Abstract:A class of problems for manufacturers are proposed to minimize joint cost. Production and outbound distribution are combined to achieve a joint scheduling in supply chain. In the production process, the manufacturers have identical parallel batching machines to process arbitrary-size jobs. The machines have a fixed capacity in size and the total size of jobs in a batch cannot exceed the machine capacity. In the distribution process, the manufacturers deliver the products using their own vehicles and the vehicles have identical transport capacities. If there are no available vehicles to deliver the products, they should be put in inventory. The total cost consists of the production cost, the distribution cost and inventory cost. An integer programming model of the problem is presented and the problem under investigation is shown to be NP-hard in the strong sense. Then a polynomial time algorithm is provided. The time complexity and performance guarantee of the proposed algorithm are analyzed.