Essays On Perioperative Services Problems In Healthcare

One of the critical challenges in healthcare operations management is to efficiently utilize the expensive resources needed while maintaining the quality of care provided. Simulation and optimization methods can be effectively used to provide better healthcare services. This can be achieved by developing models to minimize patient waiting times, minimize healthcare supply chain and logistics costs, and maximize access. In this proposal, we study some of the important problems in healthcare operations management. More specifically, we focus on perioperative services and study scheduling of operating rooms (ORs) and management of necessary resources such as staff, equipment, and surgical instruments. We develop optimization and simulation methods to coordinate material handling decisions, inventory management, and OR scheduling. In Chapter 1 of this dissertation, we investigate material handling services to improve the flow of surgical materials in hospitals. The ORs require timely supply of surgical materials such as surgical instruments, linen, and other additional equipment required to perform the surgeries. The availability of surgical instruments at the right location is crucial to both patient safety and cost reduction in hospitals. Similarly, soiled material must also be disposed of appropriately and quickly. Hospitals use automated material handling systems to perform these daily tasks, minimize workforce requirements, reduce risk of contamination, and reduce workplace injuries. Most of the literature related to AGV systems focuses on improving their performance in manufacturing settings. In the last 20 years, several articles have addressed issues relevant to healthcare systems. This literature mainly focuses on improving the design and management of AGV systems to handle the specific challenges faced in hospitals, such as interactions with patients, staff, and elevators; adhering to safety standards and hygiene, etc. In Chapter 1, we focus on optimizing the delivery of surgical instrument case carts from material departments to ORs through automated guided vehicles (AGV). We propose a framework that integrates data analysis with system simulation and optimization. We test the performance of the proposed framework through a case study developed using data from a partnering hospital, Greenville Memorial Hospital (GMH) in South Carolina. Through an extensive set of simulation experiments, we investigate whether performance measures, such as travel time and task completion time, improve after a redesign of AGV pathways. We also study the impact of fleet size on these performance measures and use simulation-optimization to evaluate the performance of the system for different fleet sizes. A pilot study was conducted at GMH to validate the results of our analysis. We further evaluated different policies for scheduling the material handling activities to assess their impact on delays and the level of inventory required. Reducing the inventory level of an instrument may negatively impact the flexibility in scheduling surgeries, cause delays, and therefore, reduce the service level provided. On the other hand, increasing inventory levels may not necessarily eliminate the delays since some delays occur because of inefficiencies in the material handling processes. Hospitals tend to maintain large inventories to ensure that the required instruments are available for scheduled surgery. Typically, the inventory level of surgical instruments is determined by the total number of surgeries scheduled in a day, the daily schedule of surgeries that use the same instrument, the processing capacity of the central sterile storage division (CSSD), and the schedule of material handling activities. Using simulation-optimization tools, we demonstrate that integrating decisions of material handling activities with inventory management has the potential to reduce the cost of the system. In Chapter 2 we focus on coordinating OR scheduling decisions with efficient management of surgical instruments. Hospitals pay more attention to OR scheduling. This is because a large portion of hospitals\u27 income is due to surgical procedures. Inventory management of decisions follows the OR schedules. Previous work points to the cost savings and benefits of optimizing the OR scheduling process. However, based on our review of the literature, only a few articles discuss the inclusion of instrument inventory-related decisions in OR schedules. Surgical instruments are classified as (1) owned by the hospital and (2) borrowed from other hospitals or vendors. Borrowed instruments incur rental costs that can be up to 12-25\% of the listed price of the surgical instrument. A daily schedule of ORs determines how many rental instruments would be required to perform all surgeries in a timely manner. A simple strategy used in most hospitals is to first schedule the ORs, followed by determining the instrument assignments. However, such a strategy may result in low utilization of surgical instruments owned by hospitals. Furthermore, creating an OR schedule that efficiently uses available surgical instruments is a challenging problem. The problem becomes even more challenging in the presence of material handling delays, stochastic demand, and uncertain surgery duration. In this study, we propose an alternative scheduling strategy in which the OR scheduling and inventory management decisions are coordinated. More specifically, we propose a mixed-integer programming model that integrates instrument assignment decisions with OR scheduling to minimize costs. This model determines how many ORs to open, determines the schedule of ORs, and also identifies the instrument assignments for each surgery. If the level of instrument inventory cannot meet the surgical requirements, our model allows instruments to be rented at a higher cost. We introduce and evaluate the solution methods for this problem. We propose a Lagrangean decomposition-based heuristic, which is an iterative procedure. This heuristic separates the scheduling problem from the inventory assignment problem. These subproblems are computationally easier to solve and provide a lower bound on the optimal cost of the integrated OR scheduling problem. The solution of the scheduling subproblem is used to generate feasible solutions in every iteration. We propose two alternatives to find feasible solutions to our problem. These alternatives provide an upper bound on the cost of the integrated scheduling problem. We conducted a thorough sensitivity analysis to evaluate the impact of different parameters, such as the length of the scheduling horizon, the number of ORs that can be used in parallel, the number of surgeries, and various cost parameters on the running time and quality of the solution. Using a case study developed at GMH, we demonstrate that integrating OR scheduling decisions with inventory management has the potential to reduce the cost of the system. The objective of Chapter 3 is to develop quick and efficient algorithms to solve the integrated OR scheduling and inventory management problem, and generate optimal/near-optimal solutions that increase the efficiency of GMH operations. In Chapter 2, we introduced the integrated OR scheduling problem which is a combinatorial optimization problem. As such, the problem is challenging to solve. We faced these challenges when trying to solve the problem directly using the Gurobi solver. The solutions obtained via construction heuristics were much farther from optimality while the Lagrangean decomposition-based heuristics take several hours to find good solutions for large-sized problems. In addition, those methods are iterative procedures and computationally expensive. These challenges have motivated the development of metaheuristics to solve OR scheduling problems, which have been shown to be very effective in solving other combinatorial problems in general and scheduling problems in particular. In Chapter 3, we adopt a metaheuristic, Tabu search, which is a versatile heuristic that is used to solve many different types of scheduling problems. We propose an improved construction heuristic to generate an initial solution. This heuristic identifies the number if ORs to be used and then the assignment of surgeries to ORs. In the second step, this heuristic identifies instrument-surgery assignments based on a first-come, first-serve basis. The proposed Tabu search method improves upon this initial solution. To explore different areas of the feasible region, we propose three neighborhoods that are searched one after the other. For each neighborhood, we create a preferred attribute candidate list which contains solutions that have attributes of good solutions. The solutions on this list are evaluated first before examining other solutions in the neighborhood. The solutions obtained with Tabu search are compared with the lower and upper bounds obtained in Chapter \ref{Ch2}. Using a case study developed at GMH, we demonstrate that high-quality solutions can be obtained by using very little computational time

