The paper deals with the appropriate form of interaction between two refineries with different demand patterns. This problem can be formulated as finding a decentralized solution of linear programming problems linked by buying and selling activities. The complete problem is first solved for central values of product demands and costs and revenues. The structure of the basis then determines the organization of the interaction in terms of which unit sets quantities and which prices, or whether centralized decisions should be made. If, for expected values of product demand and costs, the structure of the basis is the same then the related organization of trading can be used for day-to-day transactions. For a well-known oil refinery model it is found that, for fairly large demand variations, decentralized interaction is effective, but that the structure of the basis changes easily with crude price variations, and that simulations did not converge for these variations.