Optimal routing in an automated storage/retrieval system with dedicated storage

We address the sequencing of requests in an automated storage/retrieval system with dedicated storage. We consider the block sequencing approach, where a set of storage and retrieval requests is given beforehand and no new requests come in during operation. The objective for this static problem is to find a route of minimal total travel time in which all storage and retrieval requests may be performed. The problem of sequencing a list of retrievals is equivalent to the Traveling Salesman Problem (TSP), and thus NP-hard in general. We show that the special case of sequencing under the dedicated storage policy can be solved in polynomial time. The results apply to systems with arbitrary positions of the input and output stations. This generalizes the models in the literature, where only combined input/output stations are considered. Furthermore we identify a single command area in the rack. At the end we evaluate the model against heuristic procedures

An order batching algorithm for wave picking in a parallel-aisle warehouse

In this paper we address the problem of batching orders in a parallel-aisle warehouse, with the objective to minimize the maximum lead time of any of the batches. This is a typical objective for a wave picking operation. Many heuristics have been suggested to solve order batching problems. We present a branch-and-bound algorithm to solve this problem exactly. An initial upper bound for the branch-and-bound algorithm is obtained using a 2-opt heuristic. We present a basic version of the algorithm and show that major improvements are obtained by a simple but very powerful preprocessing step and an improved lower bound. The improvements for the algorithm are developed and tested using a relatively small test set. Next, the improved algorithm is tested on an extensive test set. It appears that problems of moderate size can be solved to optimality in practical time, especially when the number of batches is of importance. The 2-opt heuristic appears to be very powerful, providing tight upper bounds. Therefore, a truncated branch-and-bound algorithm would suffice in practice