We develop an approximate dynamicprogramming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a nonlinear function which is s...
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We develop an approximate dynamicprogramming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a nonlinear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach can outperform some recently proposed alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime. (C) 2011 Elsevier B.V. All rights reserved.
We consider tandem lines with finite buffers and flexible, heterogeneous servers that are synergistic in that they work more effectively in teams than on their own. Our objective is to determine how the servers should...
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We consider tandem lines with finite buffers and flexible, heterogeneous servers that are synergistic in that they work more effectively in teams than on their own. Our objective is to determine how the servers should be assigned dynamically to tasks in order to maximize the long-run average throughput. In particular, we investigate when it is better to take advantage of synergy among servers, rather than exploiting the servers' special skills, to achieve the best possible system throughput. We show that when there is no trade-off between server synergy and servers' special skills (because the servers are generalists who are equally skilled at all tasks), the optimal policy has servers working in teams of two or more at all times. Moreover, for Markovian systems with two stations and two servers, we provide a complete characterization of the optimal policy and show that, depending on how well the servers work together, the optimal policy either takes full advantage of servers' special skills, or full advantage of server synergy (and hence there is no middle ground in this case). Finally, for a class of larger Markovian systems, we provide sufficient conditions that guarantee that the optimal policy should take full advantage of server synergy at all times.
Seasonal products have an effective inventory deadline, a time by which the inventory must be ready to distribute. The deadline creates an incentive to start early with production. However, opportunities to gather inf...
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Seasonal products have an effective inventory deadline, a time by which the inventory must be ready to distribute. The deadline creates an incentive to start early with production. However, opportunities to gather information that might change production decisions provide an incentive to defer the start of production. We study the resultant dynamic decision problem with alternatives that commit to one of several courses of action now and an alternative to defer the commitment to gather more information about the possible consequences of each alternative. The deadline increases the effective cost of gathering information because that cost includes the value sacrificed by reducing the time available to produce inventory. We frame our model using the annual influenza vaccine composition decision: deciding between strains of the virus to include, which must happen in the spring to allow time for vaccine production before the fall flu season begins. Our analysis describes the optimal decision strategies for this commit-or-defer decision. Many insights are drawn from this model that could contribute to more informed flu vaccine composition decisions. We comment on the relevance of this commit-or-defer decision model to a firm's production decisions for other seasonal products with an inventory deadline such as fashion goods.
In this paper, we consider numerous inventory control problems for which the base-stock policies are known to be optimal, and we propose stochastic approximation methods to compute the optimal base-stock levels. The e...
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In this paper, we consider numerous inventory control problems for which the base-stock policies are known to be optimal, and we propose stochastic approximation methods to compute the optimal base-stock levels. The existing stochastic approximation methods in the literature guarantee that their iterates converge, but not necessarily to the optimal base-stock levels. In contrast, we prove that the iterates of our methods converge to the optimal base-stock levels. Moreover, our methods continue to enjoy the well-known advantages of the existing stochastic approximation methods. In particular, they only require the ability to obtain samples of the demand random variables, rather than to compute expectations explicitly, and they are applicable even when the demand information is censored by the amount of available inventory.
In the United States, patients with end-stage liver disease must join a waiting list to be eligible for cadaveric liver transplantation. Due to privacy concerns, the details of the composition of this waiting list are...
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In the United States, patients with end-stage liver disease must join a waiting list to be eligible for cadaveric liver transplantation. Due to privacy concerns, the details of the composition of this waiting list are not publicly available. This paper considers the benefits associated with creating a more transparent waiting list. We study these benefits by modeling the organ accept/reject decision faced by these patients as a Markov decision process in which the state of the process is described by patient health, quality of the offered liver, and a measure of the rank of the patient in the waiting list. We prove conditions under which there exist structured optimal solutions, such as monotone value functions and control-limit optimal policies. We de. ne the concept of the patient's price of privacy, namely, the number of expected life days lost due to the lack of complete waiting list information. We conduct extensive numerical studies based on clinical data, which indicate that this price of privacy is typically on the order of 5% of the optimal solution value.
Two continuous time formulations of the dynamic traffic assignment problem are considered, one that corresponds to system optimization and the other to a version of user optimization on a single mode network using opt...
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Two continuous time formulations of the dynamic traffic assignment problem are considered, one that corresponds to system optimization and the other to a version of user optimization on a single mode network using optimalcontrol theory. Pontryagin's necessary conditions are analyzed and given economic interpretations that correspond to intuitive notions regarding dynamic system optimized and dynamic user optimized traffic flow patterns. Notably, we offer the first dynamic generalization of Beckmann's equivalent optimization problem for static user optimized traffic assignment in the form of an optimalcontrol problem. The analysis further establishes that a constraint qualification and convexity requirements for the Hamiltonian, which together ensure that the necessary conditions are also sufficient, are satisfied under commonly encountered regularity conditions.
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