Operations Research current issue

In This Issue

2008-11-19

No abstract available.

OR FORUM--Catching the "Network Science" Bug: Insight and Opportunity for the Operations Researcher

Alderson, D. L. — 2008-11-19

Recent efforts to develop a universal view of complex networks have created both excitement and confusion about the way in which knowledge of network structure can be used to understand, control, or design system behavior. This paper offers perspective on the emerging field of "network science" in three ways. First, it briefly summarizes the origins, methodological approaches, and most celebrated contributions within this increasingly popular field. Second, it contrasts the predominant perspective in the network science literature (that abstracts away domain-specific function and instead focuses on graph-theoretic measures of system structure and dynamics) with that of engineers and practitioners of decision science (who emphasize the importance of network performance, constraints, and trade-offs). Third, it proposes optimization-based reverse engineering to address some important open questions within network science from an operations research perspective. We advocate for increased, yet cautious, participation in this field by operations researchers.

OR PRACTICE--Assisting Defined-Benefit Pension Plans

Mulvey, J. M., Simsek, K. D., Zhang, Z., Fabozzi, F. J., Pauling, W. R. — 2008-11-19

The defined-benefit pension system poses substantial, long-term risks for the U.S. economy. We describe a flexible asset-liability management (ALM) system for pension planning. The primary goals are to improve the performance and survivability of the pension trust. We first employ a stochastic program for enhancing investment strategies in light of company and other goals and pension risk constraints. The results are linked with a policy simulator for further analysis. We illustrate the concepts via two disparate real-world companies. The first is a slowly growing auto company, and the second a profitable pharmaceutical enterprise. We show that a stochastic program can help in the process of discovering sound policy rules. The ALM system has been employed extensively throughout the world by a large global actuarial firm.

OR PRACTICE--Optimization of Vacation Timeshare Scheduling

Sampson, S. E. — 2008-11-19

This paper reports on an application of network-flow integer programming to a vacation timeshare exchange problem. A typical timeshare owner has purchased yearly access to a specific week at a specific resort. The resulting lack of vacation variety is mitigated by systems that allow owners to exchange owned weeks for different weeks at different resorts according to their preferences, the assessed value of what they are exchanging, their contractual priority, and resort availability. The timeshare exchange problem is similar to other preference-based assignment problems such as labor scheduling, preferential bidding, and traditional timetabling, but different in the formulation of the objective function. This paper demonstrates how the effectiveness of timeshare exchange processes can be improved through mathematical optimization, as measured by increased satisfaction of participant preferences. Optimization also presents exchange managers with the opportunity to more precisely manage preference and priority trade-offs among various classes of participants. The trade-off decisions are aided by sensitivity analysis utilizing a minmax criterion.

A Single-Unit Decomposition Approach to Multiechelon Inventory Systems

Muharremoglu, A., Tsitsiklis, J. N. — 2008-11-19

We show the optimality of state-dependent echelon base-stock policies in uncapacitated serial inventory systems with Markov-modulated demand and Markov-modulated stochastic lead times in the absence of order crossing. Our results cover finite-time horizon problems as well as infinite-time horizon formulations, with either a discounted or an average cost criterion. We employ a novel approach, based on a decomposition of the problem into a series of single-unit single-customer problems that are essentially decoupled. Besides providing a simple proof technique, this approach also gives rise to efficient algorithms for the calculation of the base-stock levels.

Joint Design and Pricing on a Network

Brotcorne, L., Labbe, M., Marcotte, P., Savard, G. — 2008-11-19

To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper, we consider a streamlined version of this situation where a firm's decision variables involve both prices and investments. We model this situation as a joint design and pricing problem that we formulate as a mixed-integer bilevel program, and whose properties are investigated. In particular, we take advantage of a feature of the model that allows the development of an algorithmic framework based on Lagrangean relaxation. This approach is entirely novel, and numerical results show that it is capable of solving problems of significant sizes.

