An integrated inventory model for the single-vendor two-buyer problem

We consider the problem of a vendor which supplies an item to two different buyers. The vendor manufactures the item at a finite rate and each buyer faces a constant deterministic demand. There is a holding cost per unit stored per unit time at the vendor and at each buyer. The vendor incurs a fixed setup cost associated with each production setup. A fixed delivery cost is charged at each buyer when it places an order. We assume that shortages are not allowed. The objective is to minimize the total joint cost incurred by the vendor and the buyers. We formulate the problem in terms of integer-ratio policies and we develop a procedure for computing an optimal policy.