Allocating Small Transporters to Large Jobs

We optimize the assignment of transporters to several jobs. Each job consists of processing a large, decomposable volume. A fleet of transporters is given, each of which can only process a limited volume at a time. After processing its share, a transporter must rest for a short time before being able to process another part. This time is only dependent on the assigned job, not on the transporter. Other transporters can take over the processing while a transporter rests. Transporters assigned to the same job wait for their turn in a queue. A transporter can only be assigned to one job. Our goal is to simultaneously minimize the maximum job completion time and the number of assigned transporters by computing the frontier of Pareto optimal solutions. In general, we show that it is NP-hard in the strong sense to compute even a single point on the Pareto frontier. We provide exact methods and heuristics to compute the Pareto frontier for the general problem and compare them computationally.