Two Parallel Machines Scheduling with Two-Vehicle Job Delivery to Minimize Makespan

Abstract

A problem of parallel machine scheduling with coordinated job deliveries is handled to minimize the makespan. Different jobs call for dissimilar sizes of storing space in the process of transportation. A range of jobs of one customer in the problem have priority to be processed on two identical parallel machines without preemption and then delivered to the customer by two vehicles in batches. For this NP-hard problem, we first prove that it is impossible to have a polynomial heuristic with a worst-case performance ratio bound less than 2 unless P = NP. Thereafter, we develop a polynomial heuristic for this problem, the worst-case ratio of which is bounded by 2.

Parallel Machine Production and Transportation Operations’ Scheduling with Tight Time Windows

“…e challenges of rail time windows for time-sensitive products can be inferred according to Kang et al [10] and Wu et al [11]. Meanwhile, a trip can ship multiple orders to multiple destinations along the same railway line, which enriches the diversity of production schedules and trip selection (Diaz-Madronero et al [12] and Cao et al [13]).…”