Operations Research current issue

In This Issue

Sun, 18 Oct 2009 08:31:28 PDT

No abstract available.

Area Editor's Statement: Stochastic Models

Zwart, B. — Sun, 18 Oct 2009 08:31:28 PDT

No abstract available.

OR Practice--Supporting 3PL Decisions in the Automotive Industry by Generating Diverse Solutions to a Large-Scale Location-Routing Problem

Schittekat, P., Sorensen, K. — Sun, 18 Oct 2009 08:31:28 PDT

For the distribution of spare parts to car dealers, many automotive companies use a transport network of intermediate hubs or transport platforms, operated by a set of third-party logistics (3PL) partners. The optimization of this network, particularly the selection of 3PL providers and corresponding transport platforms, is a complex decision that needs to be supported by appropriate software tools. In this paper, we develop such a tool, implement it, and show its results on a real-life case study provided by Toyota. The tool is currently in active use at Toyota to study and improve the distribution of spare parts in Germany.

Using a tabu search metaheuristic, the developed tool essentially solves a large location-routing problem, but has several innovative features to increase its usefulness. First, the tool generates a set of high-quality but structurally different solutions, rather than a single one. This increases Toyota's negotiating power, increases its ability to analyze its current transport network against possible alternatives, and allows it to quickly switch between different transport networks if unexpected events occur. Second, a commercial vehicle-routing solver is integrated into the tool, to allow for a far more realistic modeling of the vehicle-routing decision.

An Effective Two-Finger, Two-Stage Biometric Strategy for the US-VISIT Program

Baveja, M., Wein, L. M. — Sun, 18 Oct 2009 08:31:28 PDT

Motivated by the cost and disruption involved in changing from a two-finger to a ten-finger biometric system for matching U.S. visitors to a watchlist of criminals and terrorists, we investigate whether any two-finger multistage biometric strategies would fix the inadequate matching performance of poor-quality prints that plagues the U.S. Government's original two-finger, single-stage biometric system. For several multistage strategies, we solve the Stackelberg game in which the U.S. Government chooses the biometric threshold levels to maximize the detection probability subject to constraints on the false positive probability and on the mean time per visitor to perform biometric screening, and the terrorist chooses the fingerprint image quality to minimize his detection probability. The first stage of all the strategies uses the current minutiae-based fingerprint matching system, but with thresholds that depend on image quality, which in isolation achieves a detection probability of 0.771. Using face recognition (based on 2002 data) in the second stage increases the detection probability to 0.841, whereas using a slower and more thorough texture-based fingerprint matcher in the second stage leads to a detection probability of at least 0.913 and perhaps significantly higher. (Data for the texture matcher is only available for the poorest-quality prints and we assume that this is its performance for all prints.) Adding face recognition as a third stage to this latter system does not improve performance. The two-finger, two-stage strategy may be comparable in performance to the ten-finger, single-stage strategy (which has a detection probability of 0.937), is robust against gaming and poor image acquisition, requires no additional hardware, and would generate no visible changes from the original two-finger, single-stage system from a visitor's viewpoint. The uncertainty in our performance estimates needs to be better quantified, ideally with raw data on similarity scores, before recommending this strategy for implementation.

