An Efficient Dynamic Programming Approach to Optimize Capacitated Lot-sizing Problem

In most industrial applications, determining production quantities are one of the most key decision making. In this paper, an integer mathematical programming model for lot-sizing problem with considering set-up time, safety stock, shortage cost, and different production manners, is presented. The objective is to minimize summation of production, set up, holding, and shortage costs. To solve the model, a forward dynamic programming (DP) approach is presented and compared with classical backward DP method. Finally, different numerical illustrations with different dimension are generated. The statistical analysis on computational results showed that the proposed DP approach is more applicable than the classical DP in terms of computational time.