Showing papers in "Naval Research Logistics in 2012"

A spatial rank‐based multivariate EWMA control chart

Abstract: Nonparametric control charts are useful in statistical process control when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate self-starting methodology for monitoring location parameters. It is based on adapting the multivariate spatial rank to on-linesequentialmonitoring.Theweightedversionoftherank-basedtestisusedtoformulatethechartingstatisticbyincorporating the exponentially weighted moving average control scheme. It is robust to non-normally distributed data, easy to construct, fast to compute and also very efficient in detecting multivariate process shifts, especially small or moderate shifts which occur when the process distribution is heavy-tailed or skewed. As it avoids the need for a lengthy data-gathering step before charting and it does not require knowledge of the underlying distribution, the proposed control chart is particularly useful in start-up or short-run situations. A real-data example from white wine production processes shows that it performs quite well. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 91-110, 2012

Weakest-link attacker-defender games with multiple attack technologies†

Abstract: In this article, we examine a model of terrorism that focuses on the tradeoffs facing a terrorist organization that has two qualitatively different attack modes at its disposal. The terrorist organization's objective is to successfully attack at least one target. Success for the target government is defined as defending all targets from any and all attacks. In this context, we examine how terrorist entities strategically utilize an efficient but discrete attack technology - e.g., suicide attacks - when a more conventional mode of attack is available, and the optimal anti-terrorism measures. © Copyright 2012 Wiley Periodicals, Inc.

Models and algorithms for shuffling problems in steel plants

Abstract: In this article, we study item shuffling (IS) problems arising in the logistics system of steel production. An IS problem here is to optimize shuffling operations needed in retrieving a sequence of steel items from a warehouse served by a crane. There are two types of such problems, plate shuffling problems (PSP) and coil shuffling problems (CSP), considering the item shapes. The PSP is modeled as a container storage location assignment problem. For CSP, a novel linear integer programming model is formulated considering the practical stacking and shuffling features. Several valid inequalities are constructed to accelerate the solving of the models. Some properties of optimal solutions of PSP and CSP are also derived. Because of the strong NP-hardness of the problems, we consider some special cases of them and propose polynomial time algorithms to obtain optimal solutions for these cases. A greedy heuristic is proposed to solve the general problems and its worst-case performances on both PSP and CSP are analyzed. A tabu search (TS) method with a tabu list of variable length is proposed to further improve the heuristic solutions. Without considering the crane traveling distance, we then construct a rolling variable horizon heuristic for the problems. Numerical experiments show that the proposed heuristic algorithms and the TS method are effective. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Inventory pooling games for expensive, low‐demand spare parts

Abstract: We consider several independent decision makers who stock expensive, low-demand spare parts for their high-tech machines. They can collaborate by full pooling of their inventories via free transshipments. We examine the stability of such pooling arrangements, and we address the issue of fairly distributing the collective holding and downtime costs over the participants, by applying concepts from cooperative game theory. We consider two settings: one where each party maintains a predetermined stocking level and one where base stock levels are optimized. For the setting with fixed stocking levels, we unravel the possibly conflicting effects of implementing a full pooling arrangement and study these effects separately to establish intuitive conditions for existence of a stable cost allocation. For the setting with optimized stocking levels, we provide a simple proportional rule that accomplishes a population monotonic allocation scheme if downtime costs are symmetric among participants. Although our whole analysis is motivated by spare parts applications, all results are also applicable to other pooled resource systems of which the steady-state behavior is equivalent to that of an Erlang loss system. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost

Abstract: In the last decade, there has been much progress in understanding scheduling problems in which selfish jobs aim to minimize their individual completion time. Most of this work has focused on makespan minimization as social objective. In contrast, we consider as social cost the total weighted completion time, that is, the sum of the agent costs, a standard definition of welfare in economics. In our setting, jobs are processed on restricted uniform parallel machines, where each machine has a speed and is only capable of processing a subset of jobs; a job's cost is its weighted completion time; and each machine sequences its jobs in weighted shortest processing time (WSPT) order. Whereas for the makespan social cost the price of anarchy is not bounded by a constant in most environments, we show that for our minsum social objective the price of anarchy is bounded above by a small constant, independent of the instance. Specifically, we show that the price of anarchy is exactly 2 for the class of unit jobs, unit speed instances where the finite processing time values define the edge set of a forest with the machines as nodes. For the general case of mixed job strategies and restricted uniform machines, we prove that the price of anarchy equals 4. From a classical machine scheduling perspective, our results establish the same constant performance guarantees for WSPT list scheduling. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

