Risk-adjusted Joint Optimization of Base-stock Levels and Component Allocation in an ATO System with Returns

We consider a multi-component, multi-product, periodic-review (re)assemble-to-order (RATO) system that uses an independent base-stock policy for the inventory replenishment of the components. At the beginning of each period, end-of-lease cores are returned. Because the quality of cores is random, they are tested, graded, and sorted into four pre-specified quality levels. Then, the random, jointly and continuously distributed demands for the products are realized. In our problem, partial fulfillment is not allowed. Furthermore, the system quotes a predetermined response time window for each product, and it penalizes the system if the demand is not satisfied within its time window. We model this problem through a risk-adjusted two-stage stochastic programming problem, where the first-stage decisions are the base-stock levels for all components, and the second-stage decisions are the allocations of components to different products. The risk adjustment is formulated through a chance constraint, which is then replaced by a conditional value-at-risk constraint. We solve the resulting problem through the sample average approximation method combined with the L-shaped method. We also present some encouraging numerical results.