Two-echelon production inventory model with imperfect quality items with ordering cost reduction depending on controllable lead time

Through out the paper, a study of, a two-echelon integrated vendor-buyer inventory system for a continuous review model over a finite planning horizon is considered. The vendor procures imperfect quality of items at a constant production rate which is random in nature, where unit production cost is dependent directly on technology investment cost, labor cost and capital cost used in system. The vendor produces items and supplies to the buyer to meet customer’s demand, which is stochastic and normally distributed. Also, the lead time of buyer is controllable which depends on the order quantity. Lead time may be reduced by using crashing cost from normal duration to minimim duration. The shortages are allowed and assumed to be back-ordered. Main objective is minimization of expected average cost for the integrated system by analytic process. Likewise, mathematical examples are provided numerically to illustrate applicability of our proposed model. The sensitivity analysis of the proposed model is carried out with respect to the system’s various major parameters. Results acknowledge that the proposed model is more applicable for the supply chain manufacturing system.