Applications of simulation and optimization techniques in optimizing room and pillar mining systems

The goal of this research was to apply simulation and optimization techniques in solving mine design and production sequencing problems in room and pillar mines (R&P). The specific objectives were to: (1) apply Discrete Event Simulation (DES) to determine the optimal width of coal R&P panels under specific mining conditions; (2) investigate if the shuttle car fleet size used to mine a particular panel width is optimal in different segments of the panel; (3) test the hypothesis that binary integer linear programming (BILP) can be used to account for mining risk in R&P long range mine production sequencing; and (4) test the hypothesis that heuristic pre-processing can be used to increase the computational efficiency of branch and cut solutions to the BILP problem of R&P mine sequencing. A DES model of an existing R&P mine was built, that is capable of evaluating the effect of variable panel width on the unit cost and productivity of the mining system. For the system and operating conditions evaluated, the result showed that a 17-entry panel is optimal. The result also showed that, for the 17-entry panel studied, four shuttle cars per continuous miner is optimal for 80% of the defined mining segments with three shuttle cars optimal for the other 20%. The research successfully incorporated risk management into the R&P production sequencing problem, modeling the problem as BILP with block aggregation to minimize computational complexity. Three pre-processing algorithms based on generating problem-specific cutting planes were developed and used to investigate whether heuristic pre-processing can increase computational efficiency. Although, in some instances, the implemented pre-processing algorithms improved computational efficiency, the overall computational times were higher due to the high cost of generating the cutting planes --Abstract, page iii

IMPROVING HEALTHCARE DELIVERY: LIVER HEALTH UPDATING AND SURGICAL PATIENT ROUTING

Growing healthcare expenditures in the United States require improved healthcare delivery practices. Organ allocation has been one of the most controversial subjects in healthcare due to the scarcity of donated human organs and various ethical concerns. The design of efficient surgical suites management systems and rural healthcare delivery are long-standing efforts to improve the quality of care. In this dissertation, we consider practical models in both domains with the goal of improving the quality of their services. In the United States, the liver allocation system prioritizes among patients on the waiting list based on the patients' geographical locations and their medical urgency. The prioritization policy within a given geographic area is based on the most recently reported health status of the patients, although blood type compatibility and waiting time on the list are used to break ties. Accordingly, the system imposes a health-status updating scheme, which requires patients to update their health status within a timeframe that depends on their last reported health. However, the patients' ability to update their health status at any time point within this timeframe induces information asymmetry in the system. We study the problem of mitigating this information asymmetry in the liver allocation system. Specifically, we consider a joint patient and societal perspective to determine a set of Pareto-optimal updating schemes that minimize information asymmetry and data-processing burden. This approach combines three methodologies: multi-objective optimization, stochastic programming and Markov decision processes (MDPs). Using the structural properties of our proposed modeling approach, an efficient decomposition algorithm is presented to identify the exact efficient frontier of the Pareto-optimal updating schemes within any given degree of accuracy. Many medical centers offer transportation to eligible patients. However, patients' transportation considerations are often ignored in the scheduling of medical appointments. In this dissertation, we propose an integrated approach that simultaneously considers routing and scheduling decisions of a set of elective outpatient surgery requests in the available operating rooms (ORs) of a hospital. The objective is to minimize the total service cost that incorporates transportation and hospital waiting times for all patients. Focusing on the need of specialty or low-volume hospitals, we propose a computationally tractable model formulated as a set partitioning based problem. We present a branch-and-price algorithm to solve this problem, and discuss several algorithmic strategies to enhance the efficiency of the solution method. An extensive computational test using clinical data demonstrates the efficiency of our proposed solution method. This also shows the value of integrating routing and scheduling decisions, indicating that the healthcare providers can substantially improve the quality of their services under this unified framework

Decomposition-Based Integer Programming, Stochastic Programming, and Robust Optimization Methods for Healthcare Planning, Scheduling, and Routing Problems

