A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach

Two dynamic economic lot size production systems are analyzed in this paper, the first being a single product model with backlogging and the second a multi-echelon model. In each model the objective is to find a production schedule that minimizes the total production and inventory costs. A key conceptual difficulty is that the mathematically perplexing problem of minimizing a concave function is being considered. It is shown that both models are naturally represented via single source networks. The network formulations reveal the underlying structure of the models, and facilitate development of efficient dynamic programming algorithms for calculating the optimal production schedules.