Benders decomposition with special purpose method for the sub problem in lot sizing problem under uncertain demand

We propose herein the application of Benders decomposition with stochastic linear programming instead of the mix integer linear programming (MILP) approach to solve a lot sizing problem under uncertain demand, particularly in the case of a large-scale problem involving a large number of simulated scenarios. In addition, a special purpose method is introduced to solve the sub problem of Benders decomposition and reduce the processing time. Our experiments show that Benders decomposition combined with the special purpose method (BCS) requires shorter processing times compared to the simple MILP approach in the case of large-scale problems. Furthermore, our BCS approach shows a linear relationship between the processing time and the number of scenarios, whereas the MILP approach shows a quadratic relationship between those variables, indicating that our approach is suitable in solving such problems.