Operations Research current issue

In This Issue

Wed, 16 Dec 2009 08:31:53 PST

No abstract available.

OR Practice--Catch-Up Scheduling for Childhood Vaccination

Engineer, F. G., Keskinocak, P., Pickering, L. K. — Wed, 16 Dec 2009 08:31:54 PST

In this paper, we outline the development of the core optimization technology used within a decision support tool to help providers and caretakers in constructing catch-up schedules for childhood immunization. These schedules ensure that a child continues to receive timely coverage against vaccine-preventable diseases in the likely event that one or more doses have been delayed.

This project was undertaken as part of a collaborative effort between the Centers for Disease Control and Prevention (CDC) and Georgia Institute of Technology. Our aim is to develop a decision support tool that removes from the task of constructing catch-up schedules the tedious combinatorial aspects, while maintaining a level of generality that allows easy accommodation for changes in the existing rules and adding new vaccines to the schedule lineup.

We show that the catch-up scheduling problem is NP-hard, and we develop a dynamic programming algorithm that exploits the typical size and structure of the problem to construct optimized schedules almost at the click of a button. In using an optimization-based algorithm, our approach is unique not only in methodology but also in the information, strategy, and advice we can offer to the user.

The tool is being advocated by both the CDC and the American Academy of Pediatrics (AAP) as a means of encouraging caretakers and providers to take a more proactive role in ensuring timely vaccination coverage for children, as well as ensuring the accuracy and quality of a catch-up regime.

Selfish Drug Allocation for Containing an International Influenza Pandemic at the Onset

Sun, P., Yang, L., de Vericourt, F. — Wed, 16 Dec 2009 08:31:54 PST

Recent epidemiologic studies have suggested that the prophylactic use of antiviral drugs could slow down the spread of an influenza epidemic. Because drug stockpiles are presently scattered in different countries, the outbreak of an epidemic gives rise to a game in which each country must make decisions about how best to allocate its own stockpile in order to protect its population. We develop a two-period multivariate Reed-Frost model to represent the spread of the epidemic within and across countries at its onset. We consider the first two periods only to mimic the exponential growth of an epidemic in its early stage, while keeping the model tractable. Preliminary numerical studies suggest that insights from the two-period model hold in general when considering the entire time horizon. Our model captures three critical sources of uncertainty: the number of initial infections, the spread of the disease, and drug efficacy. We show that for small probabilities of between-country infections, the underlying game is supermodular, Nash equilibrium exists, and there is a unique one that is Pareto optimal among all existing equilibria. Further, we identify sufficient conditions under which the optimal solution of a central planner (such as the World Health Organization) constitutes a Pareto improvement over the decentralized equilibrium, suggesting that countries should agree on an allocation scheme that would benefit everyone. By contrast, when the central planner's solution does not constitute a Pareto improvement, minimizing the total number of infected persons globally requires some countries to sacrifice part of their own population, which raises intriguing ethical issues.

A Deterministic Smart Market Model for Groundwater

Raffensperger, J. F., Milke, M. W., Read, E. G. — Wed, 16 Dec 2009 08:31:54 PST

Efficient management of water requires balancing environmental needs, externality considerations, and economic efficiency. Toward that end, this paper presents a deterministic linear program that could be used to operate a smart spot market for groundwater. The market design uses the existing hydrological programs MODFLOW and GWM along with standard linear programming methods. In principle, a market could be set up anywhere that a MODFLOW model is available. The market design has parallels to markets in the electricity and gas sectors, which we discuss. We present a case study with notional bids for Marlborough, New Zealand. Our approach would reduce transaction costs for a water market, reduce users' risk, and increase the reliability of environmental flows. We discuss a number of cautions and limitations to the model and recommend further work on introducing a stochastic framework to the model.

