A new production and shipment policy for a coordinated single-vendor single-buyer system with deteriorating items

This paper proposes a new production and shipment policy for a coordinated single-vendor single-buyer system with the consideration of item deterioration to minimize the joint total cost. To be more close to reality, the inventory level of the vendor is assumed to be an inflexion form which is different from the extant researches. Also, we incorporate the transportation time and the deterioration during delivery process into the coordinated model which are always neglected in the literature. A mathematical model is developed to determine the number of shipments per production cycle, the time interval between two successive shipments and the initial inventory when the production cycle starts. Different from the previously published work which concentrates on the equal sized shipment policy, we explore properties that the optimal shipment policy exhibit. We simplify the mathematical model developed based on the explored properties and propose a solution procedure to obtain near optimal solution. Numerical experiment on classical and randomly generated instances indicates that the joint total cost per unit time can be continuously reduced, comparing with the commonly applied equal sized shipment policy.