Factory Crane Scheduling by Dynamic Programming

Abstract

We describe a specialized dynamic programming algorithm for factory crane scheduling. An innovative data structure controls the memory requirements of the state space and enables solution of problems of realistic size. The algorithm finds optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is assigned a sequence of pickups and deliveries at specified locations that must be performed within given time windows. The cranes must not interfere with each other, although one may yield to the other. The state space representation permits a wide variety of constraints and objective functions. It is stored in a compressed data structure that uses a cartesian product of intervals of states and an array of two-dimensional circular queues. We also show that only certain types of trajectories need be considered. The algorithm found optimal solutions in less than a minute for medium-sized instances of the problem (160 tasks, spanning four hours). It can also be used to create benchmarks for tuning heuristic algorithms that solve larger instances.

Trajectory Predictions with Details in a Robotic Twin-Crane System

“…Method TM CA VC Zhang and Rose (2013) [1] GA × × × Legato and Trunfio (2014) [4] BB × × × Peterson et al (2014) [3] BB, BP √ × × Moccia et al (2006) [6] BC × × × Cheng et al (2015) [5] BC × × × Kasm and Diabat (2019) [12] BP × × × Chen et al (2020) [13] ADMM × × × Briskorn and Angeloudis (2016) [8] DP × × × Boysen et al (2015) [7] DP, DEC × × × Park et al (2010) [11] DP, H × × × Kung et al (2014) [10] DP × × × Aron et al (2010) [9] DP × × × Al-Dhaheri et al (2016) [19] GA × × × Chung and Choy (2012) [22] GA × × × Chung and Chan (2013) [21] GA, H × × × Kayeshgar et al (2012) [28] GA × × × Chang et al (2017) [20] GA × × × Wu and Ma (2017) [29] GA × × × Fu et al (2014) [25] H, GA × × × Correcher and Alvarez-Valdes (2017) [23] GA × × ×…”

Scheduling the operations of a double-load crane in slab yards

“…However, crane scheduling in warehouses storing slabs has received little attention. Aron et al (2011) proposed a dynamic programming (DP) algorithm to solve a CSP. In this problem, each job has been pre-assigned to a crane.…”

A Scheduling Model Framework for Crane-Assisted Pipeless Process Plants

“…They assume the prior knowledge of jobs/transfers to be executed by cranes. While Aron et al . and Ge et al schedule a special case of two cranes, the work by Peterson et al schedules two or more cranes to execute a pre-specified set of jobs/transfers in workshops.…”