Ph.D Student | Alon Dourban |
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Subject | Managing Products with a Mean Reverting Price Process |

Department | Department of Industrial Engineering and Management |

Supervisor | Dr. Yedidsion Liron |

Full Thesis text |

This research studies inventory control optimization problems with a stochastic mean reverting purchasing price process. These kind of problems are closely related to the management of commodity based inventory systems, as many studies show that mean reversion dynamic is often detected in the price process of various kinds of commodities. Organizations that use commodities as raw material in their production process, plan the purchasing of the commodity in accordance to their business needs and logistic constraints. In addition, when dealing with commodities it is also essential to take into account its fluctuating price. Hence, the inventory control policy of commodities presents a problem that combines logistic aspects with the price randomness aspect. In this research, we develop optimal policies for this kind of problems. We present a multi period model in which there is known deterministic periodic demand, and our goal is to minimize the expected total cost of the system. Under this model, two types of problems are studied: the first problem is the capacitated purchasing problem in which there is a capacity to the number of items that can be purchased in each period; the second is a lot sizing problem where a fixed setup cost is paid at each period in which at least one order is placed. These problems capture business scenarios where the purchasing of items can be done frequently, subject to the fluctuating price, but the purchased items are aggregated to a more rarely scheduled periodic shipments. We show that the optimal polices are based on a set of threshold functions that define the respective price level over time under which it is optimal to purchase an item with respect to the state of the inventory system. The characteristics of the thresholds are analyzed with respect to time, inventory level, and setup cost or capacity, for each of the respective problems. This provides important properties and insights, some of which may seem counter intuitive; however, the logic behind them is clarified with proofs and discussion.