Modeling the Impact of Market Interventions on the Strategic Evolution of Electricity Markets

Bunn, D. W., Oliveira, F. S. — 2008-11-19

This paper presents a large-scale computationally intensive model for understanding the dynamic strategic evolution of electricity-generating asset portfolios in response to various market interventions, and the consequent longer-term effects of such changes on market structure and prices. We formulate a multistage model involving a Cournot representation of the wholesale electricity market, the performance of which then determines plant trading between players and the coevolution of market structure. An algorithm to model this game is presented. We apply this model to the full England and Wales system, as it was in 2000, and simulate the strategic responses to divestiture, capacity targets, and the two market mechanism variants of pool and bilateral market clearing.

Regulation of Natural Gas Distribution Using Policy Benchmarks

Muthuraman, K., Aouam, T., Rardin, R. — 2008-11-19

Local distribution companies (LDCs) play the role of purchasing and delivering natural gas to their consumers, and state regulators oversee the pricing of natural gas to consumers. The common method of regulation, based on the cost of service, provides arguably little incentive for the LDC to optimally manage their procurement activities. In the light of recent deregulation and other changes, benchmarking-based regulatory schemes are being increasingly perceived as the right direction to pursue. Various states are experimenting with simple benchmark mechanisms that have inherent deficiencies and are often criticized. In this paper, we propose and characterize a new kind of benchmark that we call a policy benchmark as a mechanism for regulation. Using variance as the measure of risk, we formulate the regulator's and the LDC's problems as multiple-objective optimizations. We provide rigorous characterizations of the dominance frontiers for a two-stage model. We also provide multistage formulations that take into account various natural gas market microstructures. We compute solutions under parameters estimated from relevant real-world data and illustrate that the structures of the dominance frontiers remain unaltered from the characterizations provided by a stylized two-stage model.

Scoring Rules, Generalized Entropy, and Utility Maximization

Jose, V. R. R., Nau, R. F., Winkler, R. L. — 2008-11-19

Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision analysis (where new information can lead to improved decisions), and finance (where investors optimize portfolios based on their private information and risk preferences). In this paper, we generalize the two most commonly used parametric families of scoring rules and demonstrate their relation to well-known generalized entropies and utility functions, shedding new light on the characteristics of alternative scoring rules as well as duality relationships between utility maximization and entropy minimization. In particular, we show that weighted forms of the pseudospherical and power scoring rules correspond exactly to measures of relative entropy (divergence) with convenient properties, and they also correspond exactly to the solutions of expected utility maximization problems in which a risk-averse decision maker whose utility function belongs to the linear-risk-tolerance family interacts with a risk-neutral betting opponent or a complete market for contingent claims in either a one-period or a two-period setting. When the market is incomplete, the corresponding problems of maximizing linear-risk-tolerance utility with the risk-tolerance coefficient β are the duals of the problems of minimizing the pseudospherical or power divergence of order β between the decision maker's subjective probability distribution and the set of risk-neutral distributions that support asset prices.

Asymptotically Optimal Control for an Assemble-to-Order System with Capacitated Component Production and Fixed Transport Costs

Plambeck, E. L. — 2008-11-19

This paper examines a two-tier assemble-to-order system. Customer orders for various products must be filled within the product-specific target lead time, or become lost sales. A product can be assembled instantaneously if its required components are in stock at the assembly facility. The production facility for each component is geographically distant from the assembly facility, and the transportation lead time is deterministic. Each shipment of components incurs a fixed cost and a variable cost per unit. The system manager must initially commit to the production capacity for each component. Then, in response to customer orders, he must dynamically manage production (expediting and salvaging) and shipping for each component, and the sequence of customer orders for assembly (how scarce components are allocated to outstanding orders). The objective is to minimize expected discounted costs for lost sales, production, and shipping. This discounted formulation accounts for financial inventory holding costs but not physical inventory holding costs. The main result is that as the order arrival rate for each product becomes large and the discount rate becomes small, a simple threshold policy with independent control of each component is asymptotically optimal. The policy is parameterized by five numbers for each component. Expressions for these parameters, the expected discounted cost, and the long-run average rates of salvaging and expediting are obtained by solving an approximating Brownian control problem. In a numerical example from the computer industry, the Brownian approximation is remarkably accurate.

