A periodic review lot sizing problem with random yields, disruptions and inventory capacity

This paper examines a periodic-reviewed lot sizing problem with random yields, disruptions and limited inventory capacity. To characterise the continuous production, an additive random yield model is considered rather than a multiplicative one. Disruptions cause breakdowns to production. Inventory capacity is included since the production has to be shut down when the inventory buffer is full. Both disruptions and shutdowns lead to a start-up cost and a stochastic lead time to recover the production. These compound factors of uncertainty are encountered in practical planning decisions in process industries. We review the existing random yield models, which are then compared with the additive model. With a linear production cost, the additive model has an order-up-to policy to be optimal. Disruptions deteriorate the expected actual production quantity and the fill-rate dramatically, even though the optimal order-up-to level increases compared with the cases of no disruption. Considering inventory capacity makes the problem to be a non-convex dynamic programming problem. Numerical analysis shows that the performance is dramatically deteriorated when the inventory capacity is rather tight, which indicates the importance of selecting a proper inventory capacity to reduce the negative impacts and avoid redundant investment on capacity. Moreover, the start-up cost plays an important role in determining the level of inventory capacity.