Chance-constrained programming for one level assembly system under random lead times
The 18th International Symposium on Inventories, Aug 2014, Budapest, Hungary
In this study, we consider the inventory control for one level assembly system under uncertainty on lead times. The lead times can be uncertain for different reasons such as machine breakdowns, transport delays, strikes, etc. The finished product needs several components for the assembly operation for one level assembly system. We consider the case of discrete distributions to be closer to the usual assumption of MRP softwares, where the lead time is expressed as the number of periods. Typically, this is an inventory control problem where the objective is to minimize the component holding and backlog costs for the finished product due to the uncertainty of lead times. Indeed, as the finished product is assembled by using several types of components, the assembly is stopped even if a single type of component is delayed. The other components are stored between their arrival and the arrival of the latest component. Notwithstanding its non-linearity, a joint chance constrained programming model is proposed and solved via an equivalent mixed-integer linear reformulation jointly with scenario based approaches. Besides the expected optimal solution, these approaches offer alternative solutions with desired confidence level for large scale problem instances.