Analysis of an integrated production-sales problem for one-machine, two-product system

In the present study, we are concerned with the modeling and analysis of one-machine, two-product, integrated production-sales system, in which three decision-makers that take different responsibilities are considered. Through the constructed mathematical model, the relations that show the optimal solutions of decision variables are derived. It is found that the ratio of the optimal production horizons of two products is equal to the product of the ratio of the sales rates of the two products to the ratio of unit costs within their production horizons. Through the sensitivity analysis, direct or indirect influences on the optimal solution induced by the variation of parameters are discussed.