Competition in the Supply Option Market

Martinez-de-Albeniz, V., Simchi-Levi, D. — Sun, 18 Oct 2009 08:31:28 PDT

This paper develops a multiattribute competition model for procurement of short life-cycle products. In such an environment, the buyer installs dedicated production capacity at the suppliers before demand is realized. Final production orders are decided after demand materializes. Of course, the buyer is reluctant to bear all the capacity and inventory risk, and thus signs flexible contracts with several suppliers. We model the suppliers' offers as option contracts, where each supplier charges a reservation price per unit of capacity and an execution price per unit of delivered supply. These two parameters illustrate the trade-off between total price and flexibility of a contract, which are both important to the buyer. We model the interaction between suppliers and the buyer as a game in which the suppliers are the leaders and the buyer is the follower. Specifically, suppliers compete to provide supply capacity to the buyer, and the buyer optimizes its expected profit by selecting one or more suppliers. We characterize the suppliers' equilibria in pure strategies for a class of customer demand distributions. In particular, we show that this type of interaction gives rise to cluster competition. That is, in equilibrium suppliers tend to be clustered in small groups of two or three suppliers each, such that within the same group all suppliers use similar technologies and offer the same type of contract. Finally, we show that in equilibrium, supply chain inefficiencies—i.e., the loss of profit due to competition—are at most 25% of the profit of a centralized supply chain.

Conflict Resolution in the Scheduling of Television Commercials

Gaur, D. R., Krishnamurti, R., Kohli, R. — Sun, 18 Oct 2009 08:31:28 PDT

We extend a previous model for scheduling commercial advertisements during breaks in television programming. The proposed extension allows differential weighting of conflicts between pairs of commercials. We formulate the problem as a capacitated generalization of the max k-cut problem in which the vertices of a graph correspond to commercial insertions and the edge weights to the conflicts between pairs of insertions. The objective is to partition the vertices into k capacitated sets to maximize the sum of conflict weights across partitions. We note that the problem is NP-hard. We extend a previous local-search procedure to allow for the differential weighting of edge weights. We show that for problems with equal insertion lengths and break durations, the worst-case bound on the performance of the proposed algorithm increases with the number of program breaks and the number of insertions per break, and that it is independent of the number of conflicts between pairs of insertions. Simulation results suggest that the algorithm performs well even if the problem size is small.

Advertising Competition in a Dynamic Oligopoly with Multiple Brands

Erickson, G. M. — Sun, 18 Oct 2009 08:31:28 PDT

A model is developed that allows the derivation of feedback Nash equilibrium advertising strategies for oligopolistic competitors. The model is an extension of a modified Vidale-Wolfe model that incorporates multiple brands per competitor. The resulting expressions of feedback advertising strategies are combined with those for sales dynamics in an empirical model that is applied to the carbonated soft drink market, which involves three primary competitors and five primary brands. The research provides the following contributions:

A modification of the Vidale-Wolfe model is extended to allow dynamic analysis of an oligopoly in which the competitors each offer multiple brands.

The model extension permits the derivation of a feedback Nash equilibrium.

The determination of a feedback Nash equilibrium enhances empirical analysis by allowing an expanded empirical model that includes the explicit modeling of endogenous advertising along with demand relationships.

Resource and Revenue Management in Nonprofit Operations

de Vericourt, F., Lobo, M. S. — Sun, 18 Oct 2009 08:31:28 PDT

Nonprofit firms sometimes engage in for-profit activities for the purpose of generating revenue to subsidize their mission activities. The organization is then confronted with a consumption versus investment trade-off, where investment corresponds to providing capacity for revenue customers, and consumption corresponds to serving mission customers. Exemplary of this approach are the Aravind Eye Hospitals in India, where profitable paying hospitals are used to subsidize care at free hospitals. We model this problem as a multiperiod stochastic dynamic program. In each period, the organization must decide how much of the current assets should be invested in revenue-customer service capacity, and at what price the service should be sold. We provide sufficient conditions under which the optimal capacity and pricing decisions are of threshold type. Similar results are derived when the selling price is fixed, but the banking of assets from one period to the next is allowed. We compare the performance of the optimal threshold policy with heuristics that may be more appealing to managers of nonprofit organizations, and we assess the value of banking and of dynamic pricing through numerical experiments.

Constructing Risk Measures from Uncertainty Sets

Natarajan, K., Pachamanova, D., Sim, M. — Sun, 18 Oct 2009 08:31:28 PDT

We illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance and show how robust optimization can be used to generalize the concepts of these risk measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can construct coherent risk measures and address the issue of the computational tractability of the resulting formulations. Our results have implications for efficient portfolio optimization under different measures of risk.