RÉSUMÉ : Il existe de nombreuses applications de planification, d’ordonnancement et de confection de tournées dans les systèmes de santé. La résolution efficace de ces problèmes peut aider les responsables de la santé à fournir des services de meilleure qualité, en utilisant efficacement les ressources médicales disponibles. En raison de la nature combinatoire de ces problèmes, dans de nombreux cas, les algorithmes de programmation en nombres entiers standards dans les logiciels commerciaux de programmation mathématique tels que CPLEX et Gurobi ne peuvent pas résoudre efficacement les modèles correspondants. Dans cette thèse, nous étudions trois problèmes de planification, d’ordonnancement et de confection de tournées des soins de santé et proposons des approches à base de décomposition utilisant la programmation en nombres entiers, la programmation stochastique et une méthode d’optimisation robuste. Le premier article de cette thèse présente un problème intégré de planification et d’ordonnancement dans le cadre des salles d’opération. Cette situation implique d’optimiser l’ordonnancement et l’affectation des chirurgies aux différentes salles d’opération, sur un horizon de planification à court terme. Nous avons pris en compte les heures de travail quotidiennes maximales des chirurgiens, le temps de nettoyage obligatoire alloué lors du passage de cas infectieux à des cas non infectieux et le respect des dates limites des chirurgies. Nous avons aussi empêché le chevauchement des chirurgies effectuées par le même chirurgien. Nous avons formulé le problème en utilisant un modèle de programmation mathématique et développé un algorithme «branch-and-price-and-cut» basé sur un modèle de programmation par contraintes pour le sous-problème. Nous avons mis en place des règles de dominance et un algorithme de détection d’infaillibilité rapide. Cet algorithme, basé sur le problème du sac à dos multidimensionnel, nous permet d’améliorer l’efficacité du modèle de programmation de contraintes. Les résultats montrent que notre méthode présente un écart à l’optimum moyen de 2,81%, ce qui surpasse de manière significative la formulation mathématique compacte dans la littérature. Dans la deuxième partie de cette thèse, pour la première fois, nous avons étudié l’optimisation des problèmes de tournées de véhicules avec visites synchronisées (VRPS) en tenant compte de stochasticité des temps de déplacement et de service. En plus d’envisager un problème d’ordonnancement des soins de santé à domicile, nous introduisons un problème d’ordonnancement des salles d’opération avec des durées stochastiques qui est une nouvelle application de VRPS. Nous avons modélisé les VRPS qui ont des durées stochastiques en programmation stochastique à deux niveaux avec des variables entières dans les deux niveaux. L’avantage du modèle proposé est que, contrairement aux modèles déterministes de la littérature VRPS, il n’a pas de contraintes «big-M». Cet avantage entraine en contrepartie la présence d’un grand nombre de variables entières dans le second niveau. Nous avons prouvé que les contraintes d’intégralité sur les variables du deuxième niveau sont triviales ce qui nous permet d’appliquer l’algorithme «L-shaped» et son implémentation branch-and-and-cut pour résoudre le problème. Nous avons amélioré le modèle en développant des inégalités valides et une fonction de bornes inférieures. Nous avons analysé les sous-problèmes de l’algorithme en L et nous avons proposé une méthode de résolution qui est beaucoup plus rapide que les algorithmes de programmation linéaire standards. En outre, nous avons étendu notre modèle pour modéliser les VRPS avec des temps de déplacement et de service dépendant du temps. Les résultats de l’optimisation montrent que, pour le problème stochastique de soins à domicile, l’algorithme «branch-and-cut» résout à l’optimalité les exemplaires avec 15 patients et 10% à 30% de visites synchronisées. Il trouve également des solutions avec un écart à l’optimum moyen de de 3,57% pour les cas avec 20 patients. De plus l’algorithme «branch-and-cut» résout à l’optimalité les problèmes d’ordonnancement stochastique des salles d’opération avec 20 chirurgies. Ceci est une amélioration considérable par rapport à la littérature qui fait état de cas avec 11 chirurgies. En outre, la modélisation proposée pour le problème dépendant du temps trouve des solutions optimales pour d’une grande portion des exemplaires d’ordonnancement de soins de santé à domicile avec 30 à 60 patients et différents taux de visites synchronisées. Dans la dernière partie de cette thèse, nous avons étudié une catégorie de modèles d’optimisation robuste en deux étapes avec des variables entières du problème adversaire. Nous avons analysé l’importance de cette classe de problèmes lors de la modélisation à deux niveaux de problèmes de planification de ressources robuste en deux étapes où certaines tâches ont des temps d’arrivée et des durées incertains. Nous considérons un problème de répartition et d’affectation d’infirmières comme une application de cette classe de modèles robustes. Nous avons appliqué la décomposition de Dantzig-Wolfe pour exploiter la structure de ces modèles, ce qui nous a permis de montrer que le problème initial se réduit à un problème robuste à une seule étape. Nous avons proposé un algorithme Benders pour le problème reformulé. Étant donné que le problème principal et le sous-problème dans l’algorithme Benders sont des programmes à nombres entiers mixtes, il requiert une quantité de calcul importante à chaque itération de l’algorithme pour les résoudre de manière optimale. Par conséquent, nous avons développé de nouvelles conditions d’arrêt pour ces programmes à nombres entiers mixtes et fourni des preuves de convergence. Nous avons développé également un algorithme heuristique appelé «dual algorithm». Dans cette heuristique, nous dualisons la relaxation linéaire du problème adversaire dans le problème reformulé et générons des coupes itérativement pour façonner l’enveloppe convexe de l’ensemble d’incertitude. Nous avons combiné cette heuristique avec l’algorithme Benders pour créer un algorithme plus efficace appelé algorithme «Benders-dual algorithm». De nombreuses expériences de calcul sur le problème de répartition et d’affectation d’infirmières sont effectuées pour comparer ces algorithmes.