Integration Supply Chain Scheduling With Single Machine

One important issue in production and logistics management is the coordination of activities between production and delivery. In order to make the supply chain achieving good operation performance, the links of production and transportation must be coordinated together. In our research problem, we develop a single-machine scheduling model and the jobs are first processed in a processing facility and then delivered to the customers directly without intermediate inventory. The aim is to find a joint schedule of production and distribution such that an objective function that takes into account both customer service level and total distribution cost is optimized. Customer service level is measured by a function of the times when the jobs are delivered to the customers. In these models, customer service is measured by the sum of job weighted average time 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. We study two classes of problems, In the first class of problems, the number of vehicles is unlimited; in the second class, the number of vehicles is limited. When the number of vehicles is unlimited, for the single customer and more customers situation, we give dynamic programming to solve them respectively,and then give the time complexity analysis. In the second case, we only give the dynamic programming method.