A Multi-stage Stochastic Programming Approach in a Dynamic Cell Formation Problem with Uncertain Demand: A Case Study

This paper addresses a dynamic cell formation problem (DCFP) including a multi-period planning horizon in which demands for each product in each period are different and uncertain. Because the demand uncertainty is considered as stochastic data by discrete scenarios on a scenario tree, a multi-stage nonlinear mixed-integer stochastic programming is applied so that the objective function minimizes machine purchase costs, the operating costs, both inter and intra-cell material handling costs, and the machine relocation costs over the planning horizon. The main goal of the current study is to determine the optimal cell configuration in each period in order to achieve the total minimum expected costs under the given constraints. The nonlinear model is transformed into a linear form. That is why GAMS can provide global optimal solutions in linear models. In order to find the optimal solutions, by using the GAMS for small and medium-sized problems, the optimal solutions are obtained. They applied in two bounds, namely the Sum of Pairs Expected Values (SPEV) and the Expectation of Pairs Expected Value (EPEV). Also, according to the scenario-based model, the efficiency of two suggested bounds is shown in terms of the computational time. Finally, a practical case study is presented in detail to illustrate the application of the proposed model and it’s solving method. The results show the efficiency of using SPEV and EPEV for several random examples as well as the proposed case study.