摘要：Supply chain coordination problems involve a number of actors, namely suppliers, manufacturers, 3PL providers, and customers. In a typical scenario, there are m manufacturers (modeled as single machines), each of which processes a specific set of jobs (products). After their processing is completed, products are shipped to a customer by means of vehicles. The set of jobs assigned to the same vehicle in one delivery is a delivery batch. The problem consists in concurrently finding a production schedule of the jobs on the machines, a partition of jobs into delivery batches, and an assignment of delivery batches to vehicles, so that jobs are delivered within their deadlines and total costs are minimized. We focus on a scenario characterized by fixed departure times and inventory holding costs. The former means that a set of departure times is given, and for each of them there is a (given) number of vehicles, possibly having limited capacity. The latter means that each job incurs a cost proportional to the length of the time span from the job completion time to its delivery departure time. Within this general framework, in this paper we report complexity results concerning two special cases, namely (i) when each manufacturer imposes a certain production sequence to the 3PL, and (u) when there is a single manufacturer, processing times are all equal to 1, there are no binding deadlines and there are no fixed delivery costs.
