Slotting Optimization For Matrix Automated Order Picking System

With the rapid development of E-commerce and chain retail industry, the commodity picking in distribution center tends to be increasingly characterized by small volume, diversification, multiple batch, and high efficiency, which has put forward higher requirements for the piece-picking processes. The piece-picking refers to picking less than one carton of commodities. As each order contains a small number of goods, the smallest package unit needs to be rapidly picked out from thousands of the stock keeping unit (SKU). In addition, the quantity of orders is quite large. The piece-picking is therefore one of the important factors to the operating cost and order fulfillment efficiency in distribution center. In order to effectively improve the piece-picking efficiency and reduce the labor intensity, the matrix automated order picking system (MAOPS) has been designed and successfully put into application.MAOPS is a new type of automated order picking system composed of many inclined dispensers.Despite that the use of system could improve the picking efficiency; it requires much labor costs for replenishment. The decision makers therefore are eager to find an optimal slotting strategy based on the existing MAOPS, in order to achieve the target of maximizing the summation of saving labor costs and minimizing the order fulfillment time.Currently, most of the researches in China and abroad on automated picking system are concentrated on A-frame system. Compared to MAOPS, mechanical structure and operation of A-frame system is quite different, which is more suitable for the order picking in limited kinds of SKU. The existing papers in the field of slotting optimization for automated picking system are mainly about the optimization aimed to maximizing the summation of saving labor costs or minimizing the order fulfillment time, while only few researches comprehensively consider labor costs and picking efficiency. Based on this, this paper presents the research on the slotting optimization of MAOPS, which is aimed to comprehensively maximize the summation of saving labor costs and minimize the order fulfillment time through three optimization strategies of SKU disposition, SKU assignment and SKU allocation.The main contents and achievements are as follows:(1) Considering SKU disposition as a sub-problem, the math model is built with the objective of maximizing the summation of saving labor costs in MAOPS, and then the heuristics algorithm is designed to solve this sub-problem.SKU disposition is to determine which SKUs to be dispensed by MAOPS and how many dispensing channels of each SKU to be dispensed. Firstly, labor costs in the double picking zones with MAOPS and manual picking system are analyzed. Assuming that SKUs to be dispensed by MAOPS is known, a math model for dispensing channels allocations is established with the objective function the summation of saving labor costs, and the greedy algorithm is proposed to solve the problem. Based on this, the problem is generalized into SKUs assignment in the double picking zones. This problem can be classified as a type of special knapsack problem and a heuristic algorithm is adopted to solve it. Moreover, the effectiveness of the algorithm is analyzed through simulation.(2) Considering SKU assignment as a sub-problem, the math model is built with the objective of minimizing the order fulfillment time of one machine in MAOPS under serial merging mode, and then a clustering algorithm based on improved similarity coefficient is designed to solve this sub-problem.By treating each dispensing channel column as a zone, one machine in MAOPS belongs to the zone automated order picking system. The order fulfillment time under serial merging mode is equal to the summation of zone working time. The model of items assignment problem in a matrix automated picking device is established with the objective minimizing the summation of zone working time. To solve this problem, a hierarchical clustering algorithm based on tabu search is proposed based on the similarity coefficient which expressed by saving single channel picking time due to deferent items picked parallelly. The main idea of this algorithm is assigning items with closer relationship into the same zone in order to increase the number of items picked parallelly in each zone and reduce the total number of zones participating in each order picking process. The superiority of improved similarity coefficient and the validity of the algorithms have been proved by instance analysis.(3) Considering Zone SKU allocation as a sub-problem, the math model is built with the objective of minimizing the order fulfillment time of one machine in MAOPS under parallel merging mode, then a clustering algorithm is designed to solve this sub-problem.By analyzing the operation timing sequence of zones based on serial picking and parallel merging method in the array automated picking device, a math model for the order fulfillment time was established. Under the condition SKU assignment solution is known, a Zone SKU is generated according to the SKUs in each zone. This problem was converted into the Zone SKU allocation optimization model with the objective maximizing the summation of time difference of the virtual window zone. A heuristic clustering algorithm was proposed to solve this problem. Through the algorithm, Zone SKUs with higher similarity are assigned into zones far apart from each other in order to increase the summation of time difference of the virtual window zone. The simulation result shows that this algorithm can effectively reduce the order fulfillment time and improve the picking efficiency.(4) Based on the discussion results of the aboved sub-problems, we propose the comprehensive solution to solve the slotting optimization problem of MAOPS under serial merging mode, which has two objectives of maximizing the summation of saving labor costs and minimizing the order fulfillment time.By using the main object method, the multi-object optimization problem is converted into the objective problem of maximizing the summation of saving labor costs under the throughput constraint. A heuristic iterative algorithm is presented to solve the problem. The initial slotting solution of MAOPS can be generated by firstly achieving the SKU disposition aimed to maximize the summation of saving labor costs and then the SKU assignment in serial merging by the hierarchical clustering algorithm based on tabu search. Based on this, the iterative improvement algorithm is designed to adjust the initial solution tomeeting the throughput constraint. The instance analysis proves the effectiveness and superiority of this proposed method.