Abstract—We consider an integrated vendor-buyer supply chain production-inventory model with a vendor and a buyer in this paper. The vendor produces and supplies a product to the buyer so that the buyer can meet his demands. The buyer adopts a continuous review and fixed order lot size policy to deal with stochastic demands. All unmet demands are backordered. A lot-for-lot replenishment policy is implemented between the two parties. This implies that upon receiving an order from the buyer, the vendor will immediately start a production run to produce the exact quantity requested by the buyer. The buyer’s inventory level is continuously monitored and when it falls to the buyer’s reorder point, an order will be placed, and the information is sent immediately to the vendor. A production run will be started at the vendor as soon as the ordering information is received. The vendor’s production system is assumed to be subject to random breakdowns. We assume once a breakdown has taken place during a production run, it will require a significant amount of time to perform a correct maintenance activity. Hence, a no-resumption policy is adopted by the vendor. Under this policy, when a breakdown occurs before the desired production lot size is produced, the vendor will order at once the difference between the desired production lot size and the on-hand inventory from external sources. These items must be received by the end of a production run to allow the vendor to ship the planned order quantity to the buyer. An iterative solution procedure is developed to obtain a near-optimal solution for the order quantity and the reorder point.

Index Terms—Supply chain, stochastic inventory, random machine breakdown.

Gary C. Lin is with Department of Industrial & Manufacturing Engineering & Technology, Bradley University, 1501, W. Bradley Ave., Peoria, IL 61625, U.S.A. (email: clin@fsmail.bradley.edu).

Cite: Gary C. Lin, "On an Integrated Vendor-Buyer Supply Chain Model Subject to Random Breakdowns," International Journal of e-Education, e-Business, e-Management and e-Learning vol. 9, no. 4, pp. 257-268, 2019.