Integrated Supply Chain for a Single Vendor and Multiple Buyers and Products with Crashing Lead Time

In this study, an integrated inventory model was developed among one vendor, multi buyers, and multi products. The total inventory cost to be minimized in this model is a combination of the vendor's and the buyers' total inventory costs. The total vendor inventory costs consist of setup costs and holding costs and the total inventory cost of the buyer consists of ordering costs, holding costs, stockout costs, and crashing lead time costs where the crashing lead time cost is approximated with an exponential function. Three decision variables will be calculated: the number of buyer orders, the lead time of each buyer, and the frequency of vendor shipments to all buyers in one production cycle. In this study, the optimal solution of each decision variable has been developed and applied to a case to show the use of models for finding optimal solutions. The sensitivity has also been performed to show the effects of some factors on the decision variables.