Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy




Peter C. Bell

2nd Supervisor

Mehmet A. Begen


This study of practical problems in Management Science (MS) describes novel mathematical models for three different decision settings. It addresses questions of: (a) what optimal route should be taken through a time-windows and topographically complex network; (b) what optimal sequencing of scheduled surgeries best coordinates flow of patients through central recovery; and (c) what prices should be charged and what stock amounts should be produced for two markets or channels to maximize profit explicitly, given various capacity and uncertainty conditions.

The first problem is in a sport analytics context, using a novel Integer Programming and big data from Whistler-Blackcomb ski resort. The second is to coordinate dozens of surgeries at London Health Sciences Centre, using a novel Constraint Programming model mapped to and parameterized with hospital data, including a tool for visualizing process and patient flow. The third problem is relevant to almost any business with a secondary market or sales channel, as it helps them identify profit optimal prices based on simple demand estimates and cost information they can easily provide for their own setting.

The studies use fundamentally different operational research techniques, in each case uniquely extended to the problem setting. The first two are combinatorial problems, neither one extremely beyond human cognitive ability, and both involving lots of uncertainty, and thus the sort of problem managers tend to dismiss as not efficient or practical to solve analytically. We show in the first study that vastly more skiers could achieve the challenge by following our route recommendation, unintuitive as are some of its elements, initially. In the second study, our scheduling model consistently outperforms currently unstructured-independent approach at the hospital. The final study is mathematical but demonstrates that by considering distinct market costs in pricing a firm can invariably earn more profit.

Summary for Lay Audience

Three chapters of this dissertation cover a variety of important methods in management science and related disciplines e.g. statistics, economics. The problems and results are intriguing without necessarily understanding their proofs.

Chapter 2 describes what most people, even regular skiers at Whistler-Blackcomb, would not imagine as the enormity of possible routes for the problem, or the ambiguity of whether one of them is ‘best’. Many will be interested to see information that can be derived from simple time-stamp data collected from electronic tickets at lift stations, and the new technology-enabled opportunities and efforts being made to ‘gamify’ the sport.

Few cannot relate to the problem of waiting for surgery, nor take interest in rapid and standardized operating rooms being piloted to address the problem. Chapter 3 identifies how post-surgical recovery, a step in the process rarely considered by patients, can be a limiting factor to enabling faster, more voluminous patient flow. The chapter describes the coordination challenge involved, especially its high variability and uncertainty, but also scientific approaches that can better anticipate and manage the situation despite these factors.

The first two papers demonstrate conceptually similar but fundamentally different mathematical programming approaches. One uses binary decision variables (should a specific lift-to-lift transition be included in a route), and other uses a different type of data which are interval and sequence variables (where to position intervals of patient procedures and recoveries such that they fit together ‘best’ in time and space.)

Some basic understanding of microeconomics is helpful to appreciate, in Chapter 4, essentially how scientific pricing works, some reason to find the same product priced differently in two places, and especially how should it be priced differently. Several propositions can serve as a guide for pricing in one’s own situation, including when capacity is limited, and/or where (different) market demand uncertainties warrant consideration.

An integral motivation for my Ph.D. journey has been to acquire understanding that will allow me to impart a greater awareness of, appreciation for, and interest in scientific management techniques among non-practitioners, and I hope that is reflected in this thesis.

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Creative Commons Attribution-Share Alike 4.0 License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.