An efficient metaheuristic for integrated scheduling and staffing IT projects based on a generalized minimum cost flow network

Abstract: Scheduling IT projects and assigning the project work to human resources are an important and common tasks in almost any IT service company. It is particularly complex because human resources usually have multiple skills. Up to now only little work has considered IT-specific properties of the project structure and human resources. In this article, we present an optimization model that simultaneously schedules the activities of multiple IT projects with serial network structures and assigns the project work to multiskilled internal and external human resources with different efficiencies. The goal is to minimize costs. We introduce a metaheuristic that decomposes the problem into a binary scheduling problem and a continuous staffing problem where the latter is solved efficiently by exploiting its underlying network structure. For comparison, we solve the mixed–binary linear program with a state–of–the–art commercial solver. The impacts of problem parameters on computation time and solution gaps between the metaheuristic and the solver are assessed in an experimental study. Our results show that the metaheuristic provides very favorable results in considerable less time than the solver for midsize problems. For larger problems, it shows a similar performance while the solver fails to return feasible solutions. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 111–127, 2012

Equilibrium analysis of capacity allocation with demand competition

Abstract: This article examines the capacity allocation decisions in a supply chain in which a supplier sells a common product to two retailers at a fixed wholesale price. The retailers order the supplier's product subject to an allocation mechanism preannounced by the supplier, and compete for the customer demand. We perform an equilibrium analysis of the retailers' ordering decisions under uniform and individually responsive allocations. Uniform allocation guarantees equilibrium orders, but is not necessarily truth inducing in the presence of demand competition. Further, we find that (1) neither the supplier nor either one of the retailers sees its profits necessarily increasing with the supplier's capacity, and the supplier may sell more with a lower capacity level, and (2) capacity allocation may not only affect the supply chain members' profits but also change the supply chain structure by driving a retailer out of the market. This article provides managerial insights on the capacity and ordering decisions for the supplier, the Capacity allocation frequently occurs in supply chains when multiple retailers order a product from a common sup- plier. Capacity is subject to allocation when the supplier's capacity is unable to meet retailer demand. Further, the retail- ers may compete for customer demand for the product. This work is specifically motivated by a capacity allocation prob- lem in the automobile industry. Automobile manufacturers often sell the same model vehicles to multiple dealers in the same geographic region at a fixed wholesale price. The deal- ers are allowed to determine their own retail prices, which are typically lower than the manufacturer's suggested retail price. In this case, the dealers compete for both the manufac- turer's vehicle allocation and their customer demand. Similar capacity allocation also occurs in the sales of office and home supplies, electronics products, textile and apparel products, and so forth. This article examines the capacity allocation decisions in a supply chain, in which a supplier sells a common product to two retailers. The supplier charges a fixed wholesale price and allocates his capacity based on the order sizes of the two retailers, using a preannounced capacity allocation mecha- nism. The retailers order from the supplier and compete for

Nested column generation applied to the crude oil tanker routing and scheduling problem with split pickup and split delivery

Abstract: The split pickup split delivery crude oil tanker routing and scheduling problem is a difficult combinatorial optimization problem, both theoretically and practically. However, because of the large expenses in crude oil shipping it is attractive to make use of optimization that exploits as many degrees of freedom as possible to save transportation cost. We propose a nested column generation algorithm for this particular split pickup split delivery problem which bears several complexities such as a heterogeneous fleet, multiple commodities, many-to-many relations for pickup and delivery of each commodity, sequence dependent vehicle capacities, and cargo quantity dependent pickup and delivery times. Our approach builds on a branch-and-price algorithm in which the column generation subproblems are solved by branch-and-price themselves. We describe our implementation in the branch-cut-and-price framework SCIP and give computational results for realistic test instances. The high quality schedules we obtain for these instances improve on those in previous studies. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Optimization of schedule stability and efficiency under processing time variability and random machine breakdowns in a job shop environment

Abstract: The ability to cope with uncertainty in dynamic scheduling environments is becoming an increasingly important issue. In such environments, any disruption in the production schedule will translate into a disturbance of the plans for several external activities as well. Hence, from a practical point of view, deviations between the planned and realized schedules are to be avoided as much as possible. The term stability refers to this concern. We propose a proactive approach to generate efficient and stable schedules for a job shop subject to processing time variability and random machine breakdowns. In our approach, efficiency is measured by the makespan, and the stability measure is the sum of the variances of the realized completion times. Because the calculation of the original measure is mathematically intractable, we develop a surrogate stability measure. The version of the problem with the surrogate stability measure is proven to be NP-hard, even without machine breakdowns; a branch-and-bound algorithm is developed for this problem variant. A tabu search algorithm is proposed to handle larger instances of the problem with machine breakdowns. The results of extensive computational experiments indicate that the proposed algorithms are quite promising in performance. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Optimal Path Finding in Direction, Location and Time Dependent Environments.

