Integrated optimization of procurement, processing, and trade of commodities

We consider the integrated optimization problem of procurement, processing, and trade of commodities in a multiperiod setting. Motivated by the operations of a prominent commodity processing firm, we model a firm that procures an input commodity and has processing capacity to convert the input into a processed commodity. The processed commodity is sold using forward contracts, while the input itself can be traded at the end of the horizon. We solve this problem optimally and derive closed-form expressions for the marginal value of input and output inventory. We find that the optimal procurement and processing decisions are governed by price-dependent inventory thresholds. We use commodity markets data for the soybean complex to conduct numerical studies and find that approximating the joint price processes of multiple output commodities using a single, composite output product and using the approximate price process to determine procurement and processing decisions is near optimal. Compared to a myopic spread-option-based heuristic, the optimization-based dynamic programming policy provides significant benefits under conditions of tight processing capacities and high price volatilities. Finally, we propose an approximation procedure to compute heuristic policies and an upper bound to compare the heuristic against, when commodity prices follow multifactor processes.