A Single Item Lot Sizing Problem Considering Capital Flow and Trade Credit

This paper studies the influence of capital flow and trade credit to the production planning problems. That is, when a company starts to produce a certain number of products, its present capital quantity should be no less than the total production cost, but it could delay payment using trade credit. We formulate the mathematical model of this problem and propose a polynomial recursive algorithm to solve it based on dynamic programming. Under certain conditions, the algorithm could get optimal solutions. And it could get a good feasible solution in other conditions. Numerical analysis shows that our algorithm could solve the problem in short time and the computational errors are rather small compared with optimal solutions in most situations. With a heuristic adjustment step, the computational error is even lower. It also shows that using trade credit could benefit a company's production plan and increase the capital quantity