Large-Scale Solution Approaches for Healthcare and Supply Chain Scheduling

This research proposes novel solution techniques for two real world problems. We first consider a patient scheduling problem in a proton therapy facility with deterministic patient arrivals. In order to assess the impacts of several operational constraints, we propose single and multi-criteria linear programming models. In addition, we ensure that the strategic patient mix restrictions predetermined by the decision makers are also enforced within the planning horizon. We study the mathematical structures of the single criteria model with strict patient mix restrictions and derive analytical equations for the optimal solutions under several operational restrictions. These efforts lead to a set of rule of thumbs that can be utilized to assess the impacts of several input parameters and patient mix levels on the capacity utilization without solving optimization problems. The necessary and sufficient conditions to analytically generate exact efficient frontiers of the bicriteria problem without any additional side constraint are also explored. In a follow up study, we investigate the solution techniques for the same patient scheduling problem with stochastic patient arrivals. We propose two Markov Decision Process (MDP) models that are capable of tackling the stochasticity. The second problem of interest is a variant of the parallel machine scheduling problem. We propose constraint programming (CP) and logic-based Benders decomposition algorithms in order to make the best decisions for scheduling nonidentical jobs with time windows and sequence dependent setup times on dissimilar parallel machines in a fixed planning horizon. This problem is formulated with (i) maximizing total profit and (ii) minimizing makespan objectives. We conduct several sensitivity analysis to test the quality and robustness of the solutions on a real life case study

A Gamification Approach for Experiential Education of Inventory Control

In this educational research project, game-based in-class and after-class learning activities are developed to teach selected inventory control strategies to undergraduate and graduate students. Students from Supply Chain Management and System Simulation courses are targeted, who are taught by different instructors. The activities include teaching the inventory control policies to students in a regular class setting, then providing an overview on a game developed on MS Excel. In the game, the lead time and customer demand variables are defined uncertain, and not given to students, which make the assignment an ill-structured problem. A 12-month planning and execution period is given to students with qualitative and quantitative information about 3 products. The students are given a 1-week period to play the game. The game simulates selected inventory control strategies with reorder point and order quantity parameters for 12 months. The learning outcomes of the course related to inventory control, and students’ experience with the game are surveyed. Survey results are statistically and visually analyzed. Overall results indicated that the proposed gamification approach is found to have positive impact in learning effectiveness in the majority of evaluation categories. In addition, the contribution of the proposed gamification approach was found to be effectively supporting the learning outcomes of the course

Evaluating the Capacity of a Proton Therapy Facility

A relatively new consideration in proton therapy planning is the requirement that the mix of patients treated satisfy desired percentages. Since it is very dicult to satisfy an integer number of patients in light of these requirements, deviations from patient mix preferences and their impacts on operational capabilities are of particular interest to healthcare planners. Therefore, we propose a bicriteria mathematical programming model that determines an outpatient schedule maximizing the number of fractions and minimizing the deviations from the patient mix ratios over the planning horizon. The tradeos between the two objectives are identied through analysis of ecient frontiers. Our models are applicable to healthcare treatment facilities throughout the United States, but are motivated by collaboration with the University of Florida Proton Therapy Institute (UFPTI) in Jacksonville, Florida

Strategic Level Proton Therapy Patient Admission Planning: A Markov Decision Process Modeling Approach

A relatively new consideration in proton therapy planning is the requirement that the mix of patients treated from different categories satisfy desired mix percentages. Deviations from these percentages and their impacts on operational capabilities are of particular interest to healthcare planners. In this study, we investigate intelligent ways of admitting patients to a proton therapy facility that maximize the total expected number of treatment sessions (fractions) delivered to patients in a planning period with stochastic patient arrivals and penalize the deviation from the patient mix restrictions. We propose a Markov Decision Process (MDP) model that provides very useful insights in determining the best patient admission policies in the case of an unexpected opening in the facility (i.e., no-shows, appointment cancellations, etc.). In order to overcome the curse of dimensionality for larger and more realistic instances, we propose an aggregate MDP model that is able to approximate optimal patient admission policies using the worded weight aggregation technique. Our models are applicable to healthcare treatment facilities throughout the United States, but are motivated by collaboration with the University of Florida Proton Therapy Institute (UFPTI)

A Project-based Learning Approach in Teaching Simulation to Undergraduate and Graduate Students