----------ABSTRACT : There are many applications of planning, scheduling, and routing problems in healthcare systems. Efficiently solving these problems can help healthcare managers provide higher-quality services by making efficient use of available medical resources. Because of the combinatorial nature of these problems, in many cases, standard integer programming algorithms in commercial mathematical programming software such as CPLEX and Gurobi cannot solve the corresponding models effectively. In this dissertation, we study three healthcare planning, scheduling, and routing problems and propose decomposition-based integer programming, stochastic programming, and robust optimization methods for them. In the first essay of this dissertation, we study an integrated operating room planning and scheduling problem that combines the assignment of surgeries to operating rooms and scheduling over a short-term planning horizon. We take into account the maximum daily working hours of surgeons, prevent the overlapping of surgeries performed by the same surgeon, allow time for the obligatory cleaning when switching from infectious to noninfectious cases, and respect the surgery deadlines. We formulate the problem using a mathematical programming model and develop a branch-and-price-and-cut algorithm based on a constraint programming model for the subproblem. We also develop dominance rules and a fast infeasibility-detection algorithm based on a multidimensional knapsack problem to improve the efficiency of the constraint programming model. The computational results show that our method has an average optimality gap of 2.81% and significantly outperforms a compact mathematical formulation in the literature. As the second essay of this dissertation, for the first time, we study vehicle routing problems with synchronized visits (VRPS) and stochastic/time-dependent travel and service times. In addition to considering a home-health care scheduling problem, we introduce an operating room scheduling problem with stochastic durations as a novel application of VRPS. We formulate VRPS with stochastic times as a two-stage stochastic programming model with integer variables in both stages. An advantage of the proposed model is that, in contrast to the deterministic models in the VRPS literature, it does not have any big-M constraints. This advantage comes at the cost of a large number of second-stage integer variables. We prove that the integrality constraints on second-stage variables are trivial, and therefore we can apply the L-shaped algorithm and its branch-and-cut implementation to solve the problem. We enhance the model by developing valid inequalities and a lower bounding functional. We analyze the subproblems of the L-shaped algorithm and devise a solution method for them that is much faster than standard linear programming algorithms. Moreover, we extend our model to formulate VRPS with time-dependent travel and service times. Computational results show that, in the stochastic home-health care scheduling problem, the branch-and-cut algorithm optimally solves instances with 15 patients and 10% to 30% of synchronized visits. It also finds solutions with an average optimality gap of 3.57% for instances with 20 patients. Furthermore, the branch-and-cut algorithm ptimally solves stochastic operating room scheduling problems with 20 surgeries, a considerable improvement over the literature that reports on instances with 11 surgeries. In addition, the proposed formulation for the time-dependent problem solves a large portion of home-health care scheduling instances with 30 to 60 patients and different rates of synchronized visits to optimality. For the last essay of this dissertation, we also study a class of two-stage robust optimization models with integer adversarial variables. We discuss the importance of this class of problems in modeling two-stage robust resource planning problems where some tasks have uncertain arrival times and duration periods. We consider a two-stage nurse planning problem as an application of this class of robust models. We apply Dantzig-Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a singlestage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. Since the master problem and subproblem in the Benders algorithm are mixed integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed integer programs and provide the relevant convergence proofs. We also develop a heuristic algorithm called dual algorithm. In this heuristic, we dualize the linear programming relaxation of the adversarial problem in the reformulated problem and iteratively generate cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective algorithm called Benders-dual algorithm. Extensive computational experiments on the nurse planning problem are performed to compare these algorithms