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Guan, Y., Miller, A. J. — 2008-11-19

In 1958, Wagner and Whitin published a seminal paper on the deterministic uncapacitated lot-sizing problem, a fundamental model that is embedded in many practical production planning problems. In this paper, we consider a basic version of this model in which problem parameters are stochastic: the stochastic uncapacitated lot-sizing problem. We define the production-path property of an optimal solution for our model and use this property to develop a backward dynamic programming recursion. This approach allows us to show that the value function is piecewise linear and right continuous. We then use these results to show that a full characterization of the optimal value function can be obtained by a dynamic programming algorithm in polynomial time for the case that each nonleaf node contains at least two children. Moreover, we show that our approach leads to a polynomial-time algorithm to obtain an optimal solution to any instance of the stochastic uncapacitated lot-sizing problem, regardless of the structure of the scenario tree. We also show that the value function for the problem without setup costs is continuous, piecewise linear, and convex, and therefore an even more efficient dynamic programming algorithm can be developed for this special case.

Approximation Algorithms for Capacitated Stochastic Inventory Control Models

Levi, R., Roundy, R. O., Shmoys, D. B., Truong, V. A. — 2008-11-19

We develop the first algorithmic approach to compute provably good ordering policies for a multiperiod, capacitated, stochastic inventory system facing stochastic nonstationary and correlated demands that evolve over time. Our approach is computationally efficient and guaranteed to produce a policy with total expected cost no more than twice that of an optimal policy. As part of our computational approach, we propose a novel scheme to account for backlogging costs in a capacitated, multiperiod environment. Our cost-accounting scheme, called the forced marginal backlogging cost-accounting scheme, is significantly different from the period-by-period accounting approach to backlogging costs used in dynamic programming; it captures the long-term impact of a decision on system performance in the presence of capacity constraints. In the likely event that the per-unit order costs are large compared to the holding and backlogging costs, a transformation of cost parameters yields a significantly improved guarantee. We also introduce new semimyopic policies based on our new cost-accounting scheme to derive bounds on the optimal base-stock levels. We show that these bounds can be used to effectively improve any policy. Finally, empirical evidence is presented that indicates that the typical performance of this approach is significantly stronger than these worst-case guarantees.

Fast Simulation of Multifactor Portfolio Credit Risk

Glasserman, P., Kang, W., Shahabuddin, P. — 2008-11-19

This paper develops rare-event simulation methods for the estimation of portfolio credit risk—the risk of losses to a portfolio resulting from defaults of assets in the portfolio. Portfolio credit risk is measured through probabilities of large losses, which are typically due to defaults of many obligors (sources of credit risk) to which a portfolio is exposed. An essential element of a portfolio view of credit risk is a model of dependence between these sources of credit risk: large losses occur rarely and are most likely to result from systematic risk factors that affect multiple obligors. As a consequence, estimating portfolio credit risk poses a challenge both because of the rare-event property of large losses and the dependence between defaults. To address this problem, we develop an importance sampling technique within the widely used Gaussian copula model of dependence. We focus on difficulties arising in multifactor models—that is, models in which multiple factors may be common to multiple obligors, resulting in complex dependence between defaults. Our importance sampling procedure shifts the mean of the common factor to increase the frequency of large losses. In multifactor models, different combinations of factor outcomes and defaults can produce large losses, so our method combines multiple importance sampling distributions, each associated with a shift in the mean of common factors. We characterize "optimal" mean shifts. Finding these points is both a combinatorial problem and a convex optimization problem, so we address computational aspects of this step as well. We establish asymptotic optimality results for our method, showing that—unlike standard simulation—it remains efficient as the event of interest becomes rarer.

Optimization Models of Discrete-Event System Dynamics

Chan, W. K., Schruben, L. — 2008-11-19

A methodology is given for modeling the dynamics of discrete-event stochastic systems as optimization problems. The intent is to provide a means to utilize the rich mathematical theory and algorithms of optimization in the study of this important class of systems. A procedure for mapping a simulation event relationship graph into a mixed-integer program is presented, along with examples of queueing networks and manufacturing systems that illustrate the approach. Several potential applications are examined, including automatic constraint generation for optimal resource scheduling, representations of max-plus algebra models for queueing system dynamics, response gradient estimation, and an unconventional technique for simulating queueing systems using virtual resources that are identified from the optimization models for these systems.

