The balanced 2-median and 2-maxian problems on a tree

This paper deals with the facility location problems with balancing on allocation clients to servers. Two bi-objective models are considered, in which one objective is the traditional p-median or p-maxian objective and the second is to minimize the maximum demand volume allocated to any facility. An edge deletion method with time complexity O(n^2) is presented for the balanced $2$-median problem on a tree. For the balanced 2-maxian problem, it is shown the optimal solution is two end vertices of the diameter of the tree, which can be obtained in a linear time.Comment: 19 page

Collection Center Location with Equity Considerations in Reverse Logistics Networks

This is an Accepted Manuscript of an article published by Taylor & Francis in INFOR: Information Systems and Operational Research on 2014-11-01, available online: http://dx.doi.org/10.3138/infor.52.4.157In this paper, we study a collection center location problem with equity considerations within reverse logistics network design. The aim of the problem is to determine the locations and the capacities of the collection centers through the planning horizon. For each time period, the decisions to be made include the location and the capacities of the collection centers, the amounts of products to send from each generation point to each collection center, and the amounts of products to send from each collection center to each firm. The problem has three objectives. The first one is to minimize total cost, the second one is to ensure equity among different firms, and the third is to provide steady flow of products to each firm along the planning horizon. The problem is modeled as a multi-objective mixed integer programming formulation. An implementation of the problem in Turkey within the context of waste electrical and electronic equipment collection is presented. Sensitivity analyses are conducted to observe the effect of changes in the problem parameters on the solutions. The analyses include changes in the fixed costs and container capacities, changes in the amount of supply and changes in the growth rate. In addition, the solution potential of the model and value of using a multi-period model as opposed to using a static one are investigated

Models and algorithms for trauma network design.

Trauma continues to be the leading cause of death and disability in the US for people aged 44 and under, making it a major public health problem. The geographical maldistribution of Trauma Centers (TCs), and the resulting higher access time to the nearest TC, has been shown to impact trauma patient safety and increase disability or mortality. State governments often design a trauma network to provide prompt and definitive care to their citizens. However, this process is mainly manual and experience-based and often leads to a suboptimal network in terms of patient safety and resource utilization. This dissertation fills important voids in this domain and adds much-needed realism to develop insights that trauma decision-makers can use to design their trauma network. In this dissertation, we develop multiple optimization-based trauma network design approaches focusing minimizing mistriages and, in some cases, ensuring equity in care among regions. To mimic trauma care in practice, several realistic features are considered in our approach, which include the consideration of: (i) both severely and non-severely injured trauma patients and associated mistriages, (ii) intermediate trauma centers (ITCs) along with major trauma centers (MTCs), (iii) three dominant criteria for destination determination, and (iv) mistriages in on-scene clinical assessment of injuries. Our first contribution (Chapter 2) proposes the Trauma Center Location Problem (TCLP) that determines the optimal number and location of major trauma centers (MTCs) to improve patient safety. The bi-objective optimization model for TCLP explicitly considers both types of patients (severe and non-severe) and associated mistriages (specifically, system-related under- and over-triages) as a surrogate for patient safety. These mistriages are estimated using our proposed notional tasking algorithm that attempts to mimic the EMS on-scene decision of destination hospital and transportation mode. We develop a heuristic based on Particle Swarm Optimization framework to efficiently solve realistic problem sizes. We illustrate our approach using 2012 data from the state of OH and show that an optimized network for the state could achieve 31.5% improvement in patient safety compared to the 2012 network with the addition of just one MTC; redistribution of the 21 MTCs in the 2012 network led to a 30.4% improvement. Our second contribution (Chapter 3) introduces a Nested Trauma Network Design Problem (NTNDP), which is a nested multi-level, multi-customer, multi-transportation, multi-criteria, capacitated model. The NTNDP model has a bi-objective of maximizing the weighted sum of equity and effectiveness in patient safety. The proposed model includes intermediate trauma centers (TCs) that have been established in many US states to serve as feeder centers to major TCs. The model also incorporates three criteria used by EMS for destination determination; i.e., patient/family choice, closest facility, and protocol. Our proposed ‘3-phase’ approach efficiently solves the resulting MIP model by first solving a relaxed version of the model, then a Constraint Satisfaction Problem, and a modified version of the original optimization problem (if needed). A comprehensive experimental study is conducted to determine the sensitivity of the solutions to various system parameters. A case study is presented using 2019 data from the state of OH that shows more than 30% improvement in the patient safety objective. In our third contribution (Chapter 4), we introduce Trauma Network Design Problem considering Assessment-related Mistriages (TNDP-AM), where we explicitly consider mistriages in on-scene assessment of patient injuries by the EMS. The TNDP-AM model determines the number and location of major trauma centers to maximize patient safety. We model assessment-related mistriages using the Bernoulli random variable and propose a Simheuristic approach that integrates Monte Carlo Simulation with a genetic algorithm (GA) to solve the problem efficiently. Our findings indicate that the trauma network is susceptible to assessment-related mistriages; specifically, higher mistriages in assessing severe patients may lead to a 799% decrease in patient safety and potential clustering of MTCs near high trauma incidence rates. There are several implications of our findings to practice. State trauma decision-makers can use our approaches to not only better manage limited financial resources, but also understand the impact of changes in operational parameters on network performance. The design of training programs for EMS providers to build standardization in decision-making is another advantage