Multiple Risks and Mean-Variance Preferences

Eichner, T., Wagener, A. — Sun, 18 Oct 2009 08:31:28 PDT

We analyze comparative static effects under uncertainty when a decision maker has mean-variance preferences and faces a generic, quasi-linear decision problem with both an endogenous risk and a background risk. In terms of mean-variance preferences, we fully characterize the effects of changes in the location, scale, and concordance parameters of the stochastic environment on optimal risk taking. Presupposing compatibility between the mean-variance and the expected-utility approach, we then translate these mean-variance properties into their analogues for von Neumann-Morgenstern utility functions.

Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management

Zhu, S., Fukushima, M. — Sun, 18 Oct 2009 08:31:28 PDT

This paper considers the worst-case Conditional Value-at-Risk (CVaR) in the situation where only partial information on the underlying probability distribution is available. The minimization of the worst-case CVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. The application of the worst-case CVaR to robust portfolio optimization is proposed, and the corresponding problems are cast as linear programs and second-order cone programs that can be solved efficiently. Market data simulation and Monte Carlo simulation examples are presented to illustrate the proposed approach.

Dynamic Pricing for Nonperishable Products with Demand Learning

Araman, V. F., Caldentey, R. — Sun, 18 Oct 2009 08:31:29 PDT

A retailer is endowed with a finite inventory of a nonperishable product. Demand for this product is driven by a price-sensitive Poisson process that depends on an unknown parameter that is a proxy for the market size. The retailer has a prior belief on the value of this parameter that he updates as time and available information (prices and sales) evolve. The retailer's objective is to maximize the discounted long-term average profits of his operation using dynamic pricing policies. We consider two cases. In the first case, the retailer is constrained to sell the entire initial stock of the nonperishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the nonperishable product at any time and switch to a different menu of products. For both cases, we formulate the retailer's problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution, and suggest a simple and efficient approximated solution. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed policy.

Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers

Mandelbaum, A., Zeltyn, S. — Sun, 18 Oct 2009 08:31:29 PDT

Motivated by call center practice, we study asymptotically optimal staffing of many-server queues with abandonment. A call center is modelled as an M/M/n + G queue, which is characterized by Poisson arrivals, exponential service times, n servers, and generally distributed patience times of customers. Our asymptotic analysis is performed as the arrival rate, and hence the number of servers n, increases indefinitely.

We consider a constraint satisfaction problem, where one chooses the minimal staffing level n that adheres to a given cost constraint. The cost can incorporate the fraction abandoning, average wait, and tail probabilities of wait. Depending on the cost, several operational regimes arise as asymptotically optimal: Efficiency-Driven (ED), Quality and Efficiency-Driven (QED), and also a new ED + QED operational regime that enables QED tuning of the ED regime. Numerical experiments demonstrate that, over a wide range of system parameters, our approximations provide useful insight as well as excellent fit to exact optimal solutions. It turns out that the QED regime is preferable either for small-to-moderate call centers or for large call centers with relatively tight performance constraints. The other two regimes are more appropriate for large call centers with loose constraints.

We consider two versions of the constraint satisfaction problem. The first one is constraint satisfaction on a single time interval, say one hour, which is common in practice. Of special interest is a constraint on the tail probability, in which case our new ED + QED staffing turns out asymptotically optimal. We also address a global constraint problem, say over a full day. Here several time intervals, say 24 hours, are considered, with interval-dependent staffing levels allowed; one seeks to minimize staffing levels, or more generally costs, given the overall performance constraint. In this case, there is the added flexibility of trading service levels among time intervals, but we demonstrate that only little gain is associated with this flexibility if one is concerned with the fraction abandoning.