Analysis of the (Q, r) Inventory Model for Perishables with Positive Lead Times and Lost Sales

Berk, E., Gurler, U. — 2008-11-19

We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review (Q,r) policy, where r<Q. The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the (Q,r) policy with respect to a time-based benchmark policy and find that the (Q,r) policy might be impractical for rare events, but overall appears to be a good heuristic policy.

Joint Inventory and Pricing Decisions for an Assortment

Aydin, G., Porteus, E. L. — 2008-11-19

We seek optimal inventory levels and prices of multiple products in a given assortment in a newsvendor model (single period, stochastic demand) under price-based substitution, but not stockout-based substitution. We address a demand model involving multiplicative uncertainty, motivated by market share models often used in marketing. The pricing problem that arises is known not to be well behaved in the sense that, in its deterministic version, the objective function is not jointly quasi-concave in prices. However, we find that the objective function is still reasonably well behaved in the sense that there is a unique solution to the first-order conditions, and this solution is optimal for our problem.

Old and New Methods for Lost-Sales Inventory Systems

Zipkin, P. — 2008-11-19

We consider the notoriously difficult discrete-time inventory model with stochastic demands, a constant lead time, and lost sales. We show that the effective state space is a relatively manageable compact set. Then, we test various plausible heuristics. We find that several perform reasonably well, although none is perfect. However, the standard base-stock policy (a direct analogue of the optimal policy for a backlog system) performs badly. We also show that the optimal cost is increasing in the lead time.

Distribution Coordination Between Suppliers and Customers with a Consolidation Center

Song, H., Hsu, V. N., Cheung, R. K. — 2008-11-19

We study a problem faced by a third-party logistics provider (3PL) who needs to coordinate shipments between suppliers and customers through a consolidation center in a distribution network. Products from a supplier have one release time and are consolidated into a single shipment to the consolidation center. At the center, products to the same destination are also consolidated into a single shipment, and the consolidation time can be as early as possible or as late as possible, depending on the customer requirement and cost structure. The 3PL needs to determine the pickup times from the suppliers, delivery times to the customers, and the transportation options while considering product release times, latest arrival times, different consolidation policies, and the transportation and storage costs involved. In this paper, we formulate this problem as a nonlinear optimization problem, show it is an NP-hard problem, and develop a dual-based solution method for the general problem. Utilizing the problem's special structure, we show that the Lagrangian dual of the general problem can be solved optimally as a linear program, thus allowing us to accelerate the computation of a lower bound to the optimal objective function value. The experimental results show that the dual-based algorithm provides solutions with objective function values, which are on average within 3.24% of optimality. We also consider a version of the problem where each customer orders products from all suppliers, for which we develop a polynomial-time algorithm.

The DEA Game Cross-Efficiency Model and Its Nash Equilibrium

Liang, L., Wu, J., Cook, W. D., Zhu, J. — 2008-11-19

In this paper, we examine the cross-efficiency concept in data envelopment analysis (DEA). Cross efficiency links one decision-making unit's (DMU) performance with others and has the appeal that scores arise from peer evaluation. However, a number of the current cross-efficiency approaches are flawed because they use scores that are arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. One set of optimal DEA weights (possibly out of many alternate optima) may improve the cross efficiency of some DMUs, but at the expense of others. While models have been developed that incorporate secondary goals aimed at being more selective in the choice of optimal multipliers, the alternate optima issue remains. In cases where there is competition among DMUs, this situation may be seen as undesirable and unfair. To address this issue, this paper generalizes the original DEA cross-efficiency concept to game cross efficiency. Specifically, each DMU is viewed as a player that seeks to maximize its own efficiency, under the condition that the cross efficiency of each of the other DMUs does not deteriorate. The average game cross-efficiency score is obtained when the DMU's own maximized efficiency scores are averaged. To implement the DEA game cross-efficiency model, an algorithm for deriving the best (game cross-efficiency) scores is presented. We show that the optimal game cross-efficiency scores constitute a Nash equilibrium point.

