The Multi-Spreader Crane Scheduling Problem: Partitions and supersequences

Abstract

In the Multi-Spreader Crane Scheduling Problem (MSCSP), containers with identical dimensions but variable weights are arranged along a grid. A multi-spreader crane is used to lift all the containers. The crane has m>1 modes. When it is in the pth mode, the crane can remove p adjacent containers along the same row at the same time as long as the total weight of the containers does not exceed the loading capacity κp. Such a lift takes hp minutes. It also takes cp,q minutes for the crane to switch from mode p to q when p≠q. The goal is to find a crane lift sequence so that the total time it takes to lift all the containers is minimized.This paper investigates the computational complexity of MSCSP. First, we establish a connection between greedy crane lift sequences and supersequences. We then prove that MSCSP is NP-hard when the crane has three or more modes by a reduction from a version of the Shortest Common Supersequence problem. Lastly, we investigate two problems that arise naturally when heuristics are used to solve MSCSP. We show that one can be solved using dynamic programming while the other remains computationally hard. We also provide an approximation algorithm that behaves nicely when the changeover times are not much larger than the lifting times of the crane.