A capital flow-constrained lot-sizing problem with trade credit

This paper incorporates capital flow constraints and trade credit into lot-sizing problems. A capital flow constraint is different from a traditional capacity constraint; when a manufacturer begins to produce a certain number of products, its present capital should not be less than the total production costs of that period; otherwise, the manufacturer must decrease production quantity or suspend production, or he/she could delay payment using trade credit. Moreover, the capital of each period should also be greater than zero to avoid bankruptcy. A mathematical model is formulated for the single-item lot-sizing problem. Based on dynamic programming, this mixed integer problem is approximated to a traveling salesman problem to find the longest route and we divide the model into sublinear problems without integer variables, and propose a dynamic programming algorithm with heuristic adjustment to solve it. An interior point algorithm can easily solve sublinear problems. The proposed algorithm could obtain optimal solutions under certain situations. Numerical analysis shows that the proposed algorithm has small optimality deviation percentage under other situations and enjoys computation efficiency advantage, as compared with CPLEX 12.6.2. It also indicates that the capital flow constraints and the application of trade credit in lot-sizing problems could affect optimal production decisions.