Applications of stochastic and queueing models to operational decision making

An operations manager makes operational decisions in the face of a, by definition, uncertain future. In this thesis we develop tools that can improve the quality of operational decision making by modeling the stochastic environment and analyzing the trade-offs that the operations manager faces within this environment. We examine three specific settings:;The question of how to best leverage technology is fundamental to almost any industry. Using real data from EQT Corp. (an integrated natural resources company operating natural gas wells throughout the Appalachian basin) we analyze the interaction between the real options to scale different technologies and the real option to scale the extraction rate. We find that the values of these options are highly interdependent and their optimal use is rather complex. We bring to light data-driven managerial principles guiding the use of these options and provide a very effective heuristic control policy.;Prioritizing demand streams is common in inventory management. In many settings (e.g. a central warehouse), some demands can be backordered while others are lost when not immediately satisfied. A critical level (CL) policy reserves some inventory for future high-priority demand by backordering current, lower-priority, demands. We develop an efficient algorithm to find the optimal CL policy in this setting, and compare the performance to the globally optimal policy. We find that although the CL policy performs (slightly) worse, it is almost insensitive to variations in the lead time distribution.;Emergency Department (ED) demand for care is by its very nature hard to predict accurately. As ED capacity is regularly outstripped by demand, EDs attempt to decrease the inflow of patients during such periods of "crowding." We use real data to model the Pittsburgh (PA) Emergency Medial Services (EMS) system and evaluate the impact of several coordination mechanisms between ambulances and/or hospitals on the timeliness of care and total hospital revenues. We find that coordination mechanisms in which hospitals share certain indicators with EMS crews can significantly outperform the coordination mechanisms currently used in practice in term of quality of care, without being detrimental to hospital revenues.