A stochastic programming approach for chemotherapy appointment scheduling

Chemotherapy appointment scheduling is a challenging problem due to the uncertainty in pre-medication and infusion durations. In this paper, we formulate a two-stage stochastic mixed integer programming model for the chemotherapy appointment scheduling problem under limited availability and number of nurses and infusion chairs. The objective is to minimize the expected weighted sum of nurse overtime, chair idle time, and patient waiting time. The computational burden to solve real-life instances of this problem to optimality is significantly high, even in the deterministic case. To overcome this burden, we incorporate valid bounds and symmetry breaking constraints. Progressive hedging algorithm is implemented in order to solve the improved formulation heuristically. We enhance the algorithm through a penalty update method, cycle detection and variable fixing mechanisms, and a linear approximation of the objective function. Using numerical experiments based on real data from a major oncology hospital, we compare our solution approach with several scheduling heuristics from the relevant literature, generate managerial insights related to the impact of the number of nurses and chairs on appointment schedules, and estimate the value of stochastic solution to assess the significance of considering uncertainty

Integrated Scheduling Problems in Healthcare and Logistics

Scheduling is one of the important components of operation management in different services. The goal of scheduling is to allocate limited available resources over time for performing a set of activities such that one or more objectives are optimized. In this thesis, we study several interesting applications of scheduling in health care and logistics. We present several formulations and algorithms to efficiently solve the scheduling problems that arise in these areas. We first study static and dynamic variants of a multi-appointment, multi-stage outpatient scheduling problem that arises in oncology clinics offering chemotherapy treatments. We present two integer programming formulations that integrate numerous scheduling decisions, features, and objectives of a major outpatient cancer treatment clinic in Canada. We also develop integrated and sequential scheduling strategies for the dynamic case in which arriving requests are processed at specific points of time. The results of computational experiments show that the proposed scheduling strategies can achieve significant improvements with respect to the several performance measures compared to the current scheduling procedure used at the clinic. We next present a daily outpatient appointment scheduling problem that simultaneously determines the start times of consultation and chemotherapy treatment appointments for different types of patients in an oncology clinic under uncertain treatment times. We formulate this stochastic problem using two two-stage stochastic programming models. We also propose a sample average approximation algorithm to obtain high quality feasible solutions. We use an efficient specialized algorithm that quickly evaluates any given first-stage solution for a large number of scenarios. We perform several computational experiments to compare the performance of proposed two-stage stochastic programming models. In the next part of the experiments, we show that the quality of the first-stage solutions obtained by the sample average approximation is significantly higher than those of the expected value problem, and the value of stochastic solution is extremely high specially for higher degrees of uncertainty. Finally, we address two variants of a cross-dock scheduling problem with handling times that simultaneously determines dock-door assignments and the scheduling of the trucks. In the general variant of the problem we assume that unit-load transfer times are door dependent, whereas in the specific case variant, unit-load transfer times are considered to be identical for all pairs of doors. We present constraint programming formulations for both variants of the problem, and we compare the performance of these models with mixed integer programming models from the literature. For the specific case, we propose several families of valid inequalities that are then used within a branch-and-cut framework to improve the performance of a time-index model. To solve the general problem efficiently, we also develop an approximate algorithm that first solves the specific case problem with the developed branch-and-cut algorithm to obtain a valid lower-bound, and then applies a matheuristic to obtain a valid upper-bound for the general problem and to compute the optimality gap. According to the computational experiments, we show that the proposed formulations and algorithms are able to solve the studied problems efficiently, and they outperform other models and heuristics that were previously developed for the problem in the literature

Scheduling, inventory management and production planning: Formulations and solution methods

This thesis presents formulations and solution methods for three types of problems in operations management that have received major attention in the last decade and arise in several applications. We focus on the use of mixed integer programming theory, robust optimization, and decomposition-based methods to solve each of these three problems. We first study an online scheduling problem dealing with patients’ multiple requests for chemotherapy treatments. We propose an adaptive and flexible scheduling procedure capable of handling both the dynamic uncertainty arising from appointment requests that appear on waiting lists in real time and capable of dealing with unexpected changes. The proposed scheduling procedure incorporates several circumstances prevalent at oncology clinics such as specific intervals between two consecutive appointments and specific time slots and chairs. Computational experiments show the proposed procedure achieves consistently better results for all considered objective functions compared to those of the scheduling system in use at the cancer centre of a major metropolitan hospital in Canada. We next present an inventory management problem that integrates perishability, demand uncertainty, and order modification decisions. We formulate the problem as a two-stage robust integer optimization model and develop an exact column-and-row generation algorithm to solve it. Based on computational results, we show that considering order modification can significantly reduce the total cost. Moreover, comparing the results obtained by the proposed robust model to those obtained from the deterministic and stochastic variants, we note that their performances are similar in the risk-neutral setting while solutions from the robust models are significantly superior in the risk-averse setting. Finally, we study decomposition strategies for a class of production planning problems with multiple items, unlimited production capacity and, inventory bounds. Based on a new mixed integer programming formulation, we proposed a Lagrangian relaxation for the problem. We propose a deflected subgradient method and a stabilized column generation algorithm to solve the Lagrangian dual problem. Computational results confirm that the proposed formulation outperforms the previously proposed models and methods. Further analysis shows the impact of using decomposition techniques in providing tighter bounds

Modeling change in a health system: Implications on patient flows and resource allocations

This work is motivated by the recent changes in the health system in Turkey, which is a consolidation of health insurance funds, and its implications on the resource allocations and the flow of patients in the system. Our aim is to provide a model to find the best reallocation of resources between the hospitals and the best patient-hospital match to minimize the costs. © 2005 CIM