In This Issue

How to Measure Risk

In the financial industry, sell-side analysts periodically publish recommendations of underlying securities with target prices. Those recommendations reflect specific economic conditions and influence investors' decisions and thus price movements. However, they do not provide risk measures associated with underlying companies. Risk measures are not just for financial services but for every industry. For example, headlines of the past year have highlighted volatile oil prices impacting industries around the world. The impact of rising oil prices on total supply chain cost is substantial, and we cannot make the right strategic decisions without understanding the risk associated with oil price movements. In “Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics,” S. Y. Chun, A. Shapiro, and S. Uryasev study various ways to estimate risk measures for a single asset at given market conditions. This information could be useful for investors and managers when comparing prospective alternatives.

Medical Urgency-Efficiency Trade-Off in Liver Allocation System Design

Given the scarcity of donated organs, end-stage liver disease patients who need a liver transplant currently face a prolonged wait. In “A Broader View of Designing the Liver Allocation System,” M. Akan, O. Alagoz, B. Ata, F. S. Erenay, and A. Said study the allocation of livers to waiting list patients with an eye on the trade-off between medical urgency and efficiency. To capture both criteria, the authors optimize a weighted combination of the total deaths of waiting list patients and the total quality-adjusted life years (QALYs). At one extreme, the current sickest-first policy of United Network for Organ Sharing (UNOS) emerges as the optimal policy to minimize deaths. At the other, the optimal policy prioritizes patients according to their marginal benefit from transplantation. Using real data, the authors show that, compared to the current UNOS policy, their proposed policy increases total QALYs, significantly reducing both number of wasted livers and deaths after transplant.

What Does the Bullwhip Measure Tell You?

The bullwhip effect, or demand information distortion, has been a subject of both theoretical and empirical studies in the operations management literature. In “Bullwhip Effect Measurement and Its Implications,” L. Chen and H. L. Lee develop a simple set of formulas that describe the traditional bullwhip measure as a combined outcome of several important drivers, such as finite capacity, batch ordering, and seasonality. Their modeling framework features certain plausible approximations that are commonly employed in practical inventory systems. The results can be used to explain various conflicting observations in previous empirical studies. Building on the theoretical framework, the authors discuss the managerial implications of the bullwhip measurement and show that it can be completely noninformative about the underlying supply chain cost performance if it is not linked to the operational details, such as decision intervals and lead times.

Inventory Control When the Fixed Cost Changes with the Order Size

When shipping charges are incurred on a per-truck basis, the ordering cost depends on the total number of trucks used to deliver the units. During loading and off-loading, orders exceeding certain quantity limits require additional crews, and the labor costs increase with each crew assigned. Some transportation contracts explicitly consider those incremental costs and impose a monetary penalty for order sizes exceeding the contracted volume. How should companies incorporate such complex cost schemes into their optimal inventory strategy? In “Optimal Ordering Policies for Periodic-Review Inventory Systems with Quantity-Dependent Fixed Costs,” O. Caliskan-Demirag, Y. Chen, and Y. Yang develop models with different fixed-cost structures that generalize some of the other forms in the literature. For the step-function cost structure and its special cases, they provide the partial characterizations of the optimal ordering policies that minimize the firms' total costs. The study develops results and insights about optimal inventory control policy under general fixed cost structures.

Managing Supply Chain Inventories with Batching

In “On Optimal Policies for Inventory Systems with Batch Ordering,” W. T. Huh and G. Janakiraman study the problem of optimizing inventory investments in a supply chain and achieving good service in the face of uncertain demand. The service dimension is modeled by including a shortage cost when demand exceeds supply. The authors demonstrate that when replenishment orders at every stage of the supply chain are restricted to batches (whereas customer demand is not) the best inventory strategy is to order enough batches at each stage to raise inventory above a predetermined stage-specific target level.

How to Allocate Inventory? By Considering the Customer Composition!

In “Strategies for a Centralized Single Product Multi-Class M/G/1 Make-to-Stock Queue,” H. Abouee-Mehrizi, B. Balcıoğlu, and O. Baron analyze an inventory system serving different priority classes. Unlike previous studies in this popular research area, they consider general production times, which render earlier analysis inapplicable. Not surprisingly, the optimal inventory allocation and production policy for their problem is unknown. The authors analyze the first-come-first-served (FCFS), strict priority (SP), and multilevel rationing (MR) policies. They originated the idea of analyzing M/G/1 queues with priorities and different arrival rates using the customer composition, i.e., the proportion of customers of each class to the total number of customers in the queue. Using this approach, they obtain the system cost under each policy. Their comparative study demonstrates that the MR policy is superior to the FCFS and SP policies.

