregate profits in the supply chain (i.e., those of the supplier and all retailers) by implementing a specific wholesale pricing scheme. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Modeling and analysis of flexible queueing systems

Abstract: We consider queueing systems with multiple classes of customers and heteroge- neous servers where customers have the flexibility of being processed by more than one server and servers possess the capability of processing more than one customer class. We provide a unified framework for the modeling and analysis of these systems under arbitrary customer and server flexibility and for a rich set of control policies that includes customer/server-specific priority schemes for server and customer selection. We use our models to generate several insights into the effect of system configuration and control policies. In particular, we examine the relationship between flexibility, control policies and throughput under varying assumptions for system parameters. © 2004 Wiley Periodicals, Inc. Naval Research Logistics 51: 755-782, 2004. In this paper, we consider the modeling and analysis of flexible queueing systems. We use the term flexible queueing systems to refer to systems with heterogeneous servers and multiple customer classes where customers have the flexibility of being processed by more than one server and servers possess the capability of processing more than one customer class. Customer classes can vary in demand rate and routing flexibility. Servers can vary in service rates and service flexibility. The assignment of customers to servers is determined by a server selection rule, that can be customer-specific, and the selection of the next customer to serve is determined by a queue selection rule, that can be server-specific. An example of a flexible queueing system is shown in Figure 1. Flexible queueing systems arise in a variety of contexts, including manufacturing (Buzacott and Shanthikumar (8)), telecommunication networks (Ross (23)), computer systems (Kleinrock

Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

Abstract: Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17 (1988), 1857–1870] considered a hybrid censoring scheme and obtained the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution along with an exact lower confidence bound. Childs et al. [Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Ann Inst Statist Math 55 (2003), 319–330] recently derived an alternative simpler expression for the distribution of the MLE. These authors also proposed a new hybrid censoring scheme and derived similar results for the exponential model. In this paper, we propose two generalized hybrid censoring schemes which have some advantages over the hybrid censoring schemes already discussed in the literature. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under these generalized hybrid censoring schemes. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

The gradual covering problem

Abstract: In this paper we investigate the gradual covering problem. Within a certain distance from the facility the demand point is fully covered, and beyond another specified distance the demand point is not covered. Between these two given distances the coverage is linear in the distance from the facility. This formulation can be converted to the Weber problem by imposing a special structure on its cost function. The cost is zero (negligible) up to a certain minimum distance, and it is a constant beyond a certain maximum distance. Between these two extreme distances the cost is linear in the distance. The problem is analyzed and a branch and bound procedure is proposed for its solution. Computational results are presented. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Discriminating between the Weibull and log‐normal distributions

Abstract: Log-normal and Weibull distributions are the most popular distributions for modeling skewed data. In this paper, we consider the ratio of the maximized likelihood in choosing between the two distributions. The asymptotic distribution of the logarithm of the maximized likelihood ratio has been obtained. It is observed that the asymptotic distribution is independent of the unknown parameters. The asymptotic distribution has been used to determine the minimum sample size required to discriminate between two families of distributions for a user specified probability of correct selection. We perform some numerical experiments to observe how the asymptotic methods work for different sample sizes. It is observed that the asymptotic results work quite well even for small samples also. Two real data sets have been analyzed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Two-dimensional failure modeling with minimal repair

Abstract: In this paper, we discuss two-dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one-dimensional case to the two-dimensional case and characterize the failures over a two-dimensional region under minimal repair. An application of this important result to a rnanufacturer's servicing costs for a two-dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. (C) 2003 Wiley Periodicals, Inc.

Higher-order Markov chain models for categorical data sequences*

Abstract: In this paper we study higher-order Markov chain models for analyzing categorical data sequences. We propose an efficient estimation method for the model parameters. Data sequences such as DNA and sales demand are used to illustrate the predicting power of our proposed models. In particular, we apply the developed higher-order Markov chain model to the server logs data. The objective here is to model the users' behavior in accessing information and to predict their behavior in the future. Our tests are based on a realistic web log and our model shows an improvement in prediction. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

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

Abstract: 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 di erent, 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 di erent 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 di erent types of strongly NP-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.

