Multi-index base-stock policy for inventory systems with multiple capacitated suppliers

We study a periodic-review inventory system with multiple capacitated suppliers. These suppliers have different lead times and unit costs, and suppliers with shorter lead times charge higher unit costs. As the optimal ordering policy is unknown and expected to be complicated, we propose a multi-index base-stock (MIBS) policy for the system based on n tailored inventory positions. Orders are placed with each supplier according to a modified base-stock policy. We analyze the policy's system dynamics and establish separability properties of the optimal policy parameters. We also provide a simulation-based optimization procedure for the policy. Because the procedure involves an exhaustive search across n - 1 parameters, we construct a heuristic for computing near-optimal policy parameters. We numerically demonstrate the performance of the MIBS policy and the effectiveness of the heuristic. The results show that the performance of the MIBS policy is very close to that of the dynamic programming policy and that the performance of the heuristic is close to the optimal MIBS policy, with much faster computation. We also explore the performance of the MIBS policy when the number of sources is increased and find that increasing the number of sources means decreasing the average cost, while the marginal returns of adding a supplier diminish. Importantly, given sufficient capacity, by carefully selecting two of the suppliers-often the fastest and the slowest-it is possible to achieve an adequate balance between cost efficiency and responsiveness.