A Mathematical Approach to Mass-Casualty Triage

Following a mass-casualty event, medical resources (such as ambulances and operating rooms) can be overwhelmed by the sudden jump in demand. Current triage protocols determine patients' priority level based only on their injuries. However, recent work suggests that a proper triage procedure should also account for resource limitations and the event's scale. In “Priority Assignment in Emergency Response,” E. Uzun Jacobson, N. T. Argon, and S. Ziya model the mass-casualty triage problem as a clearing model with multiple classes of impatient jobs, and analyze it using sample-path methods and stochastic dynamic programming. They identify conditions under which information on resource limitations is not needed for prioritization decisions. However, in the absence of such conditions, the optimal triage decision may depend on the event's size and the number of resources. In particular, when resources are severely limited in comparison with the demand, less urgent patients with higher chances of survival should be given priority.

Informativeness of Assortments

Sales reveal information about consumer tastes. However, because most retailers sell an assortment of substitutable products, the quality of this information depends on consumer choice behavior. Conditional on the assortment offered, the more consumers substitute away from their ideal product, the less a retailer can learn from sales. How then should a retailer trade off long-term gains from gathering information about consumer tastes against immediate profits? In “Learning Consumer Tastes Through Dynamic Assortments,” C. Ulu, D. Honhon, and A. Alptekinoğlu study the informativeness of assortments for horizontally differentiated products and characterize optimal dynamic assortments over time. Their main finding is that the optimal assortment in a given period cannot be less informative than the one that would have been chosen had the retailer received perfect information about consumer tastes.

A New Algorithm for a Dynamic Principal-Agent Model

Dynamic adverse selection problems often occur in supply chain management, revenue management, and healthcare management, among other areas. In such a problem, a principal (employer, owner, firm, etc.) tries to obtain certain key information held privately by an agent (employee, manager, customer, etc.), which evolves over the course of the long-term interaction of the two parties. The evolution of the private information adds great complexity to the problem. Drawing from recent developments in the study of partially observable Markov decision processes, H. Zhang proposes a new algorithm in “Solving an Infinite Horizon Adverse Selection Model Through Finite Policy Graphs,” which outperforms a typical algorithm based on value iteration.

What Assortments Should We Offer to Customers When We Don't Know the Underlying Demand Model?

In “Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model,” P. Rusmevichientong and H. Topaloglu propose methods for finding an effective assortment of products to offer to customers when there is uncertainty in the demand model. Customers are assumed to choose products according to a multinomial logit choice model, but the true parameters of the logit model are unknown. To capture the uncertainty in the demand model, the authors represent the set of likely parameter values by a compact uncertainty set. The objective is to find an assortment that maximizes the worst-case revenue over all parameter values in the uncertainty set. They give a complete characterization of the optimal policy. Their proposed method is especially beneficial when there is significant uncertainty in the parameter values, yielding over 10% improvement in the worst-case performance, while maintaining comparable average revenue if average revenue is the performance measure of interest.

Social Networks and Optimal Pricing Strategies

The ubiquity of online social networking communities, such as Facebook and Twitter, has enabled the collection of vast amounts of data on the structure and intensity of social interactions. This motivates the question of whether firms can intelligently use the available data to improve their business strategies. In “Optimal Pricing in Networks with Externalities,” O. Candogan, K. Bimpikis, and A. Ozdaglar study optimal pricing strategies of a seller that has access to social network data. They consider three different pricing strategies for the seller: implementing perfect price discrimination, offering a single uniform price, and offering discounts to a subset of the users. In all cases, they establish a relation between the optimal pricing strategies and the network structure, and provide algorithms for efficient computation of optimal prices.

Next-Day Delivery

Inspired by a real-life problem faced by a Turkish cargo company, “Release Time Scheduling and Hub Location for Next-Day Delivery,” by H. Yaman, O. E. Karasan, and B. Y. Kara, introduces a new facet to the hub location literature. A common assumption that trucks leave their demand centers at the same time is relaxed to improve the overall service quality in terms of on-time arrivals. Models enhanced with valid inequalities deciding on the hub locations, the allocations, and the release times are introduced for different demand patterns. As a managerial insight, it has been observed that the minimum cost solutions may be very poor in terms of service and that a small increase in cost from hub relocation can provide a large increase in on-time cargo. The methodology provides a tool with which decision makers can observe the trade-off between service quality and cost.

