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Problem definition: A major task in retail operations is to optimize the assortments exhibited to consumers. To this end, retailers need to understand customers' preferences for different products. Academic/practical relevance: This is particularly challenging when only sales and product-availability data are recorded, and not all products are displayed in all periods. Similarly, in revenue management contexts, firms (airlines, hotels, etc.) need to understand customers' preferences for different options in order to optimize the menu of products to offer. Methodology: In this paper, we study the estimation of preferences under a multinomial logit model of demand when customers arrive over time in accordance with a nonhomogeneous Poisson process. This model has recently caught important attention in both academic and industrial practices. We formulate the problem as a maximum-likelihood estimation problem, which turns out to be nonconvex. Results: Our contribution is twofold: From a theoretical perspective, we characterize conditions under which the maximum-likelihood estimates are unique and the model is identifiable. From a practical perspective, we propose a minorization-maximization (MM) algorithm to ease the optimization of the likelihood function. Through an extensive numerical study, we show that our algorithm leads to better estimates in a noticeably short computational time compared with state-of-the-art benchmarks. Managerial implications: The theoretical results provide a solid foundation for the use of the model in terms of the quality of the derived estimates. At the same time, the fast MM algorithm allows the implementation of the model and the estimation procedure at large scale, compatible with real industrial applications. [ABSTRACT FROM AUTHOR]

In this paper, we describe data collected from five U.S. properties of a major hotel chain that can be used to benchmark the performance of choice-based revenue management (RM) algorithms. The process used to collect this data illustrates subtle complexities involved in extracting product availability information from current RM systems and sheds new light on practical issues that need to be addressed to successfully implement choice-based RM systems. The data described in this paper is publicly available at the journal's website at http://msom.pubs.informs.org. [ABSTRACT FROM AUTHOR]

Barter exchange markets are markets in which agents seek to directly trade their goods with each other. Exchanges occur in cycles or in chains in which each agent gives a good to the next agent. Kidney exchange is an important type of barter exchange market that allows incompatible patient--donor pairs to exchange kidneys so the involved patients can receive a transplant. The clearing problem is to find an allocation of donors to patients that is optimal with respect to multiple criteria. To achieve the best possible score on all criteria, long cycles and chains are often needed, particularly when there are many hard-to-match patients. In this paper we show why this may pose difficulties for existing approaches to the optimization of kidney exchanges. We then present a generic iterative branch-and-price algorithm that can deal effectively with multiple criteria, and we show how the pricing problem may be solved in polynomial time for a general class of criteria. Our algorithm is effective even for large, realistic patient--donor pools. Our approach and its effects are demonstrated by using simulations with kidney exchange data from the Netherlands and the United States. [ABSTRACT FROM AUTHOR]

While inventory- and revenue-management problems can be represented as Markov decision process (MDP) models, in some cases the well-known dynamic-programming curse of dimensionality makes it computationally prohibitive to solve them exactly. An alternative solution, called here the control-algorithm approach, is to use a math program (MP) to approximately represent the MDP and use its optimal solution to heuristically instantiate the parameters of the decision rules of a given set of control policies. As new information is observed over time, the control algorithm can incorporate it by re-solving the MP and revising the parameters of the decision rules with the newly obtained solution. The re-solving issue arises when one reflects on the consequences of this revision: Does the performance of the control algorithm really improve by revising its decision-rule instantiation with the solution of the re-solved MP, or should an appropriate modification of the prior solution be used? This paper analyzes the control-algorithm re-solving issue for a class of finite-horizon inventory- and revenue-management problems. It establishes sufficient conditions under which re-solving does not deteriorate the performance of a control algorithm, and it applies these results to control algorithms for network revenue management and multiproduct make-to-order production with lost sales and positive lead time. [ABSTRACT FROM AUTHOR]

Consider a firm that owns a fixed capacity of a resource that is consumed in the production or delivery of multiple products. The firm strives to maximize its total expected revenues over a finite horizon, either by choosing a dynamic pricing strategy for each product or, if prices are fixed, by selecting a dynamic rule that controls the allocation of capacity to requests for the different products. This paper shows how these well-studied revenue management problems can be reduced to a common formulation in which the firm controls the aggregate rate at which all products jointly consume resource capacity, highlighting their common structure, and in some cases leading to algorithmic simplifications through the reduction in the control dimension of the associated optimization problems. In the context of their associated deterministic (fluid) formulations, this reduction leads to a closed-form characterization of the optimal controls, and suggests several natural static and dynamic pricing heuristics. These are analyzed asymptotically and through an extensive numerical study. In the context of the former, we show that "resolving" the fluid heuristic achieves asymptotically optimal performance under fluid scaling. [ABSTRACT FROM AUTHOR]