Cumulative Dominance and Heuristic Performance in Binary Multiattribute Choice

Baucells, M., Carrasco, J. A., Hogarth, R. M. — 2008-11-19

We study the effectiveness of simple heuristics in multiattribute decision making. We consider the case of an additive separable utility function with nonnegative, nonincreasing attribute weights. In this case, cumulative dominance ensures that the so-called cumulative dominance compliant heuristics will choose a best alternative. For the case of binary attribute values and under two probabilistic models of the decision environment generalizing a simple Bernoulli model, we obtain the probabilities of simple and cumulative dominance. In contrast with the probability of simple dominance, the probability of cumulative dominance is shown to be large in many cases, explaining the effectiveness of cumulative dominance compliant heuristics in those cases. Additionally, for the subclass of the so-called fully cumulative dominance compliant heuristics, we obtain an upper bound for the expected loss that only depends on the weights being nonnegative and nonincreasing. The low values of the upper bound for cases in which the probability of cumulative dominance is not large provide an additional explanation for the effectiveness of fully cumulative dominance compliant heuristics. Examples of cumulative dominance compliant heuristics and fully cumulative dominance compliant heuristics are discussed, including the deterministic elimination by aspects (DEBA) heuristic that motivated our work.

Technical Note--A Risk-Sensitive Model for Managing Perishable Products

Feng, Y., Xiao, B. — 2008-11-19

This article presents a risk-sensitive model for managing perishable products assuming the supplier is averse to the variation of revenues. While traditional risk-neutral revenue management models offer optimal strategies in the long run, they are exposed to the variation of revenue flows. If a short-term revenue target is a primary concern for the supplier, the risk-neutral assumption fails to provide the best policy needed. The proposed model uses an exponential function with a risk-sensitive parameter instead of the conventional risk-neutral objective. The risk parameter measures how the supplier is sensitive to the deviation of revenues. We show that the new objective function captures the supplier's risk behavior. We develop a recursive procedure for the optimal solution in closed form. The optimal policy has attractive properties such as nested active price set, monotonicity with respect to the remaining time and inventory, and threshold-type control. When the supplier is more sensitive to the uncertain revenue flows, the risk-sensitive model leads to more conservative pricing policies. Finally, we show that the risk-neutral model is a special case of the proposed framework.

Technical Note--A Make-to-Stock System with Multiple Customer Classes and Batch Ordering

Huang, B., Iravani, S. M. R. — 2008-11-19

This paper examines the impact of customer order sizes on a make-to-stock system with multiple demand classes. We first characterize the manufacturer's optimal production and rationing policies when the demand is nonunitary and lost if unsatisfied. We also investigate the optimal policies of a backorder system with two demand classes and fixed order sizes. Through a numerical study, we show the effects of batch orders on the manufacturer's inventory cost as well as on the benefit of optimal stock rationing. It is shown that batch ordering may reduce the manufacturer's overall cost if carefully introduced in a first-come-first-served (FCFS) system. With the same effective demand rates, the customers' order sizes also have a strong impact on the benefit of optimal stock rationing.

Contributors

2008-11-19

No abstract available.

Appreciation to 2007 Referees

2008-11-19

The Editorial Board would like to thank the following individuals who acted as referees for papers considered or published during the 2007 calendar year. Without their assistance, it would be impossible for INFORMS to publish a journal of high professional standards.

Operations Research--2007 Meritorious Service Award Recipients

2008-11-19

All too often, the hard work that members of the scholarly community do to support our profession goes unrecognized. For the ninth year, the Editorial Board of Operations Research has decided to reward outstanding service to the journal's scholarly mission. Associate editors and referees who did an exceptionally professional job by submitting timely, unbiased, and thoughtful reviews were considered for the award. This award is just a small token of the appreciation for exceptional work performed on behalf of Operations Research and our profession. We thank these individuals for their effort to make Operations Research the premier journal of the field.