Stocking Products, The Profit Function In (r, D) Strategy

This paper mainly devotes to studying the profit functions for make-to-stock production under (R,d) policy. Based on the Markov decision processes theory, first the author constructs the HJB equations for each situation, and then gets the results by the related knowledge of differential equations. The full text is composed of five parts, and the concrete structure is as follows:Chapter one introduces the background and existing work of the growth system as well as the framework of the paper.Chapter two introduces the elementary theories which are needed in the paper, mainly including:the related concepts of make-to-stock productions, the concepts of Markov decision processes, the theory of optimality,etc.Chapter three considers one of the main results in this paper. In this chapter the author investigates the profit functions in d>R2>R1≥0.The author first rewrites the HJB equations according to initial inventory, then gets the general solutions of the corresponding conditions' profit functions by the eigenvalue method of differential equation, finally determines those coeffients by their boundary conditions to obtain the profit functions. Chapter four promotes the other main results of this paper. This chapter focuses on the profit functions for the other three situations: d>R2≥0>R1, d≥0>R2>R1 and 0≥d>R2>R1.The method of solution is similar to Chapter three.Chapter five summarizes the mainly work of this paper, and carry on this result to further discusses.