A periodic review policy for a coordinated single vendor-multiple buyers supply chain with controllable lead time and distribution-free approach

In this paper, we study a single vendor-multiple buyer integrated inventory model with controllable lead time and backorders-lost sales mixture. Each buyer adopts a periodic review policy in which the review period is an integer fraction of the production cycle time of the vendor. To reflect the practical circumstance characterized by the lack of complete information about the demand distribution, we assume that only the first two moments of the demand during the protection interval are known. The long-run expected total cost per time unit is derived, which includes stockout costs. The problem is to determine the length of the inventory cycle of the vendor, the produce-up-to level for the vendor, the replenishment policy of each buyer, and the length of lead times that minimize the cost function under the minimax distribution-free approach. Two alternative heuristics are proposed. Numerical experiments have been carried out to investigate the performance of the heuristics and to study the sensitivity of the model.