A stochastic programming approach to solve a coordinated capacitated stochastic dynamic demand lot-sizing problem with emergency supplies

We consider the coordinated capacitated lot-sizing problem (CCLSP) with stochastic non-stationary demand. Although the CCLSP with deterministic demand and the uncoordinated CLSP (UCLSP) with stochastic demand have been addressed in the literature, there is no published research on the CCLSP with stochastic demand. Motivated by the case of Stokke, we developed the formulation and solution method for a special case of the CCLSP. Our model is tested in the settings of stochastic and deterministic demand. The stochastic model out-performed the deterministic model with significantly lower total cost, leading to a reduction in inventory costs and to a slight increase in use of emergency supplies.