Integrated vendor-buyer cooperative inventory model with controllable lead time, ordering cost reduction, and service-level constraint

In this study, an integrated vendor-buyer inventory model is proposed. The vendor produces a product in a batch environment and delivers it to a buyer facing normally distributed demand. In the current study, several assumptions are used that the combination of these assumptions has not been studied in previous papers. Here is the list of these assumptions: service-level constraint instead of shortage cost is used; ordering cost reduction is allowed, and decreasing lead time by a cost dependent on two factors including shortened lead time and ordering quantity is considered. An algorithm is developed to obtain the optimal solution of the proposed model. A numerical example is included to illustrate the results of the model. Also, the effects of assumptions used in this paper are evaluated and discussed.