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

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