Mixed-Integer Linear Programming Model for Stochastic Capacitated Lot-Sizing Problem Under Static-Dynamic Uncertainty Strategy

This research paper revisited the certain equivalent mixed-integer linear programming (MILP) developed by a previous study and provided a new method for solving the problem of a stochastic capacitated lot-sizing with the constrains of backordering under the static-dynamic uncertainty strategy. The existing theories and methods that can be applied to solve the above strategy (SDUC) are available for both the two-stage and single-stage solutions. The proposed model is an extended version that will answer both "replenishment period" and "optimal replenishment order" simultaneously by considering a joint replenishment environment for multiple items with shared resources (a limited resource), also known as a capacitated lot-sizing problem. The numerical and sensitivity tests are performed to investigate the effect of the changes in critical parameters on the behavior of the proposed model, such as the change of the mean of demand or the change of the product holding cost. The result shows that the model will produce the exact amount of demand in each period for each product, resulting in zero excess inventory at the last period. Furthermore, the model also tried to balance the cost of carrying the stock and the setup cost for each production time; whenever the product has a little holding cost but a high setup cost, the model will produce high quantities for each product.