We study a periodically reviewed multiechelon serial inventory system with a capacity constraint on the order quantity at each stage. The cost criterion we use to evaluate inventory policies for this system is the sum of the expected long-run average holding and shortage costs. It is well known that for this problem, characterizing the structure of the optimal policy and computing it are very difficult. We consider the use of echelon base-stock policies for our system (even though they are known to be suboptimal) and propose algorithms for finding base-stock levels that are easy to understand and implement. We derive bounds on the ratios between the costs achieved by our algorithms and the optimal costs (over all policies). For light-tailed demand distributions, our algorithms are shown to be asymptotically optimal in the sense that our bounds are close to one in high service-level environments. Our computational investigations reveal that our algorithms perform well even under modest service levels. [ABSTRACT FROM AUTHOR]

In the small package shipping industry (as in other industries), companies try to differentiate themselves by providing high levels of customer service. This can be accomplished in several ways, including online tracking of packages, ensuring on-time delivery, and offering residential pickups. Some companies want their drivers to develop relationships with customers on a route and have the same drivers visit the same customers at roughly the same time on each day that the customers need service. These service requirements, together with traditional constraints on vehicle capacity and route length, define a variant of the classical capacitated vehicle routing problem, which we call the consistent VRP (ConVRP). In this paper, we formulate the problem as a mixed-integer program and develop an algorithm to solve the ConVRP that is based on the record-to-record travel algorithm. We compare the performance of our algorithm to the optimal mixed-integer program solutions for a set of small problems and then apply our algorithm to five simulated data sets with 1,000 customers and a real-world data set with more than 3,700 customers. We provide a technique for generating ConVRP benchmark problems from vehicle routing problem instances given in the literature and provide our solutions to these instances. The solutions produced by our algorithm on all problems do a very good job of meeting customer service objectives with routes that have a low total travel time. [ABSTRACT FROM AUTHOR]

We consider a component acquisition problem for a contract manufacturer who faces a one-time stochastic demand for a single product consisting of a number of components. Components can be ordered early at normal prices before the demand is revealed, or they can be replenished later at higher prices due to expediting. In addition, the customer pays a price for the final product that is nonincreasing in the delivery lead time to discourage late delivery. We propose a cost-minimization model and develop an efficient polynomial time algorithm to solve the problem. [ABSTRACT FROM AUTHOR]

This paper studies the optimization of the (S, T) inventory policy, where T is the replenishment interval and S is the order-up-to level. First, we demonstrate that the previously established joint convexity of the long-run average cost is false. Hence, the optimization is not straightforward. We then point out that the joint convexity concept depends on whether S and T are continuous or discrete variables, and in some situations it may not even be well defined. Nonetheless, we are able to identify several useful properties of the cost function, such as submodularity and coordinatewise convexity. Based on these properties, we develop efficient algorithms to compute the optimal policy for continuous and discrete demands. [ABSTRACT FROM AUTHOR]

We consider a choice-based, network revenue management (RM) problem in a setting where heterogeneous customers consider an assortment of products offered by a firm (e.g., different flight times, fare classes, and/or routes). Individual choice decisions are modeled through an ordered list of preferences, and minimal assumptions are made about the statistical properties of this demand sequence. The firm manages the availability of products using a bid-price control strategy, and would like to optimize the control parameters. We formulate a continuous demand and capacity model for this problem that allows for the partial acceptance of requests. The model admits a simple calculation of the sample path gradient of the revenue function. This gradient is then used to construct a stochastic steepest ascent algorithm. We show that the algorithm converges (w.p.1) to a stationary point of the expected revenue function under mild conditions. The procedure is relatively efficient from a computational standpoint, and in our synthetic and real-data experiments performs comparably to or even better than other choice-based methods that are incompatible with the current infrastructure of RM systems. These features make it an interesting candidate to be pursued for real-world applications. [ABSTRACT FROM AUTHOR]

