Production, Manufacturing and LogisticsTabu search heuristics for the order batching problem in manual order picking systems
Highlights
► The paper studies a planning issue pivotal for the efficiency of warehouse operations. ► We present how tabu search and the attribute-based hill climber can be applied to the problem. ► In numerical experiments specific suitable parameter configurations are identified. ► The proposed methods outperform existing solution approaches in terms of solution quality and computing times.
Introduction
Order picking is a warehouse function dealing with the retrieval of items from their storage locations in order to satisfy demands specified by (internal or external) customers. Order picking arises because incoming items are received and stored in (large-volume) unit loads while customers order small volumes (i.e., less-than-unit loads) of various articles (item types). On the one hand, underperformance in order picking may result in unsatisfactory customer service (e.g., long processing and delivery times, incorrect shipments, etc.); on the other, it may lead to unnecessarily high costs (e.g., labor cost, cost of additional and/or emergency shipments, etc.). Both aspects may have a negative impact on the competitiveness of the warehouse.
Like many other repetitive material-handling activities, order picking involves the employment of human operators on a large scale. Such systems can be differentiated into two categories: picker-to-parts systems, in which order pickers walk or ride through the warehouse and collect the requested items, and parts-to-picker systems, in which automated storage and retrieval systems deliver the items to stationary order pickers (Wäscher, 2004).
With respect to systems of the first kind, three planning problems can be distinguished at the operative level (Caron et al., 1998): the assignment of articles to storage locations (article location), the grouping of customer orders into batches (order batching), and the routing of order pickers through the warehouse (picker routing). This paper deals with the second activity, which has proven to be pivotal for the efficiency of warehouse operations (de Koster et al., 1999b).
Henn et al. (2010) have shown that the application of iterated local search to the order batching problem may allow for improving distribution warehouse operations substantially. In their experiments, however, the application of the proposed algorithm turned out to be very time-consuming, and, in particular, not suitable for picking environments in which solutions have to be generated quickly or even in real time. This article focuses on two other types of local search-based approaches, which have been shown to provide high-quality solutions within small computing times for related combinatorial optimization problems. The first is a (classic) tabu search (TS); the second is the attribute-based hill climber (ABHC), which is also based on the tabu search principle, but only requires the specification of a small number of parameters.
The remainder of the paper is organized as follows: The order batching problem (OBP) will be introduced in Section 2, while Section 3 presents a literature review of solution approaches to the OBP. In the subsequent section, our TS implementation is described. In Section 5, the way in which the general principle of ABHC can be applied to the OBP is shown. Section 6 describes the design of the numerical experiments which have been carried out in order to evaluate the performance of the metaheuristics. The results from the experiments are presented and analyzed in Section 7. In particular, the performance of the proposed methods is compared to that of several benchmarking heuristics and to that of an exact solution approach. In Section 8, the article concludes with a summary of its main contributions and an outlook on further research opportunities.
Section snippets
Problem description
A customer order consists of a (non-empty) set of order lines, where each order line is composed of a particular article and the corresponding requested number of items. A pick list contains the order lines which should be processed together (picking order) and guides the order picker through the warehouse. This picking order may contain the order lines of a single customer order (pick-by-order) or of a combination of multiple customer orders (pick-by-batch). Splitting of a customer order is
Literature review
So far, few approaches have been described in the literature which solve the OBP either close to, or to optimality. Gademann and van de Velde (2005) introduced the integer programming model presented in Section 2.2. They proposed a branch-and-price algorithm with column generation in which batches are added to the model successively. Their approach was able to provide optimal solutions for small instances (up to 32 customer orders). For the case of S-shape routing, Bozer and Kile (2008)
General principle
In combinatorial optimization, a solution s has to be found in the set of all feasible solutions S that has a minimal (or maximal) value for an objective function f. Thus, a minimization problem can be described as min{f(s)∣s ∈ S}. A simple and widely-used solution method for combinatorial optimization problems is local search (LS): For a solution s ∈ S, the subset of S is called neighborhood of s in which each solution can be obtained by applying a single local transformation (“move”)
General principle
For each optimization problem, ABHC characterizes the corresponding solutions as a set of attributes A = {A1, … , Aq}. An attribute can be any solution feature, such as the edges that are present in a solution to the traveling salesman problem (Whittley and Smith, 2004), or an open or close location in a solution to the warehouse location problem (Derigs and Kaiser, 2007).
For each solution s ∈ S and each attribute Ak, k ∈ {1, … , q}, an auxiliary value fk(s) can be defined as
Problem sets
In order to evaluate the performance of the proposed metaheuristics numerically, we assume a single-block warehouse as the one depicted in Fig. 1. The depot is located in front of the leftmost aisle. Layouts of this type are frequently used in numerical experiments described in the literature (de Koster et al., 1999b, Petersen and Schmenner, 1999, Henn et al., 2010).
The picking area consists of 900 storage locations and we assume that a different article has been assigned to each location. The
Comparison to benchmarking heuristics
In Table 1, Table 2 the solution quality of TS★ (i.e., /) and ABHC★ is compared to the respective results from the benchmarking heuristics. The best average improvement obtained for each problem class is bold-faced. It should be noted that the ratios of the improvements among the heuristics are similar for both routing strategies and for both demand scenarios. Therefore, it can be concluded that the results are extendable to other routing strategies and other demand scenarios,
Conclusions and outlook
This paper dealt with the order batching problem, which is pivotal for operating manual picker-to-parts order picking systems in distribution warehouses efficiently. For the solution of this problem, two metaheuristics were proposed, namely (classic) tabu search and the attribute-based hill climber. Based on extensive numerical experiments, specific suitable parameter configurations have been identified. A comparison of the proposed methods to selected benchmarking heuristics demonstrated that
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