Informs Annual Meeting 2017

MD75

INFORMS Houston – 2017

MD74

4 - Consumer Learning of Product Quality with Time Delay: Insights from Spatial Price Equilibrium Models with Differentiated Products Dong Li, Arkansas State University Jonesboro-College of Business, P.O. Box 59, State University, AR, 72467, United States, dli@astate.edu, Anna B. Nagurney, Min Yu We present spatial price equilibrium network models with differentiated products under perfect quality information for producers and consumers and under quality information asymmetry with consumer learning of product quality with a time delay. In addition, we provide measures of consumer welfare under perfect quality information and under information asymmetry as well as the value of perfect quality information for consumers. The models are especially relevant to agricultural products where spatial price equilibrium models have found wide application. We also present several numerical examples with insights provided. 372B Underground Mine Planning Sponsored: Energy, Natural Res & the Environment, Natural Resources Mining Sponsored Session Chair: Alexandra M Newman, Colorado School of Mines, Golden, CO, 80401, United States, anewman@mines.edu 1 - Optimally Locating Support Pillars in an Underground Mine Levente Sipeki, 8805 W. Geddes Pl, Littleton, CO, 80128, United States, levente.sipeki@gmail.com, Alexandra M.Newman, Candace Arai Yano In underground mining, specifically, in top-down, open-stope retreat operations, blocks are designated as pillars (and left in situ) or stopes (and extracted and processed) so as to maximize profit. Safety is ensured by abiding by geotechnicalrestrictions on (i) the hydraulic radius of a stope, (ii) the length-to- width ratio of a pillar, (iii) the ratio between adjacent pillar and stope lengths, and (iv) the proximity between veins. We present a methodology consisting of (i) preprocessing, (ii) solving an optimization model,and (iii) employing a heuristic to determine structurally stable pillars locations. 2 - Production Scheduling in Underground Mining Operations Incorporating Heat Loads Oluwaseun Babatunde Ogunmodede, MS, Colorado School of Mines, Golden, CO, 80401, United States, setotravel@gmail.com, Andrea Brickey, Levente Sipeki, Gregory Bogin, Alexandra M. Newman A problem in the mining industry is production scheduling, or determining when, if ever, notional three-dimensional blocks of ore should be mined. Often lacking in underground production scheduling models are heat limitations, driven largely by the equipment used for underground activities such as development, extraction, and backfilling. To correct this, we attribute a specific heat load to each mining activity owing to equipment use, auto compression, broken rock and strata rock. We incorporate heat into a knapsack constraint in an integer programming model that produces more realistic schedules; adhering to them could increase revenue by lowering refrigeration costs for the mine. 3 - Production and Construction Optimization in Underground Mining Nelson Morales, DIMIN.& AMTC, Av Tupper 2069, Santiago, Chile, nmorales@ing.uchile.cl The planning and design of underground mines is a very complex task that requires to balance multiple considerations like economical value and geotechnical constraints in order to generate an extraction and a construction plan. Due to this complexity, the problem is solved in different stages and scopes, which lead to suboptimal solutions or even infeasibilities. In this work we present a MIP model which aims to optimize mine plans in underground mines. We show how this model can then be coupled with other models in order to generate more comprehensive plans that integrate aspects like geomechanics or operational uncertainty. 4 - Optimizing the Cutoff Grade at an Underground Mine Alexandra Newman, Colorado School of Mines, Golden, CO, 80401, United States, anewman@mines.edu, Barry kING An important strategic decision for any operational mine is the differentiation between ore and waste material, referred to as the cutoff grade. Our mixed- integer programming optimization framework determines the cutoff grades in three different, predetermined zones for a soon-to-be-operational underground mine by exploiting an underlying mathematical structure; current industry practice would produce solutions with lower net present value, would require six to eight weeks, and would preclude scenario analysis. MD73

372C Multistage Optimization Models and Applications Sponsored: Computing Sponsored Session Chair: Jorge A Sefair, Arizona State Univerity, Tempe, AZ, 85287-8809, United States, jorge.sefair@asu.edu 1 - Supervalid Inequalities for Network Interdiction Problems Ningji Wei, 4303, Chestnut Ridge Rd., Buffalo, NY, 14228, United States, ningjiwe@buffalo.edu, Jose Luis Walteros We focus on attacker-defender network interdiction problems in which: 1) the objective minimizes the attacker’s cost of achieving a fixed disruption level over the defender’s problem; 2) the defender’s problem is to select an optimal graph structure (e.g., a shortest path, a spanning tree) over the residual graph; 3) the attacker strategies are defined over the same ground set of the graph structures. e.g., if the structures are defined over the edges, the attacker also interdicts edges. We develop a cut-generating framework that produces a general class of supervalid inequalities that remove non-trivial suboptimal solutions. We show how to addapt our framwework to tackle a wide variety of problems. 2 - On the Impact of Decentralization in Interdependent Network Restoration Scheduling Thomas Sharkey, sharkt@rpi.edu, Hongtan Sun We consider the problem of restoring disrupted services across multiple interdependent networks after extreme events. We consider integer programming approaches to determine the equilibrium (stable) solutions for this decentralized scheduling system. These approaches help to calculate the price of anarchy and the price of stability as well as allocate incentives to improve the loss from the centralized objective. 3 - Bi-level Optimization Model for Assortment Planning under Worst-case Customer Order of Preferences Saharnaz Mehrani, Arizona State University, 1500 E Broadway Road, Apt B2128, Tempe, AZ, 85282, United States, smehrani@asu.edu, Jorge A.Sefair One of the main challenges in assortment planning is to capture the customer choice behavior for substitutable products. We model customer behavior using a general ranking-based choice approach with a modified multinomial logit model to incorporate the effect of product unavailability on customer decisions. We present a bi-level optimization approach to maximize the expected revenue and protect it against the worst possible customer preferences. Our solution approach includes a single-level reformulation, which we tighten using problem-specific properties, and then solve using a cutting plane algorithm. 4 - Robust Location of Transparent Interdictions on a Shortest Path Network Nail Orkun Baycik, Rensselaer Polytechnic Institute, Troy, NY, United States, baycin@rpi.edu, Kelly Sullivan We study a shortest path network interdiction problem in which the follower seeks to find a path of minimum length on a network and the leader seeks to maximize the follower’s path length by interdicting arcs. We consider placement of interdictions that are not visible to the follower; however, we seek to locate interdictions in a manner that is robust against the possibility that some information about the interdictions becomes known to the follower. We formulate the problem as a bi-level program, and apply a Benders decomposition approach to optimally solve it. We derive supervalid inequalities to improve the performance of the algorithm and test the algorithm on randomly generated grid networks. 372D Methods for Large-scale Convex Optimization Sponsored: Optimization, Nonlinear Programming Sponsored Session Chair: Paul Grigas, pgrigas@berkeley.edu 1 - Variants of the ADMM for Block Optimization Xiang Gao, University of Minnesota, 609 Oak Street, Apt 1-11, Minneapolis, MN, 55403, United States, gaoxx460@umn.edu In this talk we present a suite of first-order algorithms which can be characterized as variants of the ADMM. In terms of the informational structure, we propose several ADMM-type methods that are applicable on a much broader class of problems where only noisy estimations of the gradient or the function values are accessible. For problems involve multi-block and non-separable objective with linear constraint, both deterministic and randomized ADMM variants are introduced. Under different conditions, sublinear convergence rates of all the aforementioned variants will be presented. MD75

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