Inventory and Procurement Management in the Presence of Spot Markets

This research develops mathematical models for inventory and procurement management in the presence of spot markets. More specifically, we consider those models by incorporating different types of supply contracts. Particular attention is paid to the quantity flexible contracts. This research is an attempt to understand how firms should adopt their operating policies in the presence of fluctuating commodity prices. In this thesis, we mainly consider the following three models.;In the first model, we study the optimal procurement strategy in a two-period framework when both the spot market and the forward contract are considered. The forward contract is agreed upon in the first period, and is then delivered in the second period, when the spot market is also available. This is followed by production and demand. The objective of the buyer is to minimize his expected cost. We study the problem for two scenarios: the buyer cannot and can sell to the spot market. Through our analysis, when the buyer can not sell to the spot market, there exists a threshold forward price, under which the buyer will enter into the forward contract. This threshold is lower than the expected spot price. Furthermore, we analytically show that the optimal order quantities via forward contract increase in the mean of the spot price, but decrease in the variability of the spot price. However, the buyer only speculates using the forward contract when he can sell to spot market.;In the second model, we consider a problem in which a buyer makes procurement decisions when he faces periodic random demand and two supply sources, one is a long-term contract supplier and the other is a spot market. When he procures from the contract supplier, a fixed unit price is charged and a predetermined minimum quantity for each period must be committed, and when he procures from the spot market, a stochastic spot price plus a fixed setup cost is charged. The spot price is only realized at the beginning of each period. We show that the optimal policy consists three different (s, S) type policies. More important, we identify certain conditions under which there exist monotone properties between the policy parameters and the current spot price for a general Markov spot price process. Then, we can divide the price space into three regions, each of which corresponds to a specific policy, for each period. We also conduct numerical analysis to gain more insights into how the spot market impacts the buyer's performance. We find the buyers benefits from a more volatile market.;The last model extends the second model by incorporating an important feature that is widely seen; i.e., the procurement from the contract supplier should fulfill a total order quantity commitment (TOQC). The TOQC requires the buyer to procure no less than the predetermined commitment during the contract period, which we call the planning horizon. Thus, in each period, the buyer trades off between the possible lower cost now (by procuring from the spot market) and the reduced cost in the future (by reducing the remaining commitment). Two types of commitment contracts are considered: a minimal TOQC contract and a definite quantity contract. Our analysis characterizes an optimal procurement policy which depends on the spot price in each period and an optimal virtual remaining commitment level. Such a structured policy can be viewed as a combination of some policies of base-stock type, each of which can be computed through an equivalent system without any commitment. Moreover, some of these equivalent systems are of simple multiple-period newsvendor type. This greatly simplifies the computation of the optimal policies. We also numerically analyze how the TOQC and the spot market affects the buyer's performance.