Optimal at Every Level

Managing inventory can be a challenging task for firms that need to synchronize product replenishments in multiple echelons to meet customer demand. In “A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands,” M. Zhang, S. Küçükyavuz, and H. Yaman study a multiechelon lot-sizing problem in series and with intermediate demands. This problem arises frequently for many wholesalers, retail chains, and manufacturers who face demands for a product in multiple levels of their supply chain. The authors give a polynomial time algorithm for the two-echelon problem, propose a class of valid inequalities, and establish a hierarchy between several alternative formulations. They show that the alternative formulations and the branch-and-cut algorithm with the proposed valid inequalities are effective in solving multi-item multiechelon test problems under various settings.

A New Approach to Multiobjective Group Decision Making Using Weight Robustness

Many practical problems have multiple conflicting objectives. Eliciting consensus weights quantifying the relative importance of these objectives is a crucial part of multiexpert multicriteria decision making. Information incompleteness and personal subjectivity leads to ambiguity, inconsistency, and lack of consensus in elicited relative weights given to the objectives. In “Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations,” J. Hu and S. Mehrotra propose a robust weight optimization framework (McRow). This framework defines the decision problems over a set of weights integrating different opinions among experts. In addition, the McRow model incorporates uncertain weights and state-dependent uncertain weights. Using the framework, the authors define the concept of robust and stochastic-robust Pareto optimality. They demonstrate, with the help of a disaster planning example, that the McRow framework is suitable to perform weight region sensitivity analysis. They also demonstrate the value of weight-robustness in decision making using a revenue management example.

123...QAP!

The quadratic assignment problem (QAP) is one of the most famous (and difficult in practice) NP-hard optimization problems. A challenging feature of the problem is that a collection of small test cases, available in the QAPLIB repository, cannot be solved by the current state of the art. For example, tho30 was solved only recently, requiring the equivalent of 8,997 days of computation on a distributed computational grid. Other instances remaining unsolved include some in the esc* class. In “Three Ideas for the Quadratic Assignment Problem,” M. Fischetti, M. Monaci, and D. Salvagnin solve instances esc128 (at present, the largest QAPLIB instance solved to proven optimality) and esc32h. They use a branch-and-cut scheme built on top of a general-purpose commercial mixed-integer linear programming solver. Proving optimality for esc32h required about two hours on a single quadcore PC, whereas solving “the big fish” esc128 required just a few seconds on the same hardware.

Pricing Under Demand Uncertainty

Finding an effective pricing policy for a product under demand uncertainty has applications in retail and revenue management. In “Dynamic Pricing Under a General Parametric Choice Model,” J. Broder and P. Rusmevichientong consider a general parametric demand model whose parameters are unknown. They then develop a pricing policy that simultaneously learns the parameters of the underlying demand model and yields near-optimal profits. Their proposed policy balances price experimentation (exploration) and best-guess optimal pricing (exploitation). Numerical experiments indicate that their policy performs well. The analysis illustrates how the geometry of the demand curves impacts the resulting tension in balancing price experimentation and exploitation.

Predicting the Steady-State Performance Measures of GI/M/n + GI Queue in Heavy Traffic

Customer abandonment in telephone call centers can significantly impact system performance. It may also have a nontrivial effect on how firms set staffing levels. This motivates the need to assess system performance in the face of abandonment. In “Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic,” J. Reed and T. Tezcan consider a many-server queuing system with abandonment. Their approach to studying this system is to consider a heavy-traffic regime that scales the hazard rate of the abandonment distribution. In this regime, the authors develop heavy-traffic approximations capable of accurately predicting steady-state performance measures such as the probability of delay and the probability of abandonment. The robustness of their approximations is also tested in the context of setting optimal staffing levels.

Overflow Networks: Approximations and Implications

Although call centers often serve as a primary interaction channel for firms and their customers, some firms outsource their call center operations entirely, and others serve a significant share of their customers in-house, routing only some of the calls to an outside provider. In “Overflow Networks: Approximations and Implications to Call Center Outsourcing,” I. Gurvich and O. Perry provide a performance analysis of cosourcing. They consider a service network in which calls are first routed to an in-house (or dedicated) service station but overflowed to an outside provider (an overflow station) if the waiting room, which has a finite size, is full. The paper provides approximations for overflow networks with many servers under a resource-pooling assumption that the fraction of overflowed calls is nonnegligible. The authors find both an approximation for the overflow processes via limit theorems, and asymptotic independence between the in-house call centers and the outside provider's queue.