SKU assignment to unidirectional picking lines using correlations

Abstract

A real life order picking system consisting of a set of unidirectional picking lines is investigated. Batches of stock keeping units (SKUs) are processed in waves defined as a set of SKUs and their corresponding store requirements. Each wave is processed independently on one of the parallel picking lines as pickers walk in a clockwise direction picking stock. Once all the orders for a wave are completed a new mutually exclusive set of SKUs are brought to the picking line for a new wave. SKUs which differ only in size classification, for example small, medium and large shirts, are grouped together into distributions (DBNs) and must be picked in the same wave. The assignment of DBNs to available picking lines for a single day of picking is considered in this paper. Different assignments of DBNs to picking lines are evaluated using three measures, namely total walking distance, the number of resulting small cartons and work balance. Several approaches to assign DBNs to picking lines have been investigated in literature. All of these approaches seek to minimise walking distance only and include mathematical formulations and greedy heuristics. Four different correlation measure are introduced in this paper to reduce the number of small cartons produced and reduce walking distance simultaneously. These correlation measures are used in a greedy insertion algorithm. The correlation measures were compared to historical assignments as well as a greedy approach which is known to address walking distances effectively. Using correlation measures to assign DBNs to picking lines reduces the total walking distance of pickers by 20% compared to the historical assignments. This is similar to the greedy approach which only considers walking distance as an objective, however, using correlations reduced the number of small cartons produced by the greedy approach.

A Multi-Objective Approach to the Assignment of Stock Keeping Units to Unidirectional Picking Lines

“…Historical data [11] was collected by PEP over a period of 12 weeks, of which seven weeks were used for static and dynamic testing. Historical solutions are currently found by hand by the picking line managers.…”

“…Matthews and Visagie [13] addressed the problem of carton use by introducing four different correlation measures, which included two desirability scores based on the Jaccard statistic. Of the four measures tested and compared with the historical case and PGI approach, the desirability score -considering the number of stores required by the candidate DBN, and the number of stores requiring at least one DBN already assigned to a specific picking line -was found to be the most effective measure of correlation.…”

“…Matthews [10] suggested the use of capacity constraints with the aim of focusing on the issue of reducing the volume of DBNs on picking lines -the issue that Matthews and Visagie [13] were unable to resolve. He formulated a mixed integer linear programming (MILP) model that included constraints in which the maximum volume for each picking line was considered.…”

“…Computational times suggested that no more than three clusters should be used, and that a further segmentation should take place, provided that there are clusters consisting of more than three picking lines. It was further proposed that a hybrid assignment algorithm be used, in which the segmentation and capacity constraint formulation is integrated with the correlation measure suggested by Matthews and Visagie [13]. An average improvement of 15 per cent on the walking distance of pickers was obtained using the hybrid approach, compared with the historical data.…”

“…The offspring population is produced in lines 5-12, where the crossover, repairing and mutation take place. All feasible solutions in are added to after which all non-dominated solutions in are kept, as is evident in lines [13][14][15]. If the size of is greater than a specified limit, then solutions are removed from according to the total crowding distance in equation (39), which may be seen in lines [16][17][18].…”