In this study, application of experiential learning into graduate and undergraduate curricula of a industrial system simulation course is presented. Simulation has been among the courses against which students feel uncomfortable or frightened due to heavy software use, prerequisite of probability, and statistics knowledge, and its application requirements. To minimize this fear and improve student’s understanding about the subject matters and have them develop ample skills to build complex models, a project-based learning approach is proposed and used in undergraduate and graduate teaching settings. To achieve the project-based learning goals, a 15-week curriculum is designed to have a balanced lecture and lab sessions, which are specifically designed to address the needs of the term project as the semester continues. In the term project, groups of 2-3 students were asked to form a group, where each group was expected to work on a real system to 1) understand, conceptualize, and model the existing system as a mental, then software-model; 2) validate the existing system model statistically; 3) identify areas for improvement (in addition to the ones given by the supervisor); 4) complete the project with testing out system improvement scenarios and conducting cost/benefit analysis. The effectiveness of project-based learning is surveyed and studied based on the course learning outcomes. The results indicated that the proposed project-based learning approach was found to be effective in students’ learning experience and critically supportive on reaching the learning outcomes, and it was found that students’ learning and skills of simulation modeling and application are improved regardless of their grade

A Benders Based Rolling Horizon Algorithm for a Dynamic Facility Location Problem

This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the stand-alone rolling horizon and accelerated Benders decomposition algorithms in the experimental range

A Constraint Programming Approach for the Team Orienteering Problem with Time Windows

The team orienteering problem with time windows (TOPTW) is a NP-hard combinatorial optimization problem. It has many real-world applications, for example, routing technicians and disaster relief routing. In the TOPTW, a set of locations is given. For each, the profit, service time and time window are known. A fleet of homogenous vehicles are available for visiting locations and collecting their associated profits. Each vehicle is constrained by a maximum tour duration. The problem is to plan a set of vehicle routes that begin and end at a depot, visit each location no more than once by incorporating time window constraints. The objective is to maximize the profit collected. In this study we discuss how to use constraint programming (CP) to formulate and solve TOPTW by applying interval variables, global constraints and domain filtering algorithms. We propose a CP model and two branching strategies for the TOPTW. The approach finds 119 of the best-known solutions for 304 TOPTW benchmark instances from the literature. Moreover, the proposed method finds one new best-known solution for TOPTW benchmark instances and proves the optimality of the best-known solutions for two additional instances

Analysis of a Parallel Machine Scheduling Problem with Sequence Dependent Setup Times and Job Availability Intervals

In this study, we propose constraint programming (CP) model and logic-based Benders algorithms in order to make the best decisions for scheduling non-identical jobs with availability intervals and sequence dependent setup times on unrelated parallel machines in a fixed planning horizon. In this problem, each job has a profit, cost and must be assigned to at most one machine in such a way that total profit is maximized. In addition, the total cost has to be less than or equal to a budget level. Computational tests are performed on a real-life case study prepared in collaboration with the U.S. Army Corps of Engineers (USACE). Our initial investigations show that the pure CP model is very efficient in obtaining good quality feasible solutions but, fails to report the optimal solution for the majority of the problem instances. On the other hand, the two logic-based Benders decomposition algorithms are able to obtain near optimal solutions for 86 instances out of 90 examinees. For the remaining instances, they provide a feasible solution. Further investigations show the high quality of the solutions obtained by the pure CP model

Carbon Footprint Stock Analysis of U.S. Manufacturing: A Time Series Input-Output LCA

The purpose of this paper is to provide an input-output life cycle assessment model to estimate the carbon footprint of US manufacturing sectors. To achieve this, the paper sets out the following objectives: develop a time series carbon footprint estimation model for US manufacturing sectors; analyze the annual and cumulative carbon footprint; analyze and identify the most carbon emitting and carbon intensive manufacturing industries in the last four decades; and analyze the supply chains of US manufacturing industries to help identify the most critical carbon emitting industries

Vulnerability Assessment and Re-routing of Freight Trains Under Disruptions: A Coal Supply Chain Network Application

In this paper, we present a two-stage mixed integer programming (MIP) interdiction model in which an interdictor chooses a limited amount of elements to attack first on a given network, and then an operator dispatches trains through the residual network. Our MIP model explicitly incorporates discrete unit flows of trains on the rail network with time-variant capacities. A real coal rail transportation network is used in order to generate scenarios to provide tactical and operational level vulnerability assessment analysis including rerouting decisions, travel and delay costs analysis, and the frequency of interdictions of facilities for the dynamic rail system