Abstract: This article examines optimal path finding problems where cost function and constraints are direction, location, and time dependent. Recent advancements in sensor and data-processing technology facilitate the collection of detailed real-time information about the environment surrounding a ground vehicle, an airplane, or a naval vessel. We present a navigation model that makes use of such information. We relax a number of assumptions from existing literature on path-finding problems and create an accurate, yet tractable, model suitable for implementation for a large class of problems. We present a dynamic programming model which integrates our earlier results for direction-dependent, time and space homogeneous environment, and consequently, improves its accuracy, efficiency, and run-time. The proposed path finding model also addresses limited information about the surrounding environment, control-feasibility of the considered paths, such as sharpest feasible turns a vehicle can make, and computational demands of a time-dependent environment. To demonstrate the applicability and performance of our path-finding algorithm, computational experiments for a short-range ship routing in dynamic wave-field problem are presented. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging

Abstract: This paper considers a dynamic lot-sizing problem with storage capacity limitation in which backlogging is allowed For general concave production and inventory costs, we present an O(T 2 ) dynamic programming algorithm where is the length of the planning horizon Furthermore, for fixed-charge and nonspeculative costs, we provide O(Tlog T) and O(T) algorithms, respectively This paper therefore concludes that the time complexity to solve the bounded inventory lot-sizing problem with backlogging is the same as the complexity to solve the uncapacitated lot-sizing problem for the commonly used cost structures

Optimal Inventory Control Policy for Periodic-Review Inventory Systems with Inventory-Level-Dependent Demand

Abstract: We consider a setting in which inventory plays both promotional and service roles; that is, higher inventories not only improve service levels but also stimulate demand by serving as a promotional tool (e.g., as the result of advertising effect by the enhanced product visibility). Specifically, we study the periodic-review inventory systems in which the demand in each period is uncertain but increases with the inventory level. We investigate the multiperiod model with normal and expediting orders in each period, that is, any shortage will be met through emergency replenishment. Such a model takes the lost sales model as a special case. For the cases without and with fixed order costs, the optimal inventory replenishment policy is shown to be of the base-stock type and of the (s, S)type, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 430-440, 2012

Production/distribution system design with inventory considerations

Abstract: This study addresses the design of a three-stage production/distribution system where the first stage includes the set of established retailers and the second and third stages include the sets of potential distribution centers (DCs) and potential capacitated suppliers, respectively. In this problem, in addition to the fixed location/operating costs associated with locating DCs and suppliers, we consider the coordinated inventory replenishment decisions at the located DCs and retailers along with the appropriate inventory costs explicitly. In particular, we account for the replenishment and holding costs at the retailers and selected DCs, and the fixed plus distance-based transportation costs between the selected plants and their assigned DCs, and between the selected DCs and their respective retailers, explicitly. The resulting formulation is a challenging mixed-integer nonlinear programming model for which we propose efficient heuristic solution approaches. Our computational results demonstrate the performance of the heuristic approaches as well as the value of integrated decision-making by verifying that significant cost savings are realizable when the inventory decisions and costs are incorporated in the production distribution system design. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 172–195, 2012

Priority Queue with Customer Upgrades

Abstract: This article is concerned with a general multi-class multi-server priority queueing system with customer priority upgrades. The queueing system has various applications in inventory control, call centers operations, and health care management. Through a novel design of Lyapunov functions, and using matrix-analytic methods, sufficient conditions for the queueing system to be stable or instable are obtained. Bounds on the queue length process are obtained by a sample path method, with the help of an auxiliary queueing system. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 362-375, 2012

Evaluating cost and reliability integrated performance of stochastic logistics systems

