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Recent documents in Tepper School of Businessen-usThu, 12 Nov 2015 01:33:13 PST3600Optimizing Liver Allocation System Incorporating Disease Evolution
http://repository.cmu.edu/tepper/1541
http://repository.cmu.edu/tepper/1541Tue, 10 Nov 2015 14:35:52 PST
We propose an efficient liver allocation system for allocating donated organs to patients waiting for transplantation, the only viable treatment for End-Stage Liver Disease. We optimize two metrics which are used to measure the efficiency: total quality adjusted life years and the number of organs wasted due to patients rejecting some organ offers. Our model incorporates the possibility that the patients may turn down the organ offers. Given the scarcity of available organs relative to the number patients waiting for transplantation, we model the system as a multiclass fluid model of overloaded queues. The fluid model we advance captures the disease evolution over time by allowing the patients to switch between classes over time, e.g. patients waiting for transplantation may get sicker/better, or may die. We characterize the optimal solution to the fluid model using the duality framework for optimal control problems developed by Rockafellar (1970a). The optimal solution for assigning livers to patients is an intuitive dynamic index policy, where the indices depend on patients' acceptance probabilities of the organ offer, immediate rewards, and the shadow prices calculated from the dual dynamical system. Finally, we perform a detailed simulation study to demonstrate the effectiveness of the proposed policy using data from the United Network for Organ Sharing System (UNOS).
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Mustafa Akan et al.Optimal Structural Results for Assemble-to-Order Generalized M-Systems
http://repository.cmu.edu/tepper/1540
http://repository.cmu.edu/tepper/1540Tue, 10 Nov 2015 14:35:46 PST
We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process and seek an optimal policy that specifies when a batch of components should be produced (i.e., inventory replenishment) and whether an arriving demand for each product should be satisfied (i.e., inventory allocation). We characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base stock and lattice-dependent rationing.
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Emre Nadar et al.Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model
http://repository.cmu.edu/tepper/1539
http://repository.cmu.edu/tepper/1539Tue, 10 Nov 2015 14:35:41 PST
We consider a manufacturer who sells both the new and remanufactured versions of a product over its life cycle. The manufacturer’s profit depends crucially on her ability to synchronize product returns with the sales of the remanufactured product. This gives rise to a challenging dynamic optimization problem where the size of both the market and the user pool are dynamic and their current values depend on the entire history. We provide an analytical characterization of the manufacturer’s optimal pricing, production, and inventory policies which lead to a practical threshold policy with a small optimality gap. In addition, our analysis offers a number of interesting insights. First, the timing of remanufacturing activity and its co-occurrence with new product manufacturing critically depends on remanufacturing cost benefits, attractiveness of the remanufactured product and product return rate. Second, there is a small upward jump in the price of the new product when remanufacturing is introduced. Third, the manufacturer keeps the new product longer on the market as the cost of remanufacturing decreases. Fourth, partially satisfying demand for the remanufactured item is never optimal, i.e., it is satisfied either fully or not at all. Finally, user pool and inventory of returned products are substitutes in ensuring the supply for future remanufacturing.
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Mustafa Akan et al.Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions
http://repository.cmu.edu/tepper/1538
http://repository.cmu.edu/tepper/1538Tue, 10 Nov 2015 14:35:36 PST
We consider a congestible system serving multiple classes of customers who differ in their delay sensitivity and valuation of service (or product). Customers are endowed with convex-concave delay cost functions. A system manager offers a menu of lead times and corresponding prices to arriving customers, who then choose the lead-time–price pair that maximizes their net utility (value minus disutility of delay and price). We investigate how such menus should be chosen dynamically (depending on the system backlog) to maximize welfare. We formulate a novel fluid model of the problem and show that the cost-balancing policy (based on the convex hulls of the delay cost functions) is socially optimal if the system manager can tell customer types apart. If types are indistinguishable to the system manager, the cost-balancing policy is also incentive compatible under social optimization. Finally, we show through a simulation study that the cost-balancing policy does well in the context of the original (stochastic) problem by testing it against various natural benchmarks.
