Setting planned orders in master production scheduling under demand uncertainty

For single end-product master production scheduling with time-varying demand uncertainty and supply capacity, we study approaches to set replenishment quantities over the planning horizon. We present a stochastic programming model along with a simulation-based optimisation and two traditional approaches for setting order quantities. We compare these approaches to two new methods: gamma approximation and safety stock search. Computational experiments show that the gamma approximation and safety stock search perform well in terms of holding and shortage costs, with expected total cost on average, respectively, within 0.06% and 0.66% of the optimal from the stochastic program. On average, the two traditional approaches incur 12% and 45% higher cost than optimal. We provide managerial insights on the effects of parameters such as demand coefficient of variation (cv), utilisation, and target service level on the optimal total cost, the corresponding fill rate, and the relative performance of the approaches. We find that, for finite-normal demand, on average, the impact of target service level on cost is larger than that of demand cv, whose impact is larger than utilisation, except at high utilisation. We illustrate that, when demand is not normal, the gamma approximation significantly outperforms the existing normal approximation from Bollapragada and Rao (2006).