Integrated production-inventory-distribution system with deterministic lead times

A model is developed for determining manufacturing and distribution lot sizes at each level of a dynamic multi-level production-inventory-distribution system. A setup cost and a setup time at production stages and deterministic production and distribution lead times are considered. The solution procedure is based on a minimum cost network flow algorithm for concave arc costs. A computer code developed for this concave cost algorithm is used to solve the model. Computational experience in solving a few problem is also reported.