A Markov decision process-based policy characterization approach for a stochastic inventory control problem with unreliable sourcing

We consider a single-product periodic-review inventory system for a retailer who has adopted a dual sourcing strategy to cope with potential supply process interruptions. Orders are placed to a perfectly reliable supplier and/or to a less reliable supplier that offers a better price. The success of an order placed to the unreliable supplier depends on his supply status that has a Markovian nature. The inventory control problem for this unreliable supply chain is modeled as a discrete-time Markov decision process (MDP) in order to find the optimal ordering decisions. Through numerical experimentation, the structure of the optimal ordering policy under several cost scenarios and different supplier reliability levels is determined. Four basic policy structures are found and are referred as case 1: order only from the unreliable supplier; case 2: order simultaneously from both suppliers or only from the unreliable supplier depending on the inventory level; case 3: order from one or the other but not both suppliers simultaneously; and case 4: order only from the reliable supplier. For all cases, (s, S)-like policies characterize perfectly the optimal ordering decisions due to the existence of the fixed ordering cost. Further experimentation is done to study the effects of changes in several system parameters (cost parameters such as fixed ordering cost, unit purchasing cost, backorder cost as well as the supplier reliability level) on the ordering policy and cost of the system.