A two stage stochastic programming model for lot sizing and scheduling under uncertainty
A lot sizing and scheduling problem with sequence dependent setups is addressed in this paper. In the production system, manufactories receive raw materials from upstream sites, and after production, the final products are shipped to downstream sites and customers. The key is to find a good production planning so that their cost is minimized. A two stage stochastic programming model is formulated to minimize the total production, inventory and backorder costs. The first stage decides the baseline production including the production quantity of each product and the sequence of production while the second stage focuses on the possible updates of baseline production such as overtime production. The goal is to find the best sequence of production quantities under random demand with backorders allowed. Uncertainty is explicitly represented with a scenario tree then selecting the most representative scenarios in order to obtain a smaller subset while preserving essential properties. Both setup time and setup cost are product dependent. A case study for a manufacturing company producing braking equipment has been conducted to illustrate and validate the model. The results show that the stochastic model outperforms the deterministic model, especially when there are sufficient production resources.