Abstract: In this paper, an integrated scheduling model of production and distribution operations is studied. In this model, a set of jobs (i.e., customer orders) are first processed on single machine and then delivered in batches to the downstream customers in different regions. The problem is to find a joint schedule of production and distribution such that an objective function that takes into account both production cost and distribution cost is optimized. Production cost is measured by a function of delivery times, namely, the times when the jobs are delivered to the customers. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. This paper considers different production costs. For the model with the sum of weighted delivery times as production costs, the strong NP-Hardness has been proven and a dynamic programming algorithm is developed for consistency constraints on jobs' processing time and weight. For the model with production costs related to the due date, the NP-Hardness is analyzed and two dynamic programming algorithms are designed.

Key words: supply chain scheduling, supplier's problem, single machine, dynamic program