Dynamics of New Product Introduction in Closed Rental Systems

Bassamboo, A., Kumar, S., Randhawa, R. S. — Wed, 16 Dec 2009 08:31:54 PST

We study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of reusable products. The online DVD rental firm Netflix provides the motivation. We assume that rental durations of each user are independent and identically distributed with finite mean. We study transient behavior in this system following the introduction of a new product that is desired by all the users. We represent the usage process for this new product in terms of an empirical distribution. This allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound, via appropriate versions of Glivenko-Cantelli and Donsker's theorems. Analyzing the usage process, we demonstrate that an increase in the variability of the rental duration distribution can actually help the firm by allowing it to set lower capacity levels to provide a desired quality of service. Further, we show that the firm is better off not imposing any deadlines for the return of the product.

End-of-Period vs. Continuous Accounting of Inventory-Related Costs

Rudi, N., Groenevelt, H., Randall, T. R. — Wed, 16 Dec 2009 08:31:54 PST

This paper investigates the effect of using an end-of-period accounting scheme for inventory-related costs when costs actually accrue in continuous time. Using a simple model, we show that (i) the end-of-period scheme results in higher than optimal order-up-to levels and inventory cost if the cost and demand parameters are unchanged, and (ii) it is possible to replicate both the optimal base-stock level and its cost by selecting the values of the cost or demand parameters judiciously. The cost adjustments often require extreme values, and no systematic cost parameter adjustment scheme is robust. However, we find a systematic adjustment to the demand parameters that serves as a good approximation and is robust. We therefore conclude that end-of-period cost accounting without parameter adjustments is in general inappropriate when costs are incurred continuously, but there are adjustments that can make it work well.

Multiattribute Utility Copulas

Abbas, A. E. — Wed, 16 Dec 2009 08:31:54 PST

We introduce the notion of a multiattribute utility copula that expresses any (i) continuous; (ii) bounded multiattribute utility function that is (iii) nondecreasing with each of its arguments, and (iv) strictly increasing with each argument for at least one reference value of the complement attributes, in terms of single-attribute utility assessments. This formulation provides a wealth of new functional forms that can be used to model preferences over utility-dependent attributes and enables sensitivity analyses to some of the widely used functional forms of utility independence. We introduce a class of utility copulas, called Archimedean utility copulas, and discuss the conditions under which it yields the additive and multiplicative forms. We also discuss linear and composite transformations of utility copulas that construct utility functions with partial utility independence. We conclude with the risk aversion functions that are induced by utility copula formulations and work through several examples to illustrate the approach.

A Decomposition Approach for a Class of Capacitated Serial Systems

Janakiraman, G., Muckstadt, J. A. — Wed, 16 Dec 2009 08:31:54 PST

We study a class of two-echelon serial systems with identical ordering/production capacities or limits for both echelons. Demands are assumed to be integer valued. For the case where the lead time to the upstream echelon is one period, the optimality of state-dependent modified echelon base-stock policies is proved using a decomposition approach. For the case where the upstream lead time is two periods, we introduce a new class of policies called "two-tier base-stock policies," and prove their optimality. Some insight about the inventory control problem in N echelon serial systems with identical capacities at all stages and arbitrary lead times everywhere is also provided. We argue that a generalization of two-tier base-stock policies, which we call "multitier base-stock policies," are optimal for these systems; we also provide a bound on the number of parameters required to specify the optimal policy.

Inventory Centralization Games with Price-Dependent Demand and Quantity Discount

Chen, X. — Wed, 16 Dec 2009 08:31:54 PST

Consider a distribution system consisting of a set of retailers facing a single-period price-dependent demand of a single product. By taking advantage of the risk-pooling effect and the quantity/volume discount provided by suppliers or third-party carriers, the retailers may place joint orders and keep inventory at central warehouses before demand realization, and allocate inventory among themselves after demand realization to reduce their operating costs. Under rather general assumptions, we prove that there is a stable allocation of profits among the retailers in the sense that the resulting inventory centralization game has a nonempty core. We also show how to compute an allocation in the core.

Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms

Besbes, O., Zeevi, A. — Wed, 16 Dec 2009 08:31:54 PST

We consider a single-product revenue management problem where, given an initial inventory, the objective is to dynamically adjust prices over a finite sales horizon to maximize expected revenues. Realized demand is observed over time, but the underlying functional relationship between price and mean demand rate that governs these observations (otherwise known as the demand function or demand curve) is not known. We consider two instances of this problem: (i) a setting where the demand function is assumed to belong to a known parametric family with unknown parameter values; and (ii) a setting where the demand function is assumed to belong to a broad class of functions that need not admit any parametric representation. In each case we develop policies that learn the demand function "on the fly," and optimize prices based on that. The performance of these algorithms is measured in terms of the regret: the revenue loss relative to the maximal revenues that can be extracted when the demand function is known prior to the start of the selling season. We derive lower bounds on the regret that hold for any admissible pricing policy, and then show that our proposed algorithms achieve a regret that is "close" to this lower bound. The magnitude of the regret can be interpreted as the economic value of prior knowledge on the demand function, manifested as the revenue loss due to model uncertainty.

The Impact of Oligopolistic Competition in Networks

Cominetti, R., Correa, J. R., Stier-Moses, N. E. — Wed, 16 Dec 2009 08:31:54 PST

In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines.

Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria.

Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

Besbes, O., Maglaras, C. — Wed, 16 Dec 2009 08:31:54 PST

We consider a revenue-maximizing make-to-order manufacturer that serves a market of price- and delay-sensitive customers and operates in an environment in which the market size varies stochastically over time. A key feature of our analysis is that no model is assumed for the evolution of the market size. We analyze two main settings: (i) the size of the market is observable at any point in time; and (ii) the size of the market is not observable and hence cannot be used for decision making. We focus on high-volume systems that are characterized by large processing capacities and market sizes, and where the latter fluctuate on a slower timescale than that of the underlying production system dynamics. We develop an approach to tackle such problems that is based on an asymptotic analysis and that yields near-optimal policy recommendations for the original system via the solution of a stochastic fluid model.

Optimal Supply Diversification Under General Supply Risks

Federgruen, A., Yang, N. — Wed, 16 Dec 2009 08:31:54 PST

We analyze a planning model for a firm or public organization that needs to cover uncertain demand for a given item by procuring supplies from multiple sources. The necessity to employ multiple suppliers arises from the fact that when an order is placed with any of the suppliers, only a random fraction of the order size is usable. The model considers a single demand season with a given demand distribution, where all supplies need to be ordered simultaneously before the start of the season. The suppliers differ from one another in terms of their yield distributions, their procurement costs, and capacity levels.

The planning model determines which of the potential suppliers are to be retained and what size order is to be placed with each. We consider two versions of the planning model: in the first, the service constraint model (SCM), the orders must be such that the available supply of usable units covers the random demand during the season with (at least) a given probability. In the second version of the model, the total cost model (TCM), the orders are determined so as to minimize the aggregate of procurement costs and end-of-the-season inventory and shortage costs. In the classical inventory model with a single, fully reliable supplier, these two models are known to be equivalent, but the equivalency breaks down under multiple suppliers with unreliable yields.

For both the service constraint and total cost models, we develop a highly efficient procedure that generates the optimal set of suppliers as well as the optimal orders to be assigned to each. Most importantly, these procedures generate a variety of important qualitative insights, for example, regarding which sets of suppliers allow for a feasible solution, both when they have ample supply and when they are capacitated, and how various model parameters influence the selected set of suppliers, the aggregate order size, and the optimal cost values.

Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts

Chen, X., Zhang, Y. — Wed, 16 Dec 2009 08:31:55 PST

In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature, in which recourse decisions are restricted to be linear in terms of the primitive uncertainties. We propose a special case of the extended affinely adjustable robust counterpart—the splitting-based extended affinely adjustable robust counterpart—and illustrate both theoretically and computationally that the potential of the affinely adjustable robust counterpart method is well beyond the one presented in the literature. Similar to the affinely adjustable robust counterpart, our approach ends up with deterministic optimization formulations that are tractable and scalable to multistage problems.

