Dual sourcing models with stock-out dependent substitution

Companies use different criteria such as lead time, cost and quality to evaluate suppliers; often using multiple suppliers with the aim of reducing stockout risk. But in many industries there may be significant differences between the quality levels of different suppliers. Thus quality-sensitive companies may prefer an item from a primary supplier, but be forced to accept substitute products of lesser quality in case of a stock-out. Motivated by an example in the aviation industry, we introduce a Dual Sourcing problem With Stock-out dependent substitution (DSWS) which includes quality differences. Due to nonconvexity of the multi-period model, analytical characterization of the optimal policy appears intractable. To overcome this problem, we prove a relation between the optimal cost of DSWS and costs of three other problems - dual sourcing without substitution and single sourcing problems with and without backlogging. This leads us to propose the use of the dual index policy (and a variant) as heuristics for DSWS, and to develop an algorithm for parameter optimization of our heuristics. Extensive numerical experiments show that the dual index policy outperforms all other candidate solutions from the literature by at least 8%. Our experiments show that the utilization of the back-up supplier leads to substantial cost savings and service rate increase, especially in case of high differences between holding cost rates of different quality items.