Integrated Optimization Research Of Dispenser System Based On Zone Picking Strategy

As the economy keeps growing, the commodity with small batch diversification are needed more frequently, which requires a faster order fulfillment time. The working efficiency of order picking system always becomes the bottleneck of throughput of distribution center. It’s said that the order picking cost accounts for about 60% of the total cost, and the order fulfillment time accounts for about 40% of the total. In order to satisfy customer’s requirement, recently more distribution center starts to apply automated order picking system to deal with orders, such as the cigarette and medicine dispenser systems of distribution center.Among all kinds of automated order picking systems, the dispenser system are most suitable to pick goods with small batch diversification. The total order fulfillment time is an important index to evaluate dispenser system. Without obvious increase of system cost, the zone picking strategy effectively decrease the total order fulfillment time. Under this strategy, the dispenser system is partitioned into several zones, each of them is working simultaneously to pick the same order and transport the picked goods to buffer areas, then they are merged together at the right time. So, it’s the study on zone picking strategy of great importance to decrease the total order fulfillment time and logistics cost.However, the literature research in this field has several problems. First is most related research focuses in manual order picking system, little refers to automated picking system. And the construction of order fulfillment time is different in both systems. Second is most study is about single factor’s optimization, such as the stock keeping unit (SKU) assignment problem, instead of integrated research. Third is in the field of dispenser system, most research focus in the equipment selection, little refers to picking strategies and methods optimization.Based on this, this paper presents the integrated optimization problem of dispenser system under zone picking strategy. The objective is to minimize the total order fulfillment time. The content includes all main factors of affecting the total order fulfillment time:zone numbers, goods merging mode, SKU assignment, SKU split. Compared to the single factor research, the problem this paper study is more complicated.During the researching process, the main content and achievement are is as below:(1) The integrated optimization problem model is built, by expressing the working procedure of dispenser system under zone picking strategy with the help of the queuing system.This paper designed a queuing system to express the working procedure of dispenser system under zone picking strategy, get the structure of total order fulfillment time:goods picking time, dispenser suspending time, goods merging time; and get the main influencing factors:zone numbers, goods merging mode, SKU assignment, SKU split. Based on this, this paper built the integrated optimization problem model of dispenser system. The objective of this model is to minimize the total order fulfillment time, and the variables include all main influencing factors. The model belongs to the complicated integer programming problem.(2) In order to reduce the difficulty of solving the model, this paper transformed the objective to the optimal picking quantity distribution result of orders, and split the integrated optimization problem to two sub-problems. The solving thinking of discussing sub-problems respectively and then proposing the integrated solving method is adopted.By the linear relaxation and surrogate relaxation of constraint conditions of model, the lower bound function is got, as well as the optimal picking quantity distribution result:each order’s picking quantity is averagely distributed among zones. Taking the optimal result as the new objective, the solving difficulty can be reduced, and the solving methods are expanded. In terms of the variable characters, the integrated optimization problem is disassembled into SKU assignment and SKU split sub-problems which are discussed respectively, so that the comprehensive solution can be got in the final.Besides, by analyzing the monotonicity of the lower bound function and zone numbers, a smaller value range of zone numbers are got, which decreases the traverse space of results.(3) In solving SKU assignment sub-problem, the SKU clustering objective is proposed based on the optimal picking quantity distribution results of orders. And a complex clustering algorithm is designed to solve this sub-problem.This paper classifies the SKU assignment problem into clustering problem. It introduces the clustering objective based on scholar Jane, analyzes the faults and proposes clustering objective based on equivalent distribution of picking quantity, which is expressed by Manhattan distance of vector space. It also introduces the common hierarchical clustering algorithm, analyzes the faults and proposes complex clustering algorithm. This algorithm firstly gets a good initial solution by improved Largest Processing Time (LPT) static clustering algorithm, then optimizes the initial solution by improved K-means dynamic clustering algorithm. The real example analysis proves the superiority of clustering objective based on equivalent distribution of picking quantity, and the complex clustering algorithm.(4) In solving SKU split sub-problem, firstly the initial SKU split is proceeded by EIQ analysis, then the sub-SKU picking quantity redistribution problem is presented, which is solved by the proposed backtracking method.In the EIQ analysis of initial SKU split, all SKUs are sorted in descending sequence by picking their picking quantity of orders, and the split SKUs are selected by the proportion of their accumulated picking quantity. Then each one is split into two sub-SKUs and its picking quantity in each order is averagely distributed to them.In order to optimize the result of initial SKU split, this paper proposes the sub-SKU picking quantity redistribution problem. The mathematical model of the problem is built with the objective of optimal picking quantity distribution result of orders. The backtracking method is proposed to solve the problem. In solving process, the search space is reduced two times. The first time happens in organizing solution space, when the search space is reduced by analyzing characters of variables. The second time happens in searching solution space, when only the specified sub-SKUs in zone are visited. The real example analysis proves the effectiveness and superiority of proposed backtracking method. (5) Based on discussing results of two sub-problems, proposes the comprehensive solution to solve the integrated optimization problem of dispenser system.The comprehensive solution combines enumeration method and multiple heuristic algorithms, firstly proceeds initial SKU split and gets the value range of zone numbers, then proceeds the SKU assignment and split optimization in two merging modes and value range of zone numbers, at last proceeds the iterative optimization by judging the end condition. In the final, the best solution is selected from finite solutions, by comparing the total order fulfillment time. The real example analysis proves the effectiveness and superiority of proposed backtracking method.