Optimal inventory control with dual-sourcing, heterogeneous ordering costs and order size constraints

We consider a dual-sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single-sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi-convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low-cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi-convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.