An amended shipment policy and model for single-vendor single-buyer system

In the existing literature, a two-phase structure of the optimal production and shipment policy for a vendor manufacturing to supply to a single buyer under the assumption that the stockholding cost of the vendor is lower than the buyer's. Actually, these policy with the structure not always be the optimal shipment. In this paper, we found that a three-phase shipment policy is more general than the two-phase policy. And a general model based on this structure is suggested and it is shown to provide a lower or equal joint total relevant cost as compared to the existing model. Finally, a particle swarm optimization (PSO) algorithm is proposed to solve the production-inventory model, which is proved to be a good algorithm by two numerical examples.