A branch and bound algorithm for one supplier and multiple heterogeneous customers to solve a coordinated scheduling problem

Considerable attention had previously been given to the single-vendor single-customer integrated inventory problem, but there had been very little work on the integrated single-vendor multi-customer and multi-product consideration. Here, we develop a generalized single-vendor multi-customer with multi-product consideration supply chain model with one transporter available to deliver the products from the supplier to the customers. The objective is to solve the proposed model and to find the minimized total cost, while guaranteeing a certain customer service level. A mathematical formulation of the problem is given in a general way. Then, we propose a branch and bound algorithm as an exact method and an efficient heuristic greedy algorithm. Both procedures are then compared through computational experiments which show that the heuristic algorithm is capable of generating near-optimal solutions within a short amount of CPU time.