Abstract: The significance of integrating reliability into logistics performance has been established [The Logistics Performance Index and Its Indicators, World Bank International Trade and Transport Departments, (2010)]. Hence, as a response to the work by the World Bank, the present article aims to evaluate the performance index Rb,d of logistics systems as the probability that a specified demand d can be distributed successfully through multistate arc capacities from the source to the destination under the constraint that the total distribution cost should not exceed the cost limitation b. This article provides a pioneering approach for a straightforward computation of the performance index Rb,d. The proposed algorithm is a hybrid between the polynomial time capacity-scaling algorithm, which was presented by Edmonds and Karp [JACM 19 (1972)], and the decomposition algorithm, which was presented by Jane and Laih [IEEE (2008)]. Currently, the proposed approach is the only algorithm that can directly compute Rb,d. An illustration of the proposed algorithm is presented. The results of the computational experiments indicate that the presented algorithm outperforms existing algorithms. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Newsvendor problems with sequentially revealed demand information

Abstract: This article analyzes a capacity/inventory planning problem with a one-time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation at a certain fee or sell off some inventory at a lower price. The problem can be viewed as a generalization of the classic newsvendor problem and can be found in many applications. One key observation of the analysis is that the dynamic programming formulation of the problem is closely related to a recursion that arises in the study of a far more complex system, a series inventory system with stochastic demand over an infinite horizon. Using this equivalence, we characterize the optimal policy and assess the value of the additional demand information. We also extend the analysis to a richer model of information. Here, demand is driven by an underlying Markov process, representing economic conditions, weather, market competition, and other environmental factors. Interestingly, under this more general model, the connection to the series inventory system is different. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 2012

Dynamic lot sizing with all‐units discount and resales

Abstract: We consider a single-product dynamic lot-sizing model with an all-units quantity discount pricing scheme available to the buyer, where the discount price breakpoints are stationary. To capture the real-life behavior of a typical buyer who often takes advantage of quantity discounts through purchasing in excess of the anticipated demand, our model allows the buyer to resell or dispose of any leftover inventory that he/she does not need. We show that the general problem with an arbitrary number of discount price breakpoints is NP-hard. We then develop a polynomial algorithm for the problem with an O(Tm+3) running time when the number of price breakpoints, m, is fixed, where T is the number of time periods in the planning horizon. We further develop an O(T2) algorithm for the special case with a single price breakpoint. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Dual Sourcing – Responsive Hedging Against Correlated Supply and Demand Uncertainty

Abstract: This paper analyzes dual sourcing decisions under stochastically dependent supply and demand uncertainty. A manufacturer faces the trade-off between investing in unreliable but high-margin offshore supply and in reliable but low-margin local supply, where the latter allows for production that is responsively contingent on the actual demand and offshore supply conditions. Cost thresholds for both types of supply determine the optimal resource allocation: single offshore sourcing, single responsive sourcing, or dual sourcing. Relying on the concept of concordance orders, we study the effects of correlation between supply and demand uncertainty. Adding offshore supply to the sourcing portfolio becomes more favorable under positive correlation, since offshore supply is likely to satisfy demand when needed. Selecting responsive capacity under correlated supply and demand uncertainty is not as straightforward, yet we establish the managerially relevant conditions under which responsive capacity either gains or loses in importance. Our key results are extended to the broad class of endogenous supply uncertainty developed by Dada et al. [8]. Free Keywords responsive capacity, demand and supply uncertainty, backup supplier, concordance order Availability The ERIM Report Series is distributed through the following platforms: Academic Repository at Erasmus University (DEAR), DEAR ERIM Series Portal Social Science Research Network (SSRN), SSRN ERIM Series Webpage Research Papers in Economics (REPEC), REPEC ERIM Series Webpage Classifications The electronic versions of the papers in the ERIM report Series contain bibliographic metadata by the following classification systems: Library of Congress Classification, (LCC) LCC Webpage Journal of Economic Literature, (JEL), JEL Webpage ACM Computing Classification System CCS Webpage Inspec Classification scheme (ICS), ICS Webpage

Bayesian analysis of queues with impatient customers: Applications to call centers

Abstract: Queuing models have been extensively used in the literature for obtaining performance measures and developing staffing policies. However, most of this work has been from a pure probabilistic point of view and has not addressed issues of statistical inference. In this article, we consider Bayesian queuing models with impatient customers with particular emphasis on call center operations and discuss further extensions. We develop the details of Bayesian inference for queues with abandonment such as the M/M/s + M model (Erlang-A). In doing so, we discuss the estimation of operating characteristics and its implications on staffing. We illustrate the implementation of the Bayesian models using actual arrival, service, and abandonment data from call centers. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 000: 000-000, 2012 of the planning functions. In this article, we study one of the most frequently used call center queuing models from a Bayesian inference perspective. Our objective is to develop the Bayesian analysis of M/M/s + M queues. More specif- ically, we consider queues where interarrival, service, and abandonment time distributions are assumed to be exponen- tial and the system is served by s identical servers. We address such issues as