Integrated production-distribution systems : Trends and perspectives

During the last two decades, integrated production-distribution problems have attracted a great deal of attention in the operations research literature. Within a short period, a large number of papers have been published and the field has expanded dramatically. The purpose of this paper is to provide a comprehensive review of the existing literature by classifying the existing models into several different categories based on multiple characteristics. The paper also discusses some trends and list promising avenues for future research

Facility Location Problem of Beverage Distribution Considering Time Window and Land Use Plan Using GIS

As the boundaries and population of urban areas expand, beverage distributors may seek to expand the capacity in their distribution centers. As a result, they may need to add new locations or increase the utilization of their existing center. This paper investigates the facility location problem through network space, considering traversable truck roads, thereby providing a strategic decision for identifying a depot location in consideration of vehicle routings from a real application. For the analysis, a geospatial tool, which is embedded in the commercial software ArcMap®, was used for routing and calibrating the model. Ten candidates from commercial and industrial zones in the cities of Fargo, West Fargo, and Moorhead were considered for future distribution centers. The candidate locations were analyzed to determine which site minimizes the total transportation costs and travel miles in consideration of time window, vehicle capacity, heterogeneous vehicle types, land use plan, and hours-of-service. Most attractive candidates are close to the intersections of major highways. From the analysis, the study recommends locating a distribution center at three alternatives based on the average ranking method. This study can be used by distributors as they consider new locations and extra depots to support strategic planning to deal with mid-term and long-term growth of demand in beverage markets. This study provides a ready-to-use example of how to adopt state-of-the-art spatial technology and operations research using Geographic Information Systems (GIS), and bring it to state-of-practice