Constructing Uncertainty Sets for Robust Linear Optimization

Bertsimas, D., Brown, D. B. — Wed, 16 Dec 2009 08:31:55 PST

In this paper, we propose a methodology for constructing uncertainty sets within the framework of robust optimization for linear optimization problems with uncertain parameters. Our approach relies on decision maker risk preferences. Specifically, we utilize the theory of coherent risk measures initiated by Artzner et al. (1999) [Artzner, P., F. Delbaen, J. Eber, D. Heath. 1999. Coherent measures of risk. Math. Finance 9 203–228.], and show that such risk measures, in conjunction with the support of the uncertain parameters, are equivalent to explicit uncertainty sets for robust optimization. We explore the structure of these sets in detail. In particular, we study a class of coherent risk measures, called distortion risk measures, which give rise to polyhedral uncertainty sets of a special structure that is tractable in the context of robust optimization. In the case of discrete distributions with rational probabilities, which is useful in practical settings when we are sampling from data, we show that the class of all distortion risk measures (and their corresponding polyhedral sets) are generated by a finite number of conditional value-at-risk (CVaR) measures. A subclass of the distortion risk measures corresponds to polyhedral uncertainty sets symmetric through the sample mean. We show that this subclass is also finitely generated and can be used to find inner approximations to arbitrary, polyhedral uncertainty sets.

Against Classification Attacks: A Decision Tree Pruning Approach to Privacy Protection in Data Mining

Li, X.-B., Sarkar, S. — Wed, 16 Dec 2009 08:31:55 PST

Data-mining techniques can be used not only to study collective behavior about customers, but also to discover private information about individuals. In this study, we demonstrate that decision trees, a popular classification technique for data mining, can be used to effectively reveal individuals' confidential data, even when the identities of the individuals are not present in the data. We propose a novel approach for organizations to protect confidential data from such a classification attack. The key components of this approach include a set of entropy-based measures to evaluate disclosure risks of individual records, an optimal pruning algorithm to identify high-risk records, and a pair of data-swapping procedures to reduce the disclosure risks. The proposed method provides the best trade-off between data utility and privacy protection against classification attacks. It can be applied to data with both numeric and categorical attributes. An experimental study on six real-world data sets shows that the proposed method is very effective in protecting privacy while enabling legitimate data mining and analysis.

Combinatorial Benders Cuts for the Minimum Tollbooth Problem

Bai, L., Rubin, P. A. — Wed, 16 Dec 2009 08:31:55 PST

We address a toll pricing problem in which the objective is to minimize the number of required toll facilities in a transportation network while inducing drivers to make the most efficient collective use of the network. We formulate the problem as a mixed-integer programming model and propose a solution method using combinatorial Benders cuts. Computational study of real networks as well as randomly generated networks indicates that our proposed method is efficient in obtaining provably optimal solutions for networks with small to medium sizes.

Technical Note--Personalized Dynamic Pricing of Limited Inventories

Aydin, G., Ziya, S. — Wed, 16 Dec 2009 08:31:55 PST

Prior work has investigated time- and inventory-level-dependent pricing of limited inventories with finite selling horizons. We consider a third dimension—in addition to time and inventory level—that the firms can use in setting their prices: the information that the firm has at the individual customer level. An arriving customer provides a signal to the firm, which is an imperfect indicator of the customer's willingness to pay, and the firm makes a personalized price offer depending on the signal, inventory level, and time. We consider two different models: full personalization and partial personalization. In the full personalization model, the firm charges any price it wishes given the customer signal, while in the partial personalization model, the firm can charge one of two prices. We find that a mere correlation between the signals and customers' willingness to pay is not sufficient to ensure intuitive relationships between the signal and the optimal prices. We determine a stronger condition, which leads to several structural properties, including the monotonicity of the optimal price with respect to the signal in the full personalization model. For the partial personalization model, we show that the optimal pricing policy is of threshold-type and that the threshold is monotonic in the inventory level and time.

Contributors

Wed, 16 Dec 2009 08:31:55 PST

No abstract available.

Indices to Volume 57: 2009

Wed, 16 Dec 2009 08:31:55 PST

No abstract available.

Operations Research Call for Papers: Special Issue on Operations Research for the Public Interest

Kress, M., Oren, S., Zenios, S. — Wed, 16 Dec 2009 08:31:55 PST

No abstract available.