2016 INFORMS Annual Meeting Program

WB38

INFORMS Nashville – 2016

WB38 206A-MCC Opt, Robust Contributed Session

optimal schedule. 2 - Efficient Transition To Post-acute Care Alex Mills, Indiana University, Bloomington, IN, United States, millsaf@indiana.edu, Sean Yu, Jonathan Helm Many hospital patients are discharged to a skilled nursing facility (SNF) for post- acute care. A shortage of SNF beds can lead to expensive discharge delays. Using a queueing model, we show that a hospital may want to contract with a SNF to reserve some capacity. However, when hospitals compete for capacity at multiple SNFs, such contracting leads to an equilibrium where total SNF capacity is de- pooled. Although this de-pooling hurts system performance overall, it benefits the hospital with the lower discharge rate, who becomes the market leader. Under the de-pooled scenario, the hospital with the higher arrival rate has an incentive to finance SNF expansion, even if it leads to free-riding. 3 - Steady-state Diffusion Approximations For Discrete-time Markov Chain In Hospital Inpatient Flow Management Jiekun Feng, Cornell Universtiy, Ithaca, NY, United States, jf646@cornell.edu, Pengyi Shi Motivated by the recent development of steady-state approximation via Stein’s method for Erlang-A and Erlang-C models, we apply the framework to a discrete- time Markov chain (DTMC), which is motivated from studying hospital inpatient flow and captures the dynamics of the midnight census in the inpatient department. We develop diffusion models to approximate the stationary distribution of the DTMC, and characterize the convergence rate of the approximations. 4 - A Queueing Model For Internal Wards Jing Dong, Northwestern University, Evanston, IL, United States, jing.dong@northwestern.edu, Ohad Perry Hospital queues have unique features, which are not captured by standard queueing assumptions. In this project we propose a queueing model that takes into account the most salient features of queues associated with large Internal Wards (IW’s). We characterize the maximum long-run workload that the IW can handle. We also introduce a deterministic (fluid) approximation for the non- stationary dynamics. The fluid model is shown to converge to a unique periodic equilibrium, so that long-run performance analysis can be carried out by simply considering that equilibrium. Chair: Harsha Honnappa, Purdue University, 315 N. Grant St., West Lafayette, IN, 47906, United States, honnappa@purdue.edu 1 - Randomized Load Balancing With General Service Distributions Kavita Ramanan, Brown University, kavita_ramanan@brown.edu Randomized algorithms are used in a variety of applications to balance load to improve performance. Randomized load balancing algorithms with exponential service distributions have received much attention, but in practice job sizes have been observed to be non-exponential. We characterize equilibrium properties of fluid limits of several randomized load balancing algorithms, including the well- known “power of two choices” algorithm in the presence of general service distributions. This is joint work with Pooja Agarwal. 2 - Beyond Heavy-traffic Regimes: Universal Bounds And Controls For The Single-server Queue Itai Gurvich, Kellogg School of Management, i-gurvich@kellogg.northwestern.edu, Junfei Huang Brownian approximations provide tractability in the analysis of queues. Their stationary distributions are used as proxies for those of the original queues and the convergence of suitably scaled primitives and processes provides mathematical support for the use of these Brownian models. From a heuristic viewpoint, however, there is an immediate Brownian analogue of the queueing model that is derived directly from the primitives. For the M/GI/1+GI queue, this direct (limitless approach) works: the Brownian model is universally accurate. It maintains the tractability and appeal of the limit approximations while avoiding many of the assumptions that facilitate them. WB40 207B-MCC Queueing in Applied Probability I Sponsored: Applied Probability Sponsored Session

Chair: Alberto Costa, NUS, Singapore, Singapore, isealc@nus.edu.sg 1 - On The Sample Compexity Of Multistage Robust Convex Optimization Problems Francesca Maggioni, Assistant Professor, University of Bergamo, Via dei Caniana n 2, Bergamo, 24127, Italy, francesca.maggioni@unibg.it, Fabrizio Dabbene, Marida Bertocchi, Roberto Tempo In this talk probabilistic guarantees for constraint sampling of multistage robust convex optimization problems are derived. The dynamic nature of these problems is tackled via the scenario-with-certificates approach. This allows to avoid the conservative use of explicit parametrizations through decision rules, and implies a significant reduction of the sample complexity to satisfy a given level of reliability. An explicit bound on the probability of violation is then given. Numerical results show the efficacy of the proposed approach. 2 - Conditions Under Which Adjustability Lowers The Cost Of A Robust Linear Program SeyyedAli Haddadsisakht, Iowa State University, Ames, IA, 50011, United States, alihadad@iastate.edu, Sarah M Ryan The adjustable robust counterpart (ARC) of an uncertain linear program lets some decision variables of the robust counterpart (RC) adjust to uncertainty. It may produce a less conservative solution than the RC does but cases are known in which it does not. The affinely adjustable RC (AARC) is a tractable compromise between RC and ARC. Numerical conditions under which the AARC optimal cost is lower than the RC optimal cost provide insight into problem structures where adjustability is valuable. 3 - Robust Optimization For The Transportation Problem Under Boundedly Rational User Equilibrium Guanxiang Yun, PhD Student, University of Central Florida, 12800 Pegasus Drive, PO Box 162993, Orlando, FL, 32816, United States, ygx8822@gmail.com, Qipeng Zheng We proposed a model for the static transportation path problem when the evacuation happens. We supposed that all the users in the system will obey the bounded rational principle. In real world instances, people will feel just fine even if they do not reach the best utility they can achieve but only attain a certain level. We proposed totally four conditions for our static models with two of them having the pricing strategy. By using the pricing strategy, we have a robust optimization model, we solve it by using the column and constraint generation method. For transportation path problem, it is also a large scale problem. In order to solve it, we use the branch and price method. 4 - A Robust Optimization Framework For Electric Power Grid Protection Alberto Costa, NUS, Singapore, Singapore, isealc@nus.edu.sg We consider a flow problem on oriented network, where the decision maker wants to send a quantity of goods from a source to a destination node, and an enemy can destroy the arcs of the network at a given cost. The decision maker can use a fortification budget to increase the cost to destroy the arcs, with the goal of maximizing the total price that the enemy must pay to disrupt the network. We model the optimal allocation of the fortification budget as a multistage robust optimization problem, and we propose an algorithm to find an -approximation of the global optimum. Computational results show that the algorithm is scalable and can solve efficiently instances with a few hundred nodes and arcs. WB39 207A-MCC Joint Session APS/MSOM: Service Systems in Applied Probability I Sponsored: Applied Probability/MSOM Sponsored Session Chair: Song-Hee Kim, USC Marshall School of Business, 3670 Trousdale Parkway, Los Angeles, CA, 90089, United States, songheek@marshall.usc.edu 1 - Optimal Appointment Schedules Mor Armony, New York University, marmony@stern.nyu.edu, Rami Atar, Harsha Honnappa We consider the problem of optimally scheduling a finite, but large, number of customers over a finite time horizon at a single server FIFO queue, in the presence of ‘no-shows’. We study the problem in a large population limiting regime as the number of customers scales to infinity and the appointment duration scales to zero. We show that in the fluid scaling heavy-traffic is obtained as a result of asymptotic optimization. We also characterize the diffusion-scale

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