Stochastic programming for City Logistics: new models and methods

The need for mobility that emerged in the last decades led to an impressive increase in the number of vehicles as well as to a saturation of transportation infrastructures. Consequently, traffic congestion, accidents, transportation delays, and polluting emissions are some of the most recurrent concerns transportation and city managers have to deal with. However, just building new infrastructures might be not sustainable because of their cost, the land usage, which usually lacks in metropolitan regions, and their negative impact on the environment. Therefore, a different way of improving the performance of transportation systems while enhancing travel safety has to be found in order to make people and good transportation operations more efficient and support their key role in the economic development of either a city or a whole country. The concept of City Logistics (CL) is being developed to answer to this need. Indeed, CL focus on reducing the number of vehicles operating in the city, controlling their dimension and characteristics. CL solutions do not only improve the transportation system but the whole logistics system within an urban area, trying to integrate interests of the several. This global view challenges researchers to develop planning models, methods and decision support tools for the optimization of the structures and the activities of the transportation system. In particular, this leads researchers to the definition of strategic and tactical problems belonging to well-known problem classes, including network design problem, vehicle routing problem (VRP), traveling salesman problem (TSP), bin packing problem (BPP), which typically act as sub-problems of the overall CL system optimization. When long planning horizons are involved, these problems become stochastic and, thus, must explicitly take into account the different sources of uncertainty that can affect the transportation system. Due to these reasons and the large-scale of CL systems, the optimization problems arising in the urban context are very challenging. Their solution requires investigations in mathematical and combinatorial optimization methods as well as the implementation of efficient exact and heuristic algorithms. However, contributions answering these challenges are still limited number. This work contributes in filling this gap in the literature in terms of both modeling framework for new planning problems in CL context and developing new and effective heuristic solving methods for the two-stage formulation of these problems. Three stochastic problems are proposed in the context of CL: the stochastic variable cost and size bin packing problem (SVCSBPP), the multi-handler knapsack problem under uncertainty (MHKPu) and the multi-path traveling salesman problem with stochastic travel times (mpTSPs). The SVCSBPP arises in supply-chain management, in which companies outsource the logistics activities to a third-party logistic firm (3PL). The procurement of sufficient capacity, expressed in terms of vehicles, containers or space in a warehouse for varying periods of time to satisfy the demand plays a crucial role. The SVCSBPP focuses on the relation between a company and its logistics capacity provider and the tactical-planning problem of determining the quantity of capacity units to secure for the next period of activity. The SVCSBPP is the first attempt to introduce a stochastic variant of the variable cost and size bin packing problem (VCSBPP) considering not only the uncertainty on the demand to deliver, but also on the renting cost of the different bins and their availability. A large number of real-life situations can be satisfactorily modeled as a MHKPu, in particular in the last mile delivery. Last mile delivery may involve different sequences of consolidation operations, each handled by different workers with different skill levels and reliability. The improper management of consolidation operations can cause delay in the operations reducing the overall profit of the deliveries. Thus, given a set of potential logistics handlers and a set of items to deliver, characterized by volume and random profit, the MHKPu consists in finding a subset of items which maximizes the expected total profit. The profit is given by the sum of a deterministic profit and a stochastic profit oscillation, with unknown probability distribution, due to the random handling costs of the handlers.The mpTSPs arises mainly in City Logistics applications. Cities offer several services, such as garbage collection, periodic delivery of goods in urban grocery distribution and bike sharing services. These services require the planning of fixed and periodic tours that will be used from one to several weeks. However, the enlarged time horizon as well as strong dynamic changes in travel times due to traffic congestion and other nuisances typical of the urban transportation induce the presence of multiple paths with stochastic travel times. Given a graph characterized by a set of nodes connected by arcs, mpTSPs considers that, for every pair of nodes, multiple paths between the two nodes are present. Each path is characterized by a random travel time. Similarly to the standard TSP, the aim of the problem is to define the Hamiltonian cycle minimizing the expected total cost. These planning problems have been formulated as two-stage integer stochastic programs with recourse. Discretization methods are usually applied to approximate the probability distribution of the random parameters. The resulting approximated program becomes a deterministic linear program with integer decision variables of generally very large dimensions, beyond the reach of exact methods. Therefore, heuristics are required. For the MHKPu, we apply the extreme value theory and derive a deterministic approximation, while for the SVCSBPP and the mpTSPs we introduce effective and accurate heuristics based on the progressive hedging (PH) ideas. The PH mitigates the computational difficulty associated with large problem instances by decomposing the stochastic program by scenario. When effective heuristic techniques exist for solving individual scenario, that is the case of the SVCSBPP and the mpTSPs, the PH further reduces the computational effort of solving scenario subproblems by means of a commercial solver. In particular, we propose a series of specific strategies to accelerate the search and efficiently address the symmetry of solutions, including an aggregated consensual solution, heuristic penalty adjustments, and a bundle fixing technique. Yet, although solution methods become more powerful, combinatorial problems in the CL context are very large and difficult to solve. Thus, in order to significantly enhance the computational efficiency, these heuristics implement parallel schemes. With the aim to make a complete analysis of the problems proposed, we perform extensive numerical experiments on a large set of instances of various dimensions, including realistic setting derived by real applications in the urban area, and combinations of different levels of variability and correlations in the stochastic parameters. The campaign includes the assessment of the efficiency of the meta-heuristic, the evaluation of the interest to explicitly consider uncertainty, an analysis of the impact of problem characteristics, the structure of solutions, as well as an evaluation of the robustness of the solutions when used as decision tool. The numerical analysis indicates that the stochastic programs have significant effects in terms of both the economic impact (e.g. cost reduction) and the operations management (e.g. prediction of the capacity needed by the firm). The proposed methodologies outperform the use of commercial solvers, also when small-size instances are considered. In fact, they find good solutions in manageable computing time. This makes these heuristics a strategic tool that can be incorporated in larger decision support systems for CL

