Integrated robust and adaptive methods in the heating oil industry

Abstract

Almost six million households in the United States alone use heating oil as their main fuel, the vast majority of these in the Northeastern US. In this thesis, we examine some problems faced by a planner who is contracted to resupply customers with heating oil through the winter season, and use robust and adaptive optimization and machine learning to develop models that allow the planner to address these problems under uncertainty at a realistic scale. In the first part of the thesis (Chapter 2), we consider the problem of resupplying customers spread over a geographical area. Due to the presence of uncertainty in demand, the planner has to choose an appropriate fleet size, decide on the most cost-effective routes and schedules, and on how much to resupply each customer. We develop novel scalable and adaptive algorithms to address this problem, demonstrating the potential for significant cost savings in simulations while being able to address problem sizes in the thousands.

In the second part of the thesis (Chapter 3), we consider the problem of executing the purchase of a commodity. In addition to price uncertainty on the daily commodity market, we model two kinds of discounts offered by commodity sellers vying for the planner's business. We develop a tractable model to formulate a purchasing strategy for a desired quantity, and use recently-developed machine learning techniques to find optimal decision trees that the planner can apply to different problem parameters to yield readily interpretable purchasing strategies, without having to re-solve the optimization models. We demonstrate experimentally that these strategies perform almost as well as those given by the actual optimization models.

Finally, in the third part of the thesis (Chapter 4), we demonstrate the possibility of solving the previous two problems as an integrated whole, allowing the planner to simultaneously optimize the routing, scheduling, and purchasing aspects of heating oil delivery. Although the integrated problem size may be too large to solve directly with realistic problem sizes, we use Lagrangean decomposition methods to make the problem tractable, and show experimentally that this allows us to get high-quality solutions that reduce the combined cost of the two subproblems.