Special Acknowledgement to the National Science Foundation (CMMI-1130507)
Integer Programming Techniques for Matroid Circuit Problems
John Arellano
Computational and Applied Mathematics
Rice University
I present a set covering problem (SCP) formulation of the matroid cogirth problem. Addressing the matroid cogirth problem can lead to significantly enhancing the design process of sensor networks. The solution to the matroid cogirth problem provides the degree of redundancy of the corresponding sensor network, and allows for the evaluation of the quality of the network. I provide computational results to validate a branch-and-cut algorithm that addresses the SCP formulation.
Computational Study of Decomposition Algorithms for Mean-Risk Stochastic Programs
Tanisha G. Cotton
Industrial and Systems Engineering
Texas A&M University
To introduce risk into stochastic programs, convexity preserving dispersion statistics such as quantile-deviation and absolute semi-deviation can be used to represent mean-risk objectives. In this poster presentation, we report on a computational study of decomposition algorithms for stochastic linear programs using standard instances from the literature.
Coxian 2-Phase Approximation and Analysis of a Terminating Queueing System: A Border Crossing Model
Hiram Moya
Industrial and Systems Engineering
Texas A&M University
The U.S. international land boundary is a volatile, security intense area. In 2009, the combined trade was $735 billion within NAFTA, with 80% transported by commercial trucks through ports of entry (POE). Increasing security and inspection requirements are seriously affecting transit times. Each POE is configured as a multi-commodity, prioritized queueing network which rarely, if ever, operates in steady state. This paper provides a summary of transient queueing network analysis conducted to analyze throughput rates, queue lengths, cycle times and configuration effectiveness. Particular emphasis is given to the dynamic reallocation of inspection (service) facilities and inspectors under time-varying arrivals (demands).
Fluid Model of the Dynamics of Patients and Physicians in Emergency Rooms
Jerome Ndayishimiye
Industrial and Systems Engineering
University of Buffalo
Hospital emergency rooms are difficult to manage because of the complexity of allocating costly resources, mainly physicians, in the light of the dynamical arrivals of patients and the costs of delayed medical treatment. We propose a fluid model using first order ordinary differential equations to approximate the dynamics of patients and physicians in emergency rooms. We then apply classical control theory mechanics to determine the optimal control function to minimize patients' holding costs and physicians' utilization costs. Numerical solutions of our fluid model suggest a continuous control function, which we discretize, using least square and mean value methods, to approximate the best shifts staffing policy of physicians.
Skewness Variance Approximation for Dynamic Rate Multi-Server Queues with Abandonment
Jamol J. Pender
Industrial and Financial Engineering
Princeton University
A fundamental dynamic rate queueing model for large scale service systems is a multi-server queue with non-homogeneous Poisson arrivals and customer abandonment. By scaling the arrival rates and number of servers of such systems, using the fluid and diffusion limit theorems found in Mandelbaum, Massey, and Reiman (1998) we can approximate the stochastic behavior of this queueing process by one that is Gaussian. Moreover, the approximations to the mean and variance produced by these limiting processes form a two-dimensional dynamical system. Recent work by Gautam and Ko (2011) found a modified version of these differential equations and obtained better estimates of the mean and variance for the original queueing system. We now introduce a new three-dimensional dynamical system that surpasses these two approaches.
Planning Transportation of Disaster Relief Goods with Rural Recipients
Luis de la Torre
Industrial Engineering and Management Sciences
Northwestern University
Disaster relief presents many unique logistics challenges, with problems including damaged transportation infrastructure, limited communication, and coordination of multiple agents. We present ongoing work on the problem of distributing goods after a disaster to many rural beneficiaries throughout the disaster-affected region. We model the problem with two-stage stochastic programming with uncertainty in the accessibility of beneficiaries and long-haul transportation to beneficiaries planned before accessibility is known. We test our model using data from simulated disaster settings, including earthquakes in the New Madrid fault zone. We use sample average approximation and local search heuristics to find high-quality solutions that consider fairness and equity to recipients along with efficiency. This is joint work with Irina Dolinskaya and Karen Smilowitz.
Emergency Medical Service Allocation in Response to Large Scale Events
Gabriel Zayas-Caban
Center of Applied Mathematics
Cornell University
In the event of a catastrophic or large scale event demand for Emergency Medical Service (EMS) vehicles in the affected region will almost certainly overwhelm the available supply. In such cases, it is necessary for cities in the affected region to request aid (in the form of added capacity) from neighboring municipalities in order to bring the affected region back to its day-to-day levels of operation. In this paper, we propose a systematic method to address such scenarios.
In particular, we consider a region consisting of several cities, where each city is in charge of managing its own set of EMS vehicles. We propose that a centralized or statewide decision-maker coordinate the temporary transfer of resources (EMS vehicles) from cities in the unaffected region into the cities in the affected region. We model the control of each city's EMS vehicles as a multi-server queueing system and use classical results to estimate the number of vehicles available at each city. We then develop a knapsack model to guide the allocation of available vehicles from the donor area into the affected one and a clearing system model to dynamically control the added resources.
As the dimension of the problem is large, a heuristic we call the buddy system is proposed where cities are paired to form city groups. This reduces the size of the problem enough to solve the knapsack problem for initially allocating vehicles to city groups. Within the city groups the clearing system model is solved via Markov decision processes. The performance of our heuristic is compared to several other reasonable heuristics via a detailed numerical study. Results show that the buddy system exhibits significant cost and time savings, and is generally robust to varying parameters.