Fitting Lanchester equations to the battles of Kursk and Ardennes

Abstract: Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good-fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Facility location models for immobile servers with stochastic demand

Abstract: This paper presents several models for the location of facilities subject to congestion. Motivated by applications to locating servers in communication networks and automatic teller machines in bank systems, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. We consider this problem from three different perspectives, that of (i) the service provider (wishing to limit costs of setup and operating servers), (ii) the customers (wishing to limit costs of accessing and waiting for service), and (iii) both the service provider and the customers combined. In all cases, a minimum level of service quality is ensured by imposing an upper bound on the server utilization rate at a service facility. The latter two perspectives also incorporate queueing delay costs as part of the objective. Some cases are amenable to an optimal solution. For those cases that are more challenging, we either propose heuristic procedures to find good solutions or establish equivalence to other well-studied facility location problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Warranty costs: An age‐dependent failure/repair model

Abstract: An age-dependent repair model is proposed The notion of the “calendar age” of the product and the degree of repair are used to define the virtual age of the product The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed Under a nonhomogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro-rata, nonrenewing free replacement and renewing free replacement warranties are evaluated Illustration of the results is given by numerical and graphical examples © 2004 Wiley Periodicals, Inc Naval Research Logistics, 2004

Designing acceptance sampling schemes for life testing with mixed censoring

Abstract: Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time-consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Efficient distributions of arms-control inspection effort

Abstract: A rule that constrains decision-makers is enforced by an inspector who is supplied with a fixed level of inspection resources - inspection personnel, equipment, or time. How should the inspector distribute its inspection resources over several independent inspectees? What minimum level of resources is required to deter all violations? Optimal enforcement problems occur in many contexts; the motivating application for this study is the role of the International Atomic Energy Agency in support of the Treaty on the Non-Proliferation of Nuclear Weapons. Using game-theoretic models, the resource level adequate for deterrence is characterized in a two-inspectee problem with inspections that are imperfect in the sense that violations can be missed. Detection functions, or probabilities of detecting a violation, are assumed to be increasing in inspection resources, permitting optimal allocations over inspectees to be described both in general and in special cases. When detection functions are convex, inspection effort should be concentrated on one inspectee chosen at random, but when they are concave it should be spread deterministicly over the inspectees. Our analysis provides guidance for the design of arms-control verification operations, and implies that a priori constraints on the distribution of inspection effort can result in significant inefficiencies.

Economic ordering decisions with market choice flexibility

Abstract: Standard approaches to classical inventory control problems treat satisfying a predefined demand level as a constraint. In many practical contexts, however, total demand is comprised of separate demands from different markets or customers. It is not always clear that constraining a producer to satisfy all markets is an optimal approach. Since the inventory-related cost of an item depends on total demand volume, no clear method exists for determining a market's profitability a priori, based simply on per unit revenue and cost. Moreover, capacity constraints often limit a producer's ability to meet all demands. This paper presents models to address economic ordering decisions when a producer can choose whether to satisfy multiple markets. These models result in a set of nonlinear binary integer programming problems that, in the uncapacitated case, lend themselves to efficient solution due to their special structure. The capacitated versions can be cast as nonlinear knapsack problems, for which we propose a heuristic solution approach that is asymptotically optimal in the number of markets. The models generalize the classical EOQ and EPQ problems and lead to interesting optimization problems with intuitively appealing solution properties and interesting implications for inventory and pricing management. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Preservation of stochastic orders for random minima and maxima, with applications

Abstract: It is shown, in this note, that the right spread order and the increasing convex order are both preserved under the taking of random maxima, and the total time on test transform order and the increasing concave order are preserved under the taking of random minima. Some inequalities and preservation properties in reliability and economics are given as applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Radar pulse interleaving for multi-target tracking

Abstract: In a multifunction radar, the maximum number of targets that can be managed or tracked is an important performance measure. Interleaving algorithms developed to operate radars exploit the dead-times between the transmitted and the received pulses to allocate new tracking tasks that might involve transmitting or receiving pulses, thus increasing the capacity of the system. The problem of interleaving N targets involves a search among N! possibilities, and suboptimal solutions are usually employed to satisfy the real-time constraints of the radar system. In this paper, we present new tight 0–1 integer programming models for the radar pulse interleaving problem and develop effective solution methods based on Lagrangian relaxation techniques. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

