Integrated Optimization of Procurement, Processing and Trade of Commodities in a Network Environment

We consider the integrated optimization problem of procurement, processing and trade of commodities over a network in a multiperiod setting. Motivated by the operations of a prominent commodity processing firm, we model a firm that operates a star network with multiple locations at which it can procure an input commodity and has processing capacity at a central location 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 show that the single-node version of this problem can be solved optimally when the procurement cost for the input is piecewise linear and convex, and derive closed form expressions for the marginal value of input and output inventory. However, these marginal values are hard to compute because of high dimensionality of the state space and we develop an efficient heuristic to compute approximate marginal values. We also show that the star network problem can be approximated as an equivalent single node problem and propose heuristics for solving the network problem. We conduct numerical studies to evaluate the performance of both the single node and network heuristics. We find that the single node heuristics are near-optimal, capturing close to 90% of the value of an upper bound on the optimal expected profits. Approximating the star network by a single node is effective, with the gap between the heuristic and upper bound ranging from 7% to 14% for longer planning horizons.