A robust capacitated lot sizing problem with setup times and overtime decisions with backordering allowed under demand uncertainty

This research work considers the multi-product multi-period capacitated lot-sizing problem with setup times and overtime with backordering allowed (CLSPSTOB) under demand uncertainty by means of a budget-uncertainty set robust optimization. We first present a mixed integer linear programming (MILP) model that describes the deterministic CLSPSTOB with production costs, setup costs, inventory holding costs, backordering costs, and overtime costs. Then, a robust optimization approach is applied to deal with the demand uncertainty with unknown probability distribution, and a robust counterpart model based on duality theory is obtained. Some numerical experiments are presented for the robust capacitated lot-sizing problem with setup times and overtime with backordering allowed (RCLSPSTOB).