We consider a firm buying a commodity from a spot market as raw material and selling a final product by submitting bids. Bidding opportunities (i.e., demand arrivals) are random, and the likelihood of winning bids (i.e., selling the product) depends on the bid price. The price of the commodity raw material is also stochastic. The objective of the firm is to jointly decide on the procurement and bidding strategies to maximize its expected total discounted profit in the face of this demand and supply randomness. We model the commodity prices in the spot market as a Markov chain and the bidding opportunities as a Poisson process. Subsequently, we formulate the decision-making problem of the firm as an infinite-horizon stochastic dynamic program and analytically characterize its structural properties. We prove that the optimal procurement strategy follows a price-dependent base-stock policy and the optimal bidding price is decreasing with respect to the inventory level. We also formulate and analyze three intuitively appealing heuristic strategies, which either do not allow for carrying inventory or adopt simpler bidding policies (e.g., a constant bid price or myopically set bid prices). Using historical daily prices of several commodities, we then calibrate our models and conduct an extensive numerical study to compare the performances of the different strategies. Our study reveals the importance of adopting the optimal integrative procurement and bidding strategy, which is particularly rewarding when the raw material prices are more volatile and/or when there is significant competition on the demand side (the probability of winning is much smaller when submitting the same bid price). We establish that the relative performances of the three heuristic strategies depend critically on the holding cost of raw material inventory and the competitive environment, and identify conditions under which the shortfalls in profits from adopting such strategies are relatively less significant.
Read full article: Annals of Operations Research, March 26, 2015