Simultaneous Price-Production Decisions

This paper deals with the problem of determining the price and production schedule of a firm over a known horizon simultaneously when the demand parameters are time-dependent. It characterizes the optimal solution and shows the similarity of our problem to the well known problem of Modigliani and Hohn [Econometrica 23, 46–66 (1955)]. It also demonstrates the possible existence of a planning horizon. These results are obtained by using control theory, in particular, by using the necessary and sufficient conditions for a state constraint in the form of a nonnegative constraint on the inventory level.