Optimal control and competitive equilibrium of production-inventory systems with application to the petroleum refining industry

This paper studies a competitive equilibrium production-inventory model with application to the petroleum refining industry. The authors first analyze a continuous-time optimal control problem of a firm (refinery) making procurement, production, and sales decisions under uncertain raw material (crude oil) price, finished goods (petroleum products) price, and operating costs. Next, they consider an economy with many raw material suppliers, production firms, and consumers. To assess the empirical usefulness of the equilibrium theory, they simulate the industry equilibrium in the special economy under various settings. They find that the simulated equilibrium price and inventory processes exhibit some patterns that are observed in the actual petroleum data. Finally, they fit the theoretical model using the actual data. The results generally support the theoretical model. They are able to show that the equilibrium conditions will involve a risk term, but finding a rational expectations equilibrium is more difficult and the subject for future research.