Informs Annual Meeting 2017

SD81

INFORMS Houston – 2017

SD79

SD81

381B 5:15 - 6:00 Lumina Decision Systems Invited: Vendor Tutorial Invited Session

382A Chance-Constrained Optimization and Applications Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Ruiwei Jiang, University of Michigan, University of Michigan, Ann Arbor, MI, 48109, United States, ruiwei@umich.edu 1 - An Algorithm for Binary Chance Constrained Problems using Infeasible Irreducible Systems Bernardo Kulnig Pagnoncelli, Universidad Adolfo Ibáñez, Diagonal Las Torres 2540, Santiago, Chile, Gianpiero Canessa, Lewis Ntaimo We propose an algorithm based on Infeasible Irreducible Systems (IIS) to solve general binary chance-constrained problems. By leveraging on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete domain is used to guide us efficiently in the search of solutions. We test our methodology on instances of a vaccine problem, and in versions of the probabilistic set covering problem. In most cases the number of nodes visited by the algorithm is drastically reduced when compared to commercial solvers. 2 - Distributional Robust Chance-constrained Optimal Power Flow with Wasserstein Ambiguity Set Yuanyuan Guo, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI, 48109, United States, yuanyg@umich.edu, Ruiwei Jiang The uncertain renewable energy creates new challenges for the power system operators to ensure network constraints. The chance-constrained program is a convenient method to ensure the constraints are satisfied with a high probability. However, it is hard to accurately estimate the joint distribution of all the random variables. We study a distributionally robust chance-constrained optimal power flow model with the Wasserstein ambiguity set, which can provide powerful out- of-sample performance guarantee. The model can be reformulated as a linear or a second-order cone programming depending on the choice of the Wasserstein metric. Our approach is compared with two benchmark approaches. 3 - An Adaptive Model with Joint Chance Constraints for a Hybrid Wind-Conventional Generator System Bismark Singh, University of Texas at Austin, 2501 Lake Austin Blvd, Apt F203, Austin, TX, 78703, United States, bismark.singh@utexas.edu, David Morton, Surya Santoso We analyze scheduling a hybrid wind-conventional generator system to make it dispatchable. Our models ensure that with high probability we satisfy the day- ahead power promised, using combined output of the conventional and wind generators. We consider two scenarios—-whether the conventional generator must commit to its schedule prior to observing the wind or has flexibility to adapt in real-time to these realizations. The adaptive model is a two-stage stochastic integer program with joint chance constraints. We develop an iterative regularization scheme in which we solve a sequence of sample average approximations under a growing sample size to dramatically reduce computational effort. 4 - Ambiguous Chance-constrained Bin Packing under Mean- covariance Information We study chance-constrained bin packing with random item weights and assume that only the mean and covariance matrix of the uncertainty is available. Using two types of ambiguity sets, we equivalently reformulate this model as 0-1 second-order cone (SOC) programs. We further exploit the submodularity of the 0-1 SOC constraints under special and general covariance matrices, and utilize the submodularity to derive extended polymatroid inequalities to strengthen the 0-1 SOC formulations. We demonstrate the computational efficacy of our approaches on various test instances. Ruiwei Jiang, University of Michigan, 1205 Beal Ave., Ann Arbor, MI, 48109, United States, ruiwei@umich.edu, Yiling Zhang, Siqian Shen

1 - Why Go “Beyond the Spreadsheet” with Analytica 5.0? Max Henrion, Lumina Decision Systems, Inc, Los Gatos, CA, United States, henrion@lumina.com Practitioners of analytics and OR increasingly recognize spreadsheets as an obstacle to clear and scalable modeling. They are moving to visual modeling tools like Analytica using influence diagrams to structure models at the same level that you conceptualize them. You identify key decisions, uncertainties, objectives, and constraints. You define relationships between these objects, which may be multidimensional rather than at the level of cells. Analytica models are typically 10 to 100 times simpler than equivalent spreadsheets, and correspondingly faster to build, understand and audit. This tutorial is a rare chance to see Max Henrion, the originator of Analytica, using influence diagrams to structure a problem. He will demonstrate agile development, using Intelligent Arrays to scale models and integrate Monte Carlo simulation and optimization. Max will also show what’s new in release 5.0 of Analytica, including an updated interface, parallel processing, and web deployment on the Analytica Cloud Player. 381C Multi-Item and Multi-Location Revenue Management Models II Sponsored: Revenue Management & Pricing Sponsored Session Chair: Candace Arai Yano, University of California-Berkeley, IEOR Department, 4141 Etcheverry Hall, Berkeley, CA, 94720-1777, United States, yano@ieor.berkeley.edu 1 - Managing Revenue via Inventory Allocation for a Multi-location Retailer with Planned Price Promotions Kevin Li, University of California—Berkeley, Berkeley, CA, 94720, United States, kbl4ew@berkeley.edu, Candace Arai Yano We address a retailer’s choice of the initial order quantity from a distant supplier and the policy for allocating inventory to stores over a multi-period horizon for a short lifecycle product when there are planned price promotions. We characterize the optimal inventory allocation policy given a fixed initial order quantity and stochastic multiplicative demand and present a near-optimal heuristic policy. We then investigate the optimal initial order quantity. We also present examples that provide insights into how promotional patterns affect optimal inventory allocations. 2 - Optimal Pricing under Diffusion-choice Models Hongmin Li, Arizona State University, WP.Carey School of Business, Dept of Supply Chain Management, Tempe, AZ, 85287, United States, hongmin.li@asu.edu We develop a solution approach to the centralized pricing problem of a firm managing multiple substitutable products. Demands of these products undergo a diffusion process and customers choose among the products, with the choice probability of each product given by the logit model. We examine the firm’s optimal pricing problem when product demand can be described by such “diffusion-choice” models. In particular, we focus on two models with proven merits, proposed by Jun and Park (1999) and Weerahandi and Dalal (1992) respectively. We establish the uniqueness of the optimal solution, propose an efficient solution approach, in addition to characterizing the optimal prices and their time trend. 3 - Car Rental Network Revenue Management Zhan Pang, City University of Hong Kong, Hong Kong, zhan.pang@cityu.edu.hk, Dong Li We consider a general car rental network of multiple stations. Customers can book round trips or one-way rentals from any station to another station for a time periods within a finite time window. The operator makes shuttling and booking limit decisions jointly to maximize its total discounted profit over an infinite horizon. We formulate this problem as a stochastic dynamic program and develop two approximate dynamic programming heuristics. We conduct a numerical study and apply our approach in case study using a sample of real world data to explore some practical insights. SD80

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