Revenue Management with Costly Price Adjustments

Celik, S., Muharremoglu, A., Savin, S. — Sun, 18 Oct 2009 08:31:29 PDT

We consider a novel variant of the perishable inventory profit management problem faced by a firm that sells a fixed inventory over a finite horizon in the presence of price-adjustment costs. In economics literature, such price-adjustment costs are widely studied and are typically assumed to include a fixed component (e.g., advertising costs), an inventory-dependent component (e.g., inventory relabeling costs), as well as a component that depends on the magnitude of the price adjustment (e.g., cognitive and coordination managerial costs).

We formulate the firm's profit management problem as a finite-horizon dynamic program in which the state of the system is described by the inventory level as well as the current price level. We derive first-order properties of the optimal value function and give a complete characterization of optimal policies for the case of ample inventory. Through a set of examples we demonstrate the complex and counterintuitive nature of optimal price-adjustment policies. Consequently, we focus on developing easily computable and implementable heuristics with demonstrably good performance. To this end, we develop and solve a fluid model based on the original stochastic dynamics and propose three fluid-based heuristic policies. We derive expressions for the expected profit generated by each one of these heuristics when applied to the stochastic problem and derive sufficient conditions for the asymptotic optimality of the policies when the initial inventory levels and planning horizons are proportionally scaled up. We test the performance of the heuristics in a numerical study and demonstrate a robust, near-optimal performance of one of the heuristics (which we call the "Fluid Time" heuristic) for a wide range of problem parameters. Finally, we demonstrate the importance of proper accounting of price-adjustment costs in several alternative business settings.

A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application

DeMiguel, V., Xu, H. — Sun, 18 Oct 2009 08:31:29 PDT

We study an oligopoly consisting of M leaders and N followers that supply a homogeneous product (or service) noncooperatively. Leaders choose their supply levels first, knowing the demand function only in distribution. Followers make their decisions after observing the leader supply levels and the realized demand function. We term the resulting equilibrium a stochastic multiple-leader Stackelberg-Nash-Cournot (SMS) equilibrium. We show the existence and uniqueness of SMS equilibrium under mild assumptions. We also propose a computational approach to find the equilibrium based on the sample average approximation method and analyze its rate of convergence. Finally, we apply this framework to model competition in the telecommunication industry.

Stochastic Scheduling Subject to Preemptive-Repeat Breakdowns with Incomplete Information

Cai, X., Wu, X., Zhou, X. — Sun, 18 Oct 2009 08:31:29 PDT

This paper considers the problem of scheduling a set of jobs on a single machine subject to stochastic breakdowns with incomplete information on the probability distributions involved in the decision process. We focus on the preemptive-repeat discipline, under which a machine breakdown leads to the loss of the work done on the job being processed. The breakdown process of the machine is allowed to depend on the job it is processing. The processing times required to complete the jobs, and the machine uptimes and downtimes, are random variables with incomplete information on their probability distributions characterized by unknown parameters. We establish the preemptive-repeat model with incomplete information and investigate its probabilistic characteristics. We show that optimal static policies can be obtained for a wide range of performance measures, which are determined by the prior distributions of the unknown parameters. We derive optimal dynamic policies via Gittins indices represented by the posterior distributions, which are updated adaptively based on processing histories. Under appropriate conditions, the optimal dynamic policies can be calculated by one-step reward rates in a closed form. As a by-product, we also show that our incomplete information model subsumes the traditional preemptive-repeat models with complete information as extreme cases.

Strategic Planning with Start-Time Dependent Variable Costs

Luedtke, J., Nemhauser, G. L. — Sun, 18 Oct 2009 08:31:29 PDT

We present a strategic planning model in which the activities to be planned, such as production and distribution in a supply network, require technology to be installed before they can be performed. The technology improves over time, so that a decision maker has incentive to delay starting an activity to take advantage of better technology and lower operational costs. The model captures the fundamental trade-off between delaying the start time of an activity and the need for some activities to be performed now. Models of this type are used in the oil industry to plan the development of oil fields. This problem is naturally formulated as a mixed-integer program with a bilinear objective. We develop a series of progressively more compact mixed-integer linear formulations, along with classes of valid inequalities that make the formulations strong. We also present a specialized branch-and-cut algorithm to solve an extremely compact concave formulation. Computational results indicate that these formulations can be used to solve large-scale instances, whereas a straightforward linearization of the mixed-integer bilinear formulation fails to solve even small instances.