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Mustafa Akan et al.Bid-Price Controls for Network Revenue Management: Martingale Characterization of Optimal Bid Prices
http://repository.cmu.edu/tepper/1537
http://repository.cmu.edu/tepper/1537Tue, 10 Nov 2015 14:35:31 PST
We consider a continuous-time, rate-based model of network revenue management. Under mild assumptions, we construct a simple ε-optimal bid-price control, which can be viewed as a perturbation of a bid-price control in the classical sense [Williamson, E. L. 1992. Airline network seat control. Ph.D. thesis, MIT, Cambridge, MA]. We show that the associated bid-price process forms a martingale and the corresponding booking controls converge in an appropriate sense to an optimal control as ε tends to 0. Moreover, we show that there exists an optimal generalized bid-price control, where the bid-price process forms a martingale and is used in conjunction with a capacity usage limit process. We also discuss its connection to the bid-price controls in the classical sense and sufficient conditions for the (near) optimality of the latter.
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Mustafa Akan et al.Replenishment and Fulfillment Based Aggregation for General Assemble-to-Order Systems
http://repository.cmu.edu/tepper/1536
http://repository.cmu.edu/tepper/1536Tue, 10 Nov 2015 14:35:26 PST
We consider an assemble-to-order system with multiple products, multiple components which may be demanded in different quantities by different products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the discounted cost criterion. A control policy specifies when a batch of components should be produced (i.e., inventory replenishment) and whether an arriving demand for each product should be satisfied (i.e., inventory allocation). As optimal solutions for such problems are computationally intractable for even moderate sized systems, we approximate the optimal cost function by reducing the state space of the original problem via a novel aggregation technique that uses knowledge of products' component requirements and components' replenishment batch sizes.

We establish that a lattice-dependent base-stock and lattice-dependent rationing policy is the optimal inventory replenishment and allocation policy for the aggregate problem under a disaggregation rule that disaggregates each aggregate state into its two extreme original states. This rule drastically reduces the per iteration computational complexity of the value iteration algorithm for the aggregate problem (without sacrificing much accuracy, according to our numerical experiments). We further alleviate the value iteration computational burden by eliminating suboptimal actions based on our optimal policy structure.

For systems in which there is a product that has fulfillment priority over all other products at optimality, we are able to derive finite error bound for the cost function of the aggregate problem. With these bounds we show that the value iteration algorithm in the original problem that starts with the aggregate solution converges to the optimal cost function. Numerical experiments indicate that such an algorithm has distinct computational advantage over the standard value iteration method in the original problem.
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Emre Nadar et al.Experimental Results Indicating Lattice-Dependent Policies May Be Optimal for General Assemble-To-Order Systems
http://repository.cmu.edu/tepper/1535
http://repository.cmu.edu/tepper/1535Tue, 10 Nov 2015 14:35:21 PST
We consider an assemble-to-order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice-dependent base-stock and lattice-dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M-system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state-dependent base-stock and state-dependent rationing (SBSR) policy, and a fixed base-stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.
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Emre Nadar et al.Optimal Portfolio Strategies for New Product Development
http://repository.cmu.edu/tepper/1534
http://repository.cmu.edu/tepper/1534Tue, 10 Nov 2015 14:35:17 PST
We study the portfolio selection problem in a new product development setting with many projects in parallel, each lasting several stages, in the face of uncertainty. Each stage of the process performs an experiment on a selected number of projects in the stage, depending on the amount of (scarce) budget allocated to the stage. Projects become differentiated through their experimental results, and all available results for a project determine its category.

We model the problem as a Markov decision process. We seek an optimal policy that specifies, for every configuration of projects in categories, which projects to test and/or terminate. For two special cases we characterize the optimal project promotion policy as following a new type of strategy, state-dependent non-congestive promotion (SDNCP). SDNCP implies that a project with the highest expected reward in any stage is advanced to the next stage if and only if the number of projects in each successor category is below a congestion-dependent threshold. For the general problem, numerical experiments reveal the outstanding performance of SDNCP (optimal in 72 of 77 instances with maximum deviation from optimal of 0.67%), highlighting when and how a fixed non-congestive promotion policy, which is easier to implement, may fall short.
