Integrating Commodity Markets in the Optimal Procurement Policies of a Stochastic Inventory System

Abstract

In this paper we develop a model for the procurement of traded commodities that incorporates the market-determined term structure of commodity prices. The economic cost of holding a commodity is affected by the spread between the spot and futures prices, which varies stochastically through time; this exogenously imposed holding cost is traded against firm-specific marginal costs and benefits associated with stocking each additional unit of inventory. In addition to storage and backlogging costs, our procurement model also incorporates differential transportation costs associated with forward and spot market procurement, and it allows for selling excess inventory in spot and forward markets. We show, in a multi-period, periodic-review inventory model with stochastic non-stationary demands, that optimal forward procurement policies are characterized by a fixed band. Optimal spot procurement policies are more intricate and can be described as a regulated band. We characterize the band thresholds and develop an algorithm to obtain them by exploiting the structural properties of the optimal policy. Our results suggest that it is possible to reduce inventory related costs significantly by incorporating spot and futures price information in the procurement decision making process. Our results also imply that, apart from price-risk reduction, the potential savings in transportation costs associated with forward procurement could entice manufacturers to procure a significant fraction of goods from forward markets, using spot procurement only to fine tune stocking levels and recover from emergencies.

Keywords: dual procurement, marginal convenience yield, forward contracts, commodity markets, stochastic inventory

JEL Classification: A12, C21, D21, E32, G13