Optimal Inventory Control with Dual‐Sourcing, Heterogeneous Ordering Costs and Order Size Constraints

Abstract

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.

Joint Inventory and Pricing Coordination with Incomplete Demand Information

“…, Zhang et al. ). K ‐approximate convexity can help us construct and analyze well‐structured heuristic policies for these inventory problems.…”

The stochastic lot sizing problem with piecewise linear concave ordering costs

“…Fox et al (2006) considered a specific case of piecewise linear concave ordering costs, and proved that a generalized (s, S) policy is optimal for a larger class of demand distributions. Zhang et al (2012) addressed the same problem under limited order capacities. Yu & Benjafaar (2014) extended earlier 2 results by establishing the optimality of generalized (s, S) policies for all demand distributions that are strongly unimodal.…”

“…It is easy to see that the setting explained above leads to a piecewise linear concave ordering cost structure, such that each supplier corresponds to a particular linear segment. A piecewise concave ordering cost function implies the following important property on the optimal ordering policy: it is always less costly to procure from a single supplier rather than multiple suppliers in any given period (Zhang et al, 2012). The problem is then to make the supplier selection and to determine replenishment schedule as well as the replenishment quantities so as to minimize the expected total cost.…”

Pricing decisions in a strategic single retailer/dual suppliers setting under order size constraints

“…Related to the order size-restricted setting studied in this paper, Zhang, Hua, and Benjaafar (2012) analyse the inventory control policy of a retailer facing an uncertain demand for a single product. In their setting, the retailer can order from two suppliers under order size restrictions.…”

“…In our setting, suppliers have order size constraints which limit the retailer's order size in each order cycle (Hariga and Haouari 1999;Yazlali and Erhun 2009;Zhang, Hua, and Benjaafar 2012). Such order size constraints can be due to physical limits of suppliers' production facilities or can be imposed by the suppliers to ration the capacity effectively among many customers (Yazlali and Erhun 2009).…”