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Emre Nadar et al.The Pennsylvania Adoption Exchange Improves Its Matching Process
http://repository.cmu.edu/tepper/1533
http://repository.cmu.edu/tepper/1533Tue, 10 Nov 2015 14:35:11 PST
he Pennsylvania Adoption Exchange (PAE) helps case workers representing children in state custody by recommending prospective families for adoption. We describe PAE's operational challenges using case worker surveys and a regression analysis of data on child outcomes over multiple years. Using a discrete-event simulation of PAE, we justify the value of a statewide adoption network and demonstrate the importance of the family preference information quality on the percentage of children who successfully nd adoptive placements. Finally, we detail a series of simple improvements implemented by PAE to increase the adoptive placement rate through collecting more valuable information, improving the family ranking algorithm, and aligning incentives for families to provide useful preference information.
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Vincent W. Slaugh et al.Revenue management by sequential screening
http://repository.cmu.edu/tepper/1532
http://repository.cmu.edu/tepper/1532Mon, 09 Nov 2015 14:28:37 PST
Using a mechanism design approach, we consider a firm's optimal pricing policy when consumers are heterogeneous and learn their valuations at different times. We show that by offering a menu of advance-purchase contracts that differ in when, and for how much, the product can be returned, a firm can more easily price discriminate between privately-informed consumers. In particular, we show that screening on when the return option can be exercised increases firm profits, relative to screening on the size of the refund alone, only if the expected gains from trade are higher for consumers who learn later. We show that in some settings (mean-preserving spread) the firm can achieve the complete-information profits and analyze the optimal contract in other settings (first-order stochastic dominance) in which the first-best allocation is not always feasible.
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Mustafa Akan et al.A Broader View of Designing the Liver Allocation System
http://repository.cmu.edu/tepper/1531
http://repository.cmu.edu/tepper/1531Mon, 09 Nov 2015 14:28:32 PST
We consider the problem of designing an efficient system for allocating donated livers to patients waiting for transplantation. The trade-off between medical urgency and efficiency is at the heart of the liver allocation problem. We model the transplant waiting list as a multiclass fluid model of overloaded queues, which captures the disease evolution by allowing the patients to switch between classes, i.e., health levels. We consider the bicriteria objective of minimizing total number of patient deaths while waiting for transplantation (NPDWT) and maximizing total quality-adjusted life years (QALYs) through a weighted combination. On one hand, under the objective of minimizing NPDWT, the current policy of United Network for Organ Sharing (UNOS) emerges as the optimal policy, providing a theoretical justification for the current practice. On the other hand, under the metric of maximizing QALYs, the optimal policy is an intuitive dynamic index policy that ranks patients based on their marginal benefit from transplantation, i.e., the difference in benefit with versus without transplantation. Finally, we perform a detailed simulation study to compare the performances of our proposed policies and the current UNOS policy along the following metrics: total QALYs, NPDWT, number of patient deaths after transplantation, number of total patient deaths, and number of wasted livers. Numerical experiments show that our proposed policy for maximizing QALYs outperforms the current UNOS policy along all metrics except the NPDWT.
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Mustafa Akan et al.Asymmetric information and economies-of-scale in service contracting
http://repository.cmu.edu/tepper/1530
http://repository.cmu.edu/tepper/1530Mon, 09 Nov 2015 14:28:27 PST
We consider outsourcing in two important service settings: call center and order fulfillment operations. An important factor in both is the inherent economies of scale. Therefore, we advance a unifying model covering both applications and study the associated contracting problem under information asymmetry. At the time of contracting, the outsourcing firm, “the originator,” faces uncertainty regarding the demand volume but has private information about its probability distribution. The true demand is quickly observed once the service commences. The service provider invests in capacity before the start of the operation and offers a menu of contracts to screen different types of the originator. Adopting a mechanism design approach, we prove that a menu of two-part tariffs achieves the full-information solution. Hence, it is optimal among all possible contracts (in both settings) because of economies of scale and contractibility of realized demand.
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Mustafa Akan et al.