Informs Annual Meeting 2017

SD22

INFORMS Houston – 2017

3 - Solution Methods for Generalized Inverse Optimization Rafid Mahmood, University of Toronto, 3831 Janice Drive, Mississauga, ON, L5M.7Y6, Canada, rafid.mahmood@mail.utoronto.ca, Timothy Chan, Taewoo Lee, Daria Terekhov Practitioners of inverse optimization often create specialized methods to solve a specific problem. A previous work introduced a generalized inverse optimization (GIO) formulation for linear programs, that could easily specialize to the different custom methods. In this work, we extend the previous formulation to the case of multiple observed decisions. Although the prior work introduced solution methods for the classically non-convex problem, we extend these results to show how the problem and it’s specializations can be solved efficiently in nearly all scenarios. Finally, we provide a set of guiding rules for practitioners in implementing inverse problems. 4 - Data-driven Objective Selection in Multi-objective Optimization Temitayo Ajayi, Rice University, Houston, TX, United States, temitayo.ajayi@rice.edu, Taewoo Lee, Andrew J.Schaefer A challenge in radiation therapy treatment planning is selecting which clinical objectives to use in the optimization. We propose the inverse optimization method with a cardinality constraint to infer the most important objectives from historical treatment plans. We use a greedy algorithm to select objectives and provide theory, a generalization of a result by Nemhauser (1978), to support our results. We compare the proposed method to the cardinality-constrained inverse problem, and show that our method efficiently finds a small number of objectives that generates clinical quality treatment plans. 342D Revenue Management with Intertemporal Consumer Behavior Sponsored: Revenue Management & Pricing Sponsored Session Chair: Ilan Lobel, New York University, New York, NY, 10012, United States, ilobel@stern.nyu.edu 1 - Dynamic Pricing Model for a Subscription Contract Offered to Strategic Customers with Fixed Term Lengths in a Growing Market Roozbeh Yousefi, Queen’s University, 310 Bath Rd., Unit 1112, Kingston, ON, K7M9H1, Canada, r.yousefi@queensu.ca, Jue Wang, Yuri Levin, Mikhail Nediak Subscriptions are agreements between a company which commits to deliver a service or provide access to a service and its customers. We present a continuous time dynamic pricing model for a monopolist offering a fixed term subscription contract without per-use charges and limit of access, to strategic customers whose utility is affected by the number of subscribers. We formulate the monopolist’s problem in terms of optimal control, derive its optimality conditions, and study the structure of the stationary optimal solution. We demonstrate the optimal pricing results in numerical experiments. 2 - Joint Pricing and Inventory Management with Strategic Customers Yiwei Chen, Singapore University of Technology and Design, Singapore, Singapore, Yiwei_chen@sutd.edu.sg, Cong Shi We study a joint pricing and inventory management problem with strategic customers. Demand is allowed to be backlogged. The seller incurs fixed ordering cost and inventory holding cost. Our model allows customers to be heterogeneous in arriving times and valuations. We use mechanism design approach to characterize the seller’s optimal pricing and inventory policy and customer equilibrium behaviors. 3 - Intertemporal Price Discrimination with Time-varying Valuations Victor Araman, American University of Beirut, Beirut, Lebanon, va03@aub.edu.lb Customers approach the firm and can either purchase the product on arrival, or remain in the system for a period of time. During this time, each customer’s valuation changes following a discrete and homogenous Markov chain. We show that, in this context, cyclic strategies are optimal, or nearly optimal. When the pace of pricing is constrained we characterize the cycle length and obtain an efficient algorithm that yields the optimal solutions. We cast part of our results in a general framework of optimizing the long-run average revenues for a class of payoffs that we call weakly coupled. SD22

4 - Dynamic Pricing with Heterogeneous Patience Levels Ilan Lobel, New York University, 44 West 4th St, Kmc 8-71, New York, NY, 10012, United States, ilobel@stern.nyu.edu We consider the problem of dynamic pricing in the presence of patient consumers. We call a consumer patient if she is willing to wait a certain number of periods for a lower price and will purchase as soon as the price is equal to or below her valuation. We allow for arbitrary joint distributions of patience levels and valuations. We propose an efficient algorithm for finding optimal pricing policies. The dynamic program requires a larger state space than its counterpart for a strategic consumers model. We find numerically that optimal policies can take the form of incomplete cyclic policies, combining features of both nested sales policies and decreasing cyclic policies.

SD23

342E Pricing and Revenue Management in Retail Operations Sponsored: Revenue Management & Pricing Sponsored Session Chair: Mehmet Sekip Altug, maltug@gwu.edu 1 - Curing the Addiction to Growth

Marshall L. Fisher, University of Pennsylvania, Wharton School Oper & Info Mgmt. Dept, Jon M. Huntsman Hall, Room 542, Philadelphia, PA, 19104, United States, fisher@wharton.upenn.edu, Vishal Gaur, Herbert Kleinberger Successful retailers grow quickly in their early years simply by opening new stores, but what happens when growth inevitably slows? To answer this question, we examined the financials of 37 publically traded retailers continuously active during 1993-2014 whose average top line growth slowed from 14.1% initially to 4.6% in the last 5 years. Despite slower top line growth, 17 of these retailers outperformed the S&P during 2011-15 by following a strategy of curtailing new store opening and instead increasing sales in their existing stores through a variety of initiatives. 2 - Assortment Planning with N-pack Purchasing Customers Ying Cao, University of Texas at Dallas, 19251 Preston Rd, For many product categories, customers often buy multiple differentiated products on a given store visit for staggered consumption until the next store visit. Such customers are referred to as n-pack purchasing customers in Fox et al (2016). We consider a retailer who makes product assortment decisions in a given product category facing n-pack purchasing customers. We study the structural properties of the optimal assortment under three different customer choice rules. And we explore how the retailer’s assortment decision and total profits are impacted when the retailer ignores the “choice premium” which captures the utility that consumers derive from variety in their shopping basket. 3 - Trusting the Computer: Adherence to the Recommendations of a Pricing Decision Support System Anna Saez de Tejada Cuenca, UCLA Anderson School of We analyze empirically the drivers of adherence to the prices recommended by a decision support system during the sales season of a fast fashion retailer. We study the effect on two interventions (nudges) aimed to encourage adherence to the DSS’s recommendations on the overall season adherence, as well as the effect of inventory levels and impatience on the evolution of adherence over each sales season. 4 - Optimal Dynamic Allocation of Sales and Rental Inventory at a Retailer Mehmet Sekip Altug, George Washington University, 2201 G. Street NW, Funger 415, Washington, DC, 20052, United States, maltug@gwu.edu, Oben Ceryan We consider a retailer that simultaneously sells and rents its product over a given horizon. In every period, the retailer faces uncertain demand that splits between renters and buyers based on their utility. We characterize the optimal dynamic rental allocation policy and study its properties. We propose various implementable heuristics. We then extend our results to the duopoly case and characterize the equilibrium. We derive the conditions that lead to “pure sales”, “pure rental” or “mixed” strategy equilibrium and discuss their implications. Apt 1324, Dallas, TX, 75252, United States, Ying.Cao@utdallas.edu, Dorothee Honhon Management, Los Angeles, CA, United States, anna.sdtc.1@anderson.ucla.edu, Felipe Caro

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