Resource constrained routing and scheduling: Review and research prospects

In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects

Optimization of Healthcare Delivery System under Uncertainty: Schedule Elective Surgery in an Ambulatory Surgical Center and Schedule Appointment in an Outpatient Clinic

This work investigates two types of scheduling problems in the healthcare industry. One is the elective surgery scheduling problem in an ambulatory center, and the other is the appointment scheduling problem in an outpatient clinic. The ambulatory surgical center is usually equipped with an intake area, several operating rooms (ORs), and a recovery area. The set of surgeries to be scheduled are known in advance. Besides the surgery itself, the sequence-dependent setup time and the surgery recovery are also considered when making the scheduling decision. The scheduling decisions depend on the availability of the ORs, surgeons, and the recovery beds. The objective is to minimize the total cost by making decision in three aspects, number of ORs to open, surgery assignment to ORs, and surgery sequence in each OR. The problem is solved in two steps. In the first step, we propose a constraint programming model and a mixed integer programming model to solve a deterministic version of the problem. In the second step, we consider the variability of the surgery and recovery durations when making scheduling decisions and build a two stage stochastic programming model and solve it by an L-shaped algorithm. The stochastic nature of the outpatient clinic appointment scheduling system, caused by demands, patient arrivals, and service duration, makes it difficult to develop an optimal schedule policy. Once an appointment request is received, decision makers determine whether to accept the appointment and put it into a slot or reject it. Patients may cancel their scheduled appointment or simply not show up. The no-show and cancellation probability of the patients are modeled as the functions of the indirect waiting time of the patients. The performance measure is to maximize the expected net rewards, i.e., the revenue of seeing patients minus the cost of patients\u27 indirect and direct waiting as well as the physician\u27s overtime. We build a Markov Decision Process model and proposed a backward induction algorithm to obtain the optimal policy. The optimal policy is tested on random instances and compared with other heuristic policies. The backward induction algorithm and the heuristic methods are programmed in Matlab

Robust Optimization Framework to Operating Room Planning and Scheduling in Stochastic Environment

Arrangement of surgical activities can be classified as a three-level process that directly impacts the overall performance of a healthcare system. The goal of this dissertation is to study hierarchical planning and scheduling problems of operating room (OR) departments that arise in a publicly funded hospital. Uncertainty in surgery durations and patient arrivals, the existence of multiple resources and competing performance measures are among the important aspect of OR problems in practice. While planning can be viewed as the compromise of supply and demand within the strategic and tactical stages, scheduling is referred to the development of a detailed timetable that determines operational daily assignment of individual cases. Therefore, it is worthwhile to put effort in optimization of OR planning and surgical scheduling. We have considered several extensions of previous models and described several real-world applications. Firstly, we have developed a novel transformation framework for the robust optimization (RO) method to be used as a generalized approach to overcome the drawback of conventional RO approach owing to its difficulty in obtaining information regarding numerous control variable terms as well as added extra variables and constraints into the model in transforming deterministic models into the robust form. We have determined an optimal case mix planning for a given set of specialties for a single operating room department using the proposed standard RO framework. In this case-mix planning problem, demands for elective and emergency surgery are considered to be random variables realized over a set of probabilistic scenarios. A deterministic and a two-stage stochastic recourse programming model is also developed for the uncertain surgery case mix planning to demonstrate the applicability of the proposed RO models. The objective is to minimize the expected total loss incurred due to postponed and unmet demand as well as the underutilization costs. We have shown that the optimum solution can be found in polynomial time. Secondly, the tactical and operational level decision of OR block scheduling and advance scheduling problems are considered simultaneously to overcome the drawback of current literature in addressing these problems in isolation. We have focused on a hybrid master surgery scheduling (MSS) and surgical case assignment (SCA) problem under the assumption that both surgery durations and emergency arrivals follow probability distributions defined over a discrete set of scenarios. We have developed an integrated robust MSS and SCA model using the proposed standard transformation framework and determined the allocation of surgical specialties to the ORs as well as the assignment of surgeries within each specialty to the corresponding ORs in a coordinated way to minimize the costs associated with patients waiting time and hospital resource utilization. To demonstrate the usefulness and applicability of the two proposed models, a simulation study is carried utilizing data provided by Windsor Regional Hospital (WRH). The simulation results demonstrate that the two proposed models can mitigate the existing variability in parameter uncertainty. This provides a more reliable decision tool for the OR managers while limiting the negative impact of waiting time to the patients as well as welfare loss to the hospital