An Exact Algorithm for the Input/Output Scheduling Problem in an End-of-Aisle Multi-Shuttle Automated Storage/Retrieval System with Dedicated Storage

Abstract

In this paper we propose an exact algorithm for the input/output scheduling problem in an end-of-aisle multi-shuttle automated storage/retrieval system (AS/RS) with dedicated storage. This problem is to determine an optimal travel route of a multi-shuttle stacker crane to meet a given set of storage and retrieval orders, and it can be formulated as a class of capacitated vehicle routing problems. In our algorithm, column and cut generation is applied to a linear relaxation problem of the original problem to obtain a good lower bound. In the course of the lower bound calculation, we apply a greedy heuristics and a local search to a solution of the relaxed problem in order to obtain a good upper bound (a heuristic solution). If there is a gap between the lower and upper bounds, we try to obtain an exact solution by solving a binary programming problem with a restricted number of columns. We examine the effectiveness of our algorithm by numerical experiments.