A Decision-Analytic Approach to Reliability-Based Design Optimization

Bordley, R. F., Pollock, S. M. — Sun, 18 Oct 2009 08:31:29 PDT

Reliability-based design optimization is concerned with designing a product to optimize an objective function, given uncertainties about whether various design constraints will be satisfied. However, the widespread practice of formulating such problems as chance-constrained programs can lead to misleading solutions. While a decision-analytic approach would avoid this undesirable result, many engineers find it difficult to determine the utility functions required for a traditional decision analysis. This paper presents an alternative decision-analytic formulation that, although implicitly using utility functions, is more closely related to probability maximization formulations with which engineers are comfortable and skilled. This result combines the rigor of decision analysis with the convenience of existing optimization approaches.

Dantzig-Wolfe Decomposition for Solving Multistage Stochastic Capacity-Planning Problems

Singh, K. J., Philpott, A. B., Wood, R. K. — Sun, 18 Oct 2009 08:31:29 PDT

We describe a multistage, stochastic, mixed-integer programming model for planning capacity expansion of production facilities. A scenario tree represents uncertainty in the model; a general mixed-integer program defines the operational submodel at each scenario-tree node, and capacity-expansion decisions link the stages. We apply "variable splitting" to two model variants, and solve those variants using Dantzig-Wolfe decomposition. The Dantzig-Wolfe master problem can have a much stronger linear programming relaxation than is possible without variable splitting, over 700% stronger in one case. The master problem solves easily and tends to yield integer solutions, obviating the need for a full branch-and-price solution procedure. For each scenario-tree node, the decomposition defines a subproblem that may be viewed as a single-period, deterministic, capacity-planning problem. An effective solution procedure results as long as the subproblems solve efficiently, and the procedure incorporates a good "duals stabilization method." We present computational results for a model to plan the capacity expansion of an electricity distribution network in New Zealand, given uncertain future demand. The largest problem we solve to optimality has six stages and 243 scenarios, and corresponds to a deterministic equivalent with a quarter of a million binary variables.

Evaluating Quantile Assessments

Jose, V. R. R., Winkler, R. L. — Sun, 18 Oct 2009 08:31:29 PDT

Quantile assessments are commonly encountered in the elicitation of probability distributions in decision analysis, forecasting, and risk analysis. Scoring rules have been developed to provide ex ante incentives for careful and truthful assessments and ex post evaluation measures in the context of probability assessment. We show that these scoring rules designed for probability assessment provide inappropriate incentives if used for quantile assessment. We investigate the properties of a linear family of scoring rules that are intended specifically for quantile assessment (including the assessment of multiple quantiles) and can be related to a realistic decision-making problem. These rules provide proper incentives for quantile assessment and yield higher expected scores for distributions that are more informative in the sense of having less dispersion. We discuss the special case of interval forecasts and a generalization involving transformations, and we briefly mention other possible extensions.

Technical Note--Price Trends in a Dynamic Pricing Model with Heterogeneous Customers: A Martingale Perspective

Xu, X., Hopp, W. J. — Sun, 18 Oct 2009 08:31:29 PDT

This note describes probabilistic properties of optimal price sample paths in a dynamic pricing model with a finite horizon and limited stock. We assume that customer arrivals follow a nonhomogeneous Poisson process. We show that if customers' willingness-to-pay increases rapidly over time, then the optimal price process follows a submartingale, which implies an upward price trend. Alternatively, if customers' willingness-to-pay decreases rapidly over time, then the optimal price process follows a supermartingale, which implies a downward price trend.

Contributors

Sun, 18 Oct 2009 08:31:29 PDT

No abstract available.