Abstract

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.