The focus of this work is an industrial refinery model developed by TotalEnergies SE. The model is a sparse, large-scale, nonconvex, mixed-integer nonlinear program (MINLP). The nonconvexity of the problem arises from the many bilinear, trilinear, fractional, logarithmic, exponential, and sigmoidal terms. In order to account for various sources of uncertainty in refinery planning, the industrial refinery model is extended into a two-stage stochastic program, where binary scheduling decisions must be made prior to the realization of the uncertainty, and mixed-integer recourse decisions are made afterwards. Two case studies involving uncertainty are formulated and solved in order to demonstrate the economic and logistical benefits of robust solutions over their deterministic counterparts. A full-space solution strategy is proposed wherein the integrality constraints are relaxed and a multi-step initialization strategy is employed in order to gradually approach the feasible region of the multi-scenario problem. The full-space solution strategy was significantly hampered by difficulties with finding a feasible point and numerical problems. In order to facilitate the identification of a feasible point and to reduce the incidence of numerical difficulties, a hybrid surrogate refinery model was developed using the ALAMO modelling tool. An evaluation procedure was employed to assess the surrogate model, which was shown to be reasonably accurate for most output variables and to be more reliable than the high-fidelity model. Feasible solutions are obtained for the continuous relaxations of both case studies using the full-space solution strategy in conjunction with the surrogate model. In order to solve the original MINLP problems, a decomposition strategy based on the generalized Benders decomposition (GBD) algorithm is proposed. The binary decisions are designated as complicating variables that, when fixed, reduce the full-space problem to a series of independent scenario subproblems. Through the application of the GBD algorithm, feasible mixed-integer solutions are obtained for both case studies, however optimality could not be guaranteed. Solutions obtained via the stochastic programming framework are shown to be more robust than solutions obtained via a deterministic problem formulation. / Thesis / Master of Applied Science (MASc)

With the rise of online retailer giants like Amazon, and enhancements in internet and mobile technologies, online shopping is becoming increasingly popular. This has lead to new opportunities in online price optimization. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions. In Chapter 2 a multi-period revenue maximization and pricing optimization problem in the presence of reference prices is formulated as a mixed integer nonlinear program. Two algorithms are developed to solve the optimization problem: a generalized Benders' decomposition algorithm and a myopic heuristic. This is followed by numerical computations to illustrate the effciency of the solution approaches as well as some managerial pricing insights. In Chapter 3 a data-driven quadratic programming optimization model for online pricing in the presence of customer ratings is proposed. A new demand function is developed for a multi-product, nite horizon, online retail environment. To solve the optimization problem, a myopic pricing heuristic as well as exact solution approaches are introduced. Using customer reviews ratings data from Amazon.com, a new customer rating forecasting model is validated. This is followed by several analytical and numerical insights. In Chapter 4 a multinomial choice model is used for customer purchase decision to find optimal personalized price discounts for an online retailer that incorporates customer locations and feedback from their reviews. Closed form solutions are derived for two special cases of this problem. To gain some analytical insights extensive numerical experiments are carried followed by several analytical and numerical insights. / Thesis / Doctor of Philosophy (PhD) / The increase in online retail and the improvements in mobile technologies has lead to advantages and opportunities for both customers and retailers. One of these advantages is the ability to keep and efficiently access records of historical orders for both customers and retailers. In addition, online retailing has dramatically decreased the cost of price adjustments and discounts compared to the brick and mortar environment. At the same time, with the increase in online retailing we are witnessing proliferations of online reviews in e-commerce platforms. Given this availability of data and the new capabilities in an online retail environment, there is a need to develop pricing optimization models that integrate all these new features. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions.

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