We examine the placement of safety stocks in a supply chain for which we have an evolving demand forecast. Under assumptions about the forecasts, the demand process, and the supply chain structure, we show that safety-stock placement for such systems is effectively equivalent to the corresponding well-studied problem for systems with stationary demand bounds and base-stock policies. Hence, we can use existing algorithms to find the optimal safety stocks. We use a case study with real data to demonstrate that there are significant benefits from the inclusion of the forecast process when determining the optimal safety stocks. We also conduct a computational experiment to explore how the placement and size of the safety stocks depend on the nature of the forecast evolution process. [ABSTRACT FROM AUTHOR]

Call centers usually handle several types of calls, but it is usually not possible or cost effective to have every agent be able to handle every type of call. Thus, the agents tend to have different skills, in different combinations. In such an environment, it is challenging to route calls effectively and determine the staff requirements. This paper addresses both of these routing and staffing problems by exploiting limited cross-training. Consistent with the literature on flexible manufacturing, we find that minimal flexibility can provide great benefits: Simulation experiments show that when (1) the service-time distribution does not depend on the call type or the agent and (2) each agent has only two skills, in appropriate combinations, the performance is almost as good as when each agent has all skills. We apply this flexibility property to develop an algorithm for both routing and staffing, aiming to minimize the total staff subject to per-class performance constraints. With appropriate flexibility, it suffices to use a suboptimal routing algorithm. Simulation experiments show that the overall procedure can be remarkably effective: The required staff with limited cross-training can be nearly the same as if all agents had all skills. Hence, the overall algorithm is nearly optimal for that scenario. [ABSTRACT FROM AUTHOR]

Proposes a model for multiple resource types used for multiple product families. Mathematical formulation of the strategic capacity planning problem; Discussion on demand modeling; Calculation of the expected value of the instantaneous lost sales cost; Outline of an efficient divide-and-conquer algorithm.

A retailer's product selection decisions are largely driven by her assumptions on how consumers make choices. We use a ranking-based consumer choice model to represent consumer preferences: every customer has a ranking of the potential products in the category and purchases his highest ranked product (if any) offered in the assortment. We consider four practically motivated special cases of this model, namely, the one-way substitution, the locational choice, the outtree, and the intree preference models, and we study the retailer's product selection problem when products have different price and cost parameters. We assume that the retailer incurs a fixed carrying cost per product offered, a goodwill penalty for each customer who does not purchase his first choice and a lost sale penalty for each customer who does not find an acceptable product to buy. For the first three models, we obtain efficient solution methods that simplify to either a shortest path method or a dynamic program. For the fourth model, we construct an effective algorithm and show numerically that, in practice, it is much faster than enumeration. We also obtain valuable insights on the structure of the optimal assortment. [ABSTRACT FROM AUTHOR]

The effective local reuse of physical cash by depository institutions (DIs) is the primary goal of the new cash recirculation policy of the Federal Reserve System (Fed) of the United States. These guidelines, implemented since July 2007, encourage the reuse of cash by (i) penalizing a DI for the practice of cross shipping, the nearsimultaneous deposit of used cash to--and withdrawal of fit cash from--the Fed; and (ii) offering a custodial inventory program that enables a DI to transfer fit cash to the Fed's books, but physically hold it within the DI's secured facility. The effective management of the inventory of cash under these new guidelines is both a challenging and important issue for DIs. We introduce two new multiperiod models--designed specifically to capture the operations of a medium-size DI--that emerge from the DI's objective to minimize the total cost incurred in managing the inventory of cash over a finite planning horizon. The Basic Model (BM) captures the DI's mode of operations if it chooses not to locally reuse cash and, instead, incur the cross-shipping penalty. Using two important structural properties, we provide a polynomial-time dynamic programming algorithm for BM. The Reuse Model (RM) represents the DI's actions when it locally recirculates cash. We first prove the hardness of RM and then develop an integer programming formulation. A comprehensive test bed--based on our interaction with a leading secure-logistics provider--helps us to develop several useful insights into the relative impacts of the DI-specific parameters and the Fed's cross-shipping fee on the effective management of cash. In particular, we show that the Value of Local Reuse for a DI, measured as the percentage cost saving between the optimal solutions of BM and RM, is substantial, and we analyze the forces that influence the volume of cross shipping. We also develop a rolling-horizon procedure to adapt the optimal solutions of BM and RM for obtaining near-optimal real-time solutions in the presence of a modest amount of uncertainty. Finally, we provide a comparative analysis of a DI's decisions under the Fed's mechanism and those under a socially optimal mechanism. [ABSTRACT FROM AUTHOR]