A least squares temporal difference actor–critic algorithm with applications to warehouse management

Abstract: This article develops a new approximate dynamic programming (DP) algorithm for Markov decision problems and applies it to a vehicle dispatching problem arising in warehouse management. The algorithm is of the actor-critic type and uses a least squares temporal difference learning method. It operates on a sample-path of the system and optimizes the policy within a prespecified class parameterized by a parsimonious set of parameters. The method is applicable to a partially observable Markov decision process setting where the measurements of state variables are potentially corrupted, and the cost is only observed through the imperfect state observations. We show that under reasonable assumptions, the algorithm converges to a locally optimal parameter set. We also show that the imperfect cost observations do not affect the policy and the algorithm minimizes the true expected cost. In the warehouse application, the problem is to dispatch sensor-equipped forklifts in order to minimize operating costs involving product movement delays and forklift maintenance. We consider instances where standard DP is computationally intractable. Simulation results confirm the theoretical claims of the article and show that our algorithm converges more smoothly than earlier actor–critic algorithms while substantially outperforming heuristics used in practice. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Batch scheduling with step‐deteriorating processing times to minimize flowtime

Abstract: Both topics of batch scheduling and of scheduling deteriorating jobs have been very popular among researchers in the last two decades. In this article, we study a model combining these two topics. We consider a classical batch scheduling model with unit-jobs and batch-independent setup times, and a model of step-deterioration of processing times. The objective function is minimum flowtime. The optimal solution of the relaxed version (allowing non-integer batch sizes) is shown to have a unique structure consisting of two consecutive decreasing arithmetic sequences of batch sizes. We also introduce a simple and efficient rounding procedure that guarantees integer batch sizes. The entire solution procedure requires an effort of O(n) (where nis the number of jobs.) © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Mixed integer least squares optimization for flight and maintenance planning of mission aircraft

Abstract: We address the problem of generating a joint flight and maintenance plan for a unit of mission aircraft. The objective is to establish a balanced allocation of the flight load and the maintenance capacity to the individual aircraft of the unit, so that its long-term availability is kept at a high and steady level. We propose a mixed integer nonlinear model to formulate the problem, the objective function of which minimizes a least squares index expressing the total deviation of the individual aircraft flight and maintenance times from their corresponding target values. Using the model's special structure and properties, we develop an exact search algorithm for its solution. We analyze the computational complexity of this algorithm, and we present computational results comparing its performance against that of a commercial optimization package. Besides demonstrating the superiority of the proposed algorithm, these results reveal that the total computational effort required for the solution of the problem depends mainly on two crucial parameters: the size of the unit (i.e., the number of aircraft that comprise it) and the space capacity of the maintenance station. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Optimal pricing for a short life‐cycle product when customer price‐sensitivity varies over time

Abstract: Technology products often experience a life-cycle demand pattern that resembles a diffusion process, with weak demand in the beginning and the end of the life cycle and high demand intensity in between. The customer price-sensitivity also changes over the life cycle of the product. We study the prespecified pricing decision for a product that exhibits such demand characteristics. In particular, we determine the optimal set of discrete prices and the times to switch from one price to another, when a limited number of price changes are allowed. Our study shows that the optimal prices and switching times show interesting patterns that depend on the product's demand pattern and the change in the customers' price sensitivity over the life cycle of the product. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Determining crane areas for balancing workload among interfering and noninterfering cranes

Abstract: This article treats the problem of subdividing an area for storing containers such that the workload is evenly shared among the cranes operating the resulting subareas. We consider two crane sets: while noncrossing constraints between cranes of the same set need to be observed, cranes of different sets do not interfere. Such a problem setting is, for instance, relevant for scheduling the (un-)loading of vessels by parallel quay cranes operating on opposing berths or in container yards with cross-over cranes. We formalize the resulting optimization problem, prove computational complexity, and present exact and heuristic solution procedures. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Averaging frameworks for simulation optimization with applications to simulated annealing

