Optimization under Uncertainty

Abstract

Planning and controlling production in a large make-to-order manufacturing network poses complex and costly operational problems. As customers continually submit customized orders, a centralized decision-maker must quickly allocate each order to production facilities with limited but flexible labor, production capacity, and parts availability. In collaboration with a major desktop manufacturing firm, we study these relatively unexplored problems, the firm's solutions to it, and alternate approaches based on mathematical optimization.We develop and analyze three distinct models for these problems which incorporate the firm's data, testing, and feedback, emphasizing realism and usability. The problem is cast as a Dynamic Program with a detailed model of demand uncertainty. Decisions include planning production over time, from a few hours to a quarter year, and determining the appropriate amount of labor at each factory. The objective is to minimize shipping and labor costs while providing superb customer service by producing orders on-time. Because the stochastic Dynamic Program is too difficult to solve directly, we propose deterministic, rolling-horizon, Mixed Integer Linear Programs, including one that uses recently developed affinely-adjustable Robust Optimization techniques, that can be solved in a few minutes. Simulations and a perfect hindsight upper bound show that they can be near-optimal. Consistent results indicate that these solutions offer several hundred thousand dollars in daily cost saving opportunities by accounting for future demand and repeatedly re-balancing factory loads via re-allocating orders, improving capacity utilization, and improving on-time delivery.Thesis Supervisor: J6r6mie Gallien Title: Associate Professor of Management Science and Operations London Business School Foremost, I would like to thank my advisor, Jeremie Gallien, who made this work possible by introducing me to the problem, providing contacts and professional knowledge, and easing responsibility into my hands. I greatly appreciate his kind, just and wise guidance, which continued throughout my doctoral work.Steve Graves and Cindy Barnhart, the other members of my thesis committee, imparted crucial feedback. John Foreman, who worked on a related project, aided me in many ways. Several employees at the firm motivating this work, especially Juan Correa, Spencer Wheelwright, and Jerry Becker, were instrumental in the acquisition of data and model development in this thesis.This firm, the Singapore-MIT Alliance, research assistantships from Jeremie, and teaching assistantships funded my graduate eduction. It was an honor and a pleasure to teach with Jer6mie,