Synchronizing inventory and transport within supply chain management

The problem considers synchronized optimization of inventory and transport, and focuses on producer-distributor relations. Particular attention is paid to developing a mathematical model and an optimization problem that can be used to minimize the overall distribution cost by an appropriate placement of warehouses and cross-docking points. Solutions to this problem are explored using genetic algorithms and ideas from graph/network theory. Note: there are three separate reports contained within the uploaded .pdf file

Optimizing Block-Stacking Operations with Relocation

The focus of the dissertation is developing the optimization problem of finding the minimum-cost operational plan of block stacking with relocation as well as devising a solution procedure to solve practical-sized instances of the problem. Assuming changeable row depth instead of permanent row depth, this research is distinguished from conventional block stacking studies. The first contribution of the dissertation is the development of the optimization problem under the assumption of deterministic demand. The problem is modeled using integer programming as a variation of the unsplittable multi-commodity flow problem. To find a good feasible solution of practical-sized instances in reasonable time, we decompose the original problem into a series of generalized assignment problems. In addition, to establish a good lower bound on the optimal objective function value, we apply a relaxation based upon Lagrangean decomposition in which the relaxed problem separates into a set of shortest path problems and a set of binary knapsack problems. The second contribution of the dissertation is the development of the optimization problem under the assumption of stochastic demand. The problem is formulated as a discrete time finite horizon Markov decision process model, incorporating the recursive daily situation of determining the assignment of product lots to storage areas for a day based on uncertain daily demand and observed system information. To tackle computational intractability in solving practical-sized instances, we develop a heuristic solution approach taking an on-line manner by instantly determining an action for a single observed state rather than an off-line manner by predetermining an action for every state