Abstract: We present two frameworks for designing random search methods for discrete simulation optimization. One of our frameworks is very broad (in that it includes many random search methods), whereas the other one considers a special class of random search methods called point-based methods, that move iteratively between points within the feasible region. Our frameworks involve averaging, in that all decisions that require estimates of the objective function values at various feasible solutions are based on the averages of all observations collected at these solutions so far. Also, the methods are adaptive in that they can use information gathered in previous iterations to decide how simulation effort is expended in the current iteration. We show that the methods within our frameworks are almost surely globally convergent under mild conditions. Thus, the generality of our frameworks and associated convergence guarantees makes the frameworks useful to algorithm developers wishing to design efficient and rigorous procedures for simulation optimization. We also present two variants of the simulated annealing (SA) algorithm and provide their convergence analysis as example application of our point-based framework. Finally, we provide numerical results that demonstrate the empirical effectiveness of averaging and adaptivity in the context of SA. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Economic lot sizing with constant capacities and concave inventory costs

Abstract: This article studies the classical single-item economic lot-sizing problem with constant capacities, fixed-plus-linear order costs, and concave inventory costs, where backlogging is allowed. We propose an O(T3) optimal algorithm for the problem, which improves upon the O(T4) running time of the famous algorithm developed by Florian and Klein (Manage Sci18 (1971) 12–20). Instead of using the standard dynamic programming approach by predetermining the minimal cost for every possible subplan, we develop a backward dynamic programming algorithm to obtain a more efficient implementation. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

A note on optimal allocations for the second elementary symmetric function with applications for optimal reliability design

Abstract: This article considers the problem of determining the optimal size allocation and optimal number of experimental conditions for a second elementary symmetric function with different coefficients. Analytical solutions for several practical applications are derived and the general formulation is used to elucidate the foundation between different parametric models found in recent studies. A geometrical interpretation of the structure of some theoretical results is also provided. This approach renders some complex problems more tractable than what numerical search algorithms would allow. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

A standardized scan statistic for detecting spatial clusters with estimated parameters

Abstract: The scan statistic based on likelihood ratios (LRs) have been widely discussed for detecting spatial clusters. When developing the scan statistic, it uses the maximum likelihood estimates of the incidence rates inside and outside candidate clusters to substitute the true values in the LR statistic. However, the parameter estimation has a significant impact on the sensitivity of the scan statistic, which favors the detection of clusters in areas with large population sizes. By presenting the effects of parameter estimation on Kulldorff's scan statistic, we suggest a standardized scan statistic for spatial cluster detection. Compared to the traditional scan statistic, the standardized scan statistic can account for the varying mean and variance of the LR statistic due to inhomogeneous background population sizes. Extensive simulations have been performed to compare the power of the two cluster detection methods with known or/and estimated parameters. The simulation results show that the standardization can help alleviate the effects of parameter estimation and improve the detection of localized clusters. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Service design at diagnostic service centers

Abstract: We study a service design problem in diagnostic service centers, call centers that provide medical advice to patients over the phone about what the appropriate course of action is, based on the caller's symptoms. Due to the tension between increased diagnostic accuracy and the increase in waiting times more in-depth service requires, managers face a difficult decision in determining the optimal service depth to guide the diagnostic process. The specific problem we consider models the situation when the capacity (staffing level) at the center is fixed, and when the callers have both congestion- and noncongestion-related costs relating to their call. We develop a queueing model incorporating these features and find that the optimal service depth can take one of two different structures, depending on factors such as the nurses' skill level and the maximum potential demand. Sensitivity analyses of the two optimal structures show that they are quite different. In some situations, it may (or may not) be optimal for the manager to try to expand the demand at the center, and increasing skill level may (or may not) increase congestion. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Stein-Chen Approximation and Error Bounds for Order Fill Rates in Assemble-to-Order Systems

Abstract: Assemble-to-order (ATO) is an important operational strategy for manufacturing firms to achieve quick response to customer orders while keeping low finished good inventories. This strategy has been successfully used not only by manufacturers (e.g., Dell, IBM) but also by retailers (e.g., Amazon.com). The evaluation of order-based performance is known to be an important but difficult task, and the existing literature has been mainly focused on stochastic comparison to obtain performance bounds. In this article, we develop an extremely simple Stein-Chen approximation as well as its error-bound for order-based fill rate for a multiproductmulticomponentATOsystemwithrandomleadtimestoreplenishcomponents.Thisapproximationgivesanexpression for order-based fill rate in terms of component-based fill rates. The approximation has the property that the higher the component replenishment leadtime variability, the smaller the error bound. The result allows an operations manager to analyze the improvement inorder-basedfillrateswhenthebase-stocklevelforanycomponentchanges.Numericalstudiesdemonstratethattheapproximation performs well, especially when the demand processes of different components are highly correlated; when the components have high base-stock levels; or when the component replenishment leadtimes have high variability. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 643-655, 2012