Using list-based simulated annealing and genetic algorithm for order batching and picker routing in put wall based picking systems

Highlights

• Order picking and picker routing in put wall based picking systems are modeled.

• Two genetic algorithms, a list-based simulated annealing are proposed.

• A hybrid of genetic algorithm and list-based simulated annealing is proposed.

• Performance of proposed metaheuristics are compared against each other and Gurobi.

• It is observed that depending on the problem size, each method performs differently.

Abstract

A put wall is a hardware composed of containers that is usually used as a sorting station. In this study, the order picking operations, including order batching and picker routing, in a put wall based picking system is studied. Put walls usually have limited capacity and can accommodate only a part of received orders at a time. Hence, scheduling of the orders on the put wall should be considered along with the order batching and picker routing. For this, a mathematical formulation for order batching and picker routing in a put wall based picking system is proposed. To solve the problem, two genetic algorithms (GAs) with random shuffling and inverse–insert–swap mutation operators, a list-based simulated annealing (LBSA) and a hybrid GA–LBSA are proposed. To show the effectiveness of the proposed methods, their results are compared against the best solutions found by Gurobi 7.0. It is found that while for smaller size problems LBSA is a better choice in terms of solution quality, when CPU time is considered, depending on the problem size, GA and GA–LBSA might be the better options.

Introduction

Order fulfillment operations significantly affects supply chain performance. Companies such as Amazon and Walmart, are continuously investing in their warehouse and fulfillment capabilities [1], [2], [3]. One of the critical activities in order fulfillment operations is order picking. Order picking refers to the retrieval of stock keeping units (SKU) from their location in a warehouse to fulfill customer demands [4]. Order picking is a labor intensive activity that can contribute up to 60% of the warehouse costs [5], [6]. Approximately 50% of the pickers’ time is spent in traveling [7], [8]. By improving the travel time/distance of the order picking operation, an organization can significantly improve a warehouse operations.

In order to improve the efficiency of the order picking operation, order can be batched together and picked in a common tour [9], [10]. The batching decision depends on factors such as the capacity of the pickers and the layout of warehouse. After the order batches are determined, it is then necessary to find a set of routes that minimizes the distance traversed or time spent by the pickers for picking the SKUs from warehouse aisles [11]. Order batching and picker routing problems have been studied under different circumstances and constraints. To the best of the authors’ knowledge, this problem has not been addressed in a picking system which takes advantage of put wall. A put wall is a hardware composed of containers typically used as a sorting station. Each container in the put wall is associated with an order. After receiving a picklist, composed of SKUs from different orders, a picker traverses the warehouse aisles to pick the SKUs and returns to the put wall at the end of the tour. After placing each SKU in the proper put wall container, the picker starts the next tour. After all the SKUs of an order are picked, the order is unloaded from the put wall and sent to the packaging area. In this study, each SKU occupies one distinct location, however, two SKUs can occupy the same location. For example, two different SKUs can be located on the same rack but on different selves. In this scenario, the distance among the location of the two SKUs will be considered as zero. Additionally, it is assumed that there is enough inventory to fulfill all orders on a picklist. This is generally a valid assumption because if a SKU is out of stock, it will be eliminated from the picklist and fulfilled later when there is sufficient inventory. Thus, for order batching and routing it is not necessary to consider out of stock situations.

Depending on the capacity of a put wall and the number of orders received, it might not be possible to accommodate all the orders on the put wall at once. In this scenario, besides the order batching and picker routing problems, it is necessary to determine the sequence of orders being loaded on the put wall as well. If an order is not yet loaded on the put wall, a picker cannot begin a tour to pick its SKUs. Thus, the capacity of put wall and sequence of orders loaded on it directly affects the problems of order batching and picker routing.

Unlike previous studies, one critical aspect of this research is the dependencies of tours on each other. This is because of the limited capacity of put wall and the fact that some orders must wait for others to finish before being loaded in the put wall. Therefore, some tours need to be done after the others to make sure an order is picked after all its precedent orders are picked. Another unique aspect of this study is the use of a precedency network. In previous studies, it was generally assumed that it is possible to estimate the total travel time based on the total travel distance or vice versa [4], [11]. In this study, that assumption is not generally valid. This is because the tours are dependent on each other and form a precedency network. In a precedency network, the longest path determines the total time and is not necessarily possible to estimate the total traveled distance based on it. Thus, summing the picking time of all tours does not necessarily yields the picking makespan. Moreover, the number of pickers available and their assignment to the tours can significantly affect the completion time while not affect the total traveled distance. To avoid these complexities, the focus of this paper will only be on minimizing the total pickers’ distance traveled. When minimizing the total traveled distance it is not necessary to define the assignment of pickers to tours.

Fig. 1 depicts a small example of order batching and picker routing in a put wall based picking system with four orders, four SKUs and put wall capacity of two orders. Each order includes multiple SKUs (order line). Order 4 includes two units of SKU 4. A tour can only include orders that are on the put wall. Green dotted arrow shows the precedency of the orders. In this example, orders 2 and 4, will be loaded on the put wall after orders 1 and 3. In Fig. 1 there are three tours (O is the origin point of each tour). The red tour, covers all the SKUs in order 3 and some SKUs in order 1. The yellow tour covers the remaining SKU in order 1 and all the SKUs in order 4; and finally, the blue tour covers all the SKUs in order 2. To start the yellow tour, and since it includes SKUs from the order 4, it is necessary to finish the red tour in order to fulfill order 3 and load order 4 on the put wall. Thus, the start of yellow tour is dependent on finishing the red tour. Similarly, the start of blue tour is dependent on finishing the yellow tour. Fig. 2 shows the dependency of tours (yellow tour depends on red tour and blue tour depends on yellow and red tours). As depicted in Fig. 1, in addition to the batching decision, a picker routing decision is also made. For instance, in tour 1, SKU 4 needs to be picked after SKU 1.

This research addresses the problem of order batching and picker routing in a put wall based picking system. The main motivation of this paper comes from a series of discussions with a major US retailer that takes advantage of put wall in its warehouses.

The contributions of this study are as follows:

• A new mathematical model for minimizing the distance traveled by pickers while determining the order batching, picker routing and sequencing of orders on put wall is proposed.

• Two genetic algorithms (GAs) with different mutation operators, a list-based simulated annealing (LBSA) and a hybrid of the GA and the LBSA (GA–LBSA) for solving the model are proposed. The results are compared against the solutions obtained by Gurobi 7.0.

The remainder of this paper is arranged as follows. Section 2 reviews the related literature. In Section 3, mathematical model is proposed. Methodologies used for solving the proposed model are introduced in Section 4. Section 5 is dedicated to numerical experiments and in Section 6, the overall conclusions are stated.