Suppliers routinely sell goods to retailers on credit. Common credit terms are tantamount to a schedule of declining discounts (escalating penalties) that depend on how long the retailer takes to pay off the supplier's loan. However, issues such as which stocking policies are optimal in the presence of supplier-provided credit have been investigated only when demand is assumed deterministic. Nearly all stochastic inventory models assume either time-invariant finance charges or charges that may vary with time but not with the age of the credit. In this article we present a discrete time model of the retailer's operations with random demand, which is used to prove that the structure of the optimal policy is not affected by credit terms, although the value of the optimal policy parameter is. This is followed by a continuous time model, which leads to an algorithm for finding the optimal stock level. We also model the supplier's problem and calculate the optimal credit parameters in numerical experiments. [ABSTRACT FROM AUTHOR]

We consider a revenue management, network capacity control problem in a setting where heterogeneous customers choose among the various products offered by a firm (e.g., different flight times, fare classes, and/or routings). Customers may therefore substitute if their preferred products are not offered. These individual customer choice decisions are modeled as a very general stochastic sequence of customers, each of whom has an ordered list of preferences. Minimal assumptions are made about the statistical properties of this demand sequence. We assume that the firm controls the availability of products using a virtual nesting control strategy and would like to optimize the protection levels for its virtual classes accounting for the (potentially quite complex) choice behavior of its customers. We formulate a continuous demand and capacity approximation for this problem, which allows for the partial acceptance of requests for products. The model admits an efficient calculation of the sample path gradient of the network revenue function. This gradient is then used to construct a stochastic steepest ascent algorithm. We show the algorithm converges in probability to a stationary point of the expected revenue function under mild conditions. The algorithm is relatively efficient even on large network problems, and in our simulation experiments it produces significant revenue increases relative to traditional virtual nesting methods. On a large-scale, real-world airline example using choice behavior models fit to actual booking data, the method produced an estimated 10% improvement in revenue relative to the controls used by the airline. The examples also provide interesting insights into how protection levels should be adjusted to account for choice behavior. Overall, the results indicate that choice behavior has a significant impact on both capacity control decisions and revenue performance and that our method is a viable approach for addressing the problem. [ABSTRACT FROM AUTHOR]

We analyze the problem of optimal location of a set of facilities in the presence of stochastic demand and congestion. Customers travel to the closest facility to obtain service; the problem is to determine the number, locations, and capacity of the facilities. Under rather general assumptions (spatially distributed continuous demand, general arrival and service processes, and nonlinear location and capacity costs) we show that the problem can be decomposed, and construct an efficient optimization algorithm. The analysis yields several insights, including the importance of equitable facility configurations (EFCs), the behavior of optimal and near-optimal capacities, and robust class of solutions that can be constructed for this problem. [ABSTRACT FROM AUTHOR]

The dynamic pricing problem concerns the determination of selling prices over time for a product whose demand is random and whose supply is fixed. We approach this problem in a novel way by formulating a dynamic optimization model in which the demand function is isoelastic but the random demand process is quite general. Ultimately, what we find is a strong parallel between the dynamic pricing problem and dynamic inventory models. This parallel leads to a reinterpretation of the dynamic pricing problem as a price-setting news vendor problem with recourse, which is useful not only because it yields insights into the optimal solution, but also because it leads to additional insights into how pricing recourse affects the actions and profits of a price-setting news vendor. We make contributions in three areas: First, we develop structural properties that define an optimal pricing strategy over a finite horizon and investigate how that policy impacts a news vendor's optimal procurement policy and optimal expected profit. Second, we establish a practical and efficient algorithm for computing the optimal prices. Third, we examine how market parameters affect the optimal solution through a series of numerical experiments that utilize the algorithm. [ABSTRACT FROM AUTHOR]

Develops a coordination strategy that provides a common incentive scheme to independent buyers in a distribution system and improves the profit of the vendors. Use of a numerical algorithm; Comparison of the proposed coordination strategy with the simple quantity-discount decision; Managerial issues for coordinating the replenishment time and order quantity of independent buyers.