A multiprocessor task scheduling model for berth allocation: Heuristic and worst-case analysis

We consider a scheduling problem in which the processors are arranged along a straight line, and each job requires simultaneous processing by multiple consecutive processors. We assume that the job sizes and processing times are agreeable. Our objective is to minimize the total weighted completion time of the jobs. This problem is motivated by the operation of berth allocation, which is to allocate vessels (jobs) to a berth with multiple quay cranes (processors), where a vessel may be processed by multiple consecutive cranes simultaneously. We develop a heuristic for the problem and perform worst-case analysis.