An FPTAS for scheduling a two-machine flowshop with one unavailability interval

Abstract: We study a deterministic two-machine flowshop scheduling problem with an assumption that one of the two machines is not available in a specified time period. This period can be due to a breakdown, preventive maintenance, or processing unfinished jobs from a previous planning horizon. The problem is known to be NP-hard. Pseudopolynomial dynamic programming algorithms and heuristics with worst case error bounds are given in the literature to solve the problem. They are different for the cases when the unavailability interval is for the first or second machine. The existence of a fully polynomial time approximation scheme (FPTAS) was formulated as an open conjecture in the literature. In this paper, we show that the two cases of the problem under study are equivalent to similar partition type problems. Then we derive a generic FPTAS for the latter problems with O(n5/e4) time complexity. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Strategies for managing the flexible capacity in the airline industry

Abstract: The ability to effectively match supply and demand under uncertainty can result in significant revenue benefits in the airline industry. We study the benefits of a Demand Driven Swapping (DDS) approach that takes advantage of the flexibilities in the system and dynamically swaps aircraft as departures near and more accurate demand information is obtained. We analyze the effectiveness of different DDS strategies, characterized by their frequency (how often the swapping decision is revised), in hedging against demand uncertainty. Swapping aircraft several weeks prior to departures will not cause much disturbance to revenue management and operations, but will be based on highly uncertain demands. On the other hand, revising the swapping decision later will decrease the possibility of bad swaps, but at a higher cost of disrupting airport services and operations. Our objective is to provide guidelines on how the flexible (swappable) capacity should be managed in the system. We study analytical models to gain insights into the critical parameters that affect the revenue benefits of the different swapping strategies. Our study determines the conditions under which each of the different DDS strategies is effective. We complement our analysis by testing the proposed DDS strategies on a set of flight legs, using data obtained from United Airlines. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

A balancing problem for mixed model assembly lines with a paced moving conveyor

Abstract: We state a balancing problem for mixed model assembly lines with a paced moving conveyor as: Given the daily assembling sequence of the models, the tasks of each model, the precedence relations among the tasks, and the operations parameters of the assembly line, assign the tasks of the models to the workstations so as to minimize the total overload time. Several characteristics of the problem are investigated. A line-balancing heuristic is proposed based on a lower bound of the total overload time. A practical procedure is provided for estimating the deviation of any given line-balance solution from the theoretical optimum. Numerical examples are given to illustrate the methodology. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

An adaptive forecasting algorithm and inventory policy for products with short life cycles

Abstract: Products with short life cycles are becoming increasingly common in many industries, such as the personal computer (PC) and mobile phone industries. Traditional forecasting methods and inventory policies can be inappropriate for forecasting demand and managing inventory for a product with a short life cycle because they usually do not take into account the characteristics of the product life cycle. This can result in inaccurate forecasts, high inventory cost, and low service levels. Besides, many forecasting methods require a significant demand history, which is available only after the product has been sold for some time. In this paper, we present an adaptive forecasting algorithm with two characteristics. First, it uses structural knowledge on the product life cycle to model the demand. Second, it combines knowledge on the demand that is available prior to the launch of the product with actual demand data that become available after the introduction of the product to generate and update demand forecasts. Based on the forecasting algorithm, we develop an optimal inventory policy. Since the optimal inventory policy is computationally expensive, we propose three heuristics and show in a numerical study that one of the heuristics generates near-optimal solutions. The evaluation of our approach is based on demand data from a leading PC manufacturer in the United States, where the forecasting algorithm has been implemented. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

A sequential dynamic pricing model and its applications

Abstract: Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous-time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Revenue management: A real options approach

Abstract: Revenue management is the process of actively managing inventory or capacity to maximize revenues. The active management typically occurs through managerial levers such as price, promotion, or availability. We present a novel real options approach to revenue management that is specifically suited to the car rental business. We illustrate the concept with actual car rental data. The model produces minimally acceptable prices and inventory release quantities (number of cars available for rent at a given price) as a function of remaining time and available inventory. The pricing and inventory release recommendations of the developed model confirm earlier empirical analysis that suggested current practises discount too deeply early in the booking cycle. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Lot streaming with supplier–manufacturer coordination

Abstract: Lot splitting refers to breaking a production lot into smaller sublots during production. Coordinating lot splitting decisions across multiple stages of a production process is a challenging task. Traditional lot splitting and lot streaming models implicitly assume that the entire system is operated and owned by the same firm, or there exists a coordinator who controls the operation of all machines in the system. In this paper, we consider the situation where the machines in a multiple-stage production process are owned and managed by different companies. Every item in a given production lot has to go through the processing by the supplier's machine, followed by the manufacturer's machine, and so on. We develop and analyze coordination mechanisms that enable different parties in the supply chain to coordinate their lot splitting decisions so as to achieve a systemwide optimum. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Coordinating independent buyers with integer‐ratio time coordination and quantity discounts

Abstract: Supply chain members can gain substantial benefits by coordinating their activities. However, a remaining challenge is to create useful coordination mechanisms when channel members are independent. This paper develops a coordination strategy with which a supplier uses quantity discounts to entice independent buyers to comply with an integer-ratio time coordination scheme. The problem is analyzed as a Stackelberg game in which the supplier acts as the leader by announcing its coordination policy in advance and buyers act as followers by deciding their ordering decisions with this information. The strategy is compared to a coordination mechanism with quantity discounts and power-of-two time coordination. While both strategies are able to produce substantial benefits over simple quantity discounts, integer-ratio time coordination provides a better coordination mechanism for a decentralized supply chain. It is shown that power-of-two time coordination may not be able to provide a stable equilibrium coordination strategy when buyers act independently and opportunistically. Furthermore, if this is not the case, integer-ratio time coordination is at least equally effective. Unlike a centralized solution, under which the improvement by integer-ratio over power-of-two time coordination is limited to 2% of optimality, system cost reduction from a decentralized coordination strategy could be much more significant. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

The (s, Q) inventory model with Erlang lead time and deterministic demand

Abstract: We develop a simple, approximately optimal solution to a model with Erlang lead time and deterministic demand. The method is robust to misspecification of the lead time and has good accuracy. We compare our approximate solution to the optimal for the case where we have prior information on the lead-time distribution, and another where we have no information, except for computer-generated sample data. It turns out that our solution is as easy as the EOQ's, with an accuracy rate of 99.41% when prior information on the lead-time distribution is available and 97.54–99.09% when only computer-generated sample information is available. Apart from supplying the inventory practitioner with an easy heuristic, we gain insights into the efficacy of stochastic lead time models and how these could be used to find the cost and a near-optimal policy for the general model, where both demand rate and lead time are stochastic. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

A note on scheduling parallel machines subject to breakdown and repair

Abstract: In this paper we consider n jobs and a number of machines in parallel. The machines are identical and subject to breakdown and repair. The number may therefore vary over time and is at time t equal to m(t). Preemptions are allowed. We consider three objectives, namely, the total completion time, ∑ Cj, the makespan Cmax, and the maximum lateness Lmax. We study the conditions on m(t) under which various rules minimize the objective functions under consideration. We analyze cases when the jobs have deadlines to meet and when the jobs are subject to precedence constraints. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Stochastic scheduling subject to machine breakdowns: The preemptive-repeat model with discounted reward and other criteria

Abstract: We consider the problem of scheduling a set of jobs on a single machine subject to random breakdowns We focus on the preemptive-repeat model, which addresses the situation where, if a machine breaks down during the processing of a job, the work done on the job prior to the breakdown is lost and the job will have to be started from the beginning again when the machine resumes its work We allow that (i) the uptimes and downtimes of the machine follow general probability distributions, (ii) the breakdown process of the machine depends upon the job being processed, (iii) the processing times of the jobs are random variables following arbitrary distributions, and (iv) after a breakdown, the processing time of a job may either remain a same but unknown amount, or be resampled according to its probability distribution We first derive the optimal policy for a class of problems under the criterion to maximize the expected discounted reward earned from completing all jobs The result is then applied to further obtain the optimal policies for other due date-related criteria We also discuss a method to compute the moments and probability distributions of job completion times by using their Laplace transforms, which can convert a general stochastic scheduling problem to its deterministic equivalent The weighted squared flowtime problem and the maintenance checkup and repair problem are analyzed as applications © 2004 Wiley Periodicals, Inc Naval Research Logistics, 2004

Single machine parallel batch scheduling subject to precedence constraints

Abstract: We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP-hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O(n2) time algorithm to minimize the makespan. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Due‐window assignment with unit processing‐time jobs

Abstract: In due-window assignment problems, jobs completed within a designated time interval are regarded as being on time, whereas early and tardy jobs are penalized. The objective is to determine the location and size of the due-window, as well as the job schedule. We address a common due-window assignment problem on parallel identical machines with unit processing time jobs. We show that the number of candidate values for the optimal due-window starting time and for the optimal due-window completion time are bounded by 2. We also prove that the starting time of the first job on each of the machines is either 0 or 1, thus introducing a fairly simple, constant-time solution for the problem. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004