Shortening Picking Distance by using Rank-Order Clustering and Genetic Algorithm for Distribution Centers

Transcription

1 Shortening Picking Distance by using Rank-Order Clustering and Genetic Algorithm for Distribution Centers Rong-Chang Chen, Yi-Ru Liao, Ting-Yao Lin, Chia-Hsin Chuang, Department of Distribution Management, National Taichung University of Science and Technology, Taiwan. Abstract To encourage shoppers to buy more, not a few companies are providing express delivery service. The shoppers can order goods they want online and the company delivers them directly to a designated destination within very short periods of time. In this business model, a crucial factor influencing its success is picking time. To reduce the picking time, the picking distance relating to travel should be shortened. The aim of this study is to employ a two-stage mechanism to help managers to shorten the picking time. At the first stage, customer orders are clustered by a rank-order clustering (ROC) scheme. At the second stage, a genetic algorithm (GA) is used to minimize the total travel distance. Experimental results show that the proposed approach is feasible and very potential in dealing with the present picking distance shortening problem. Key Words: Picking, ROC, genetic algorithm, distribution center, route planning JEL Classification: C 61 1

2 1. Introduction To make shoppers buy more, a number of companies are making shopping further convenient and providing express delivery service [1-2]. The shoppers can order goods they want online and the company delivers them rapidly to the designated destinations. In this business model, a crucial process to its success is the picking operation. More than half time of picking is likely to relate to travel, as depicted in the order batching problem in the warehouse system [3]. If one can reduce the total travel distance, the picking time can be significantly reduced. An effective approach is thus greatly needed for distribution centers (DCs). In this paper, we present an effective approach to solve the picking problem for DCs. A two-stage approach is employed. At the first stage, customer orders are clustered and batched by a rank-order clustering (ROC) scheme [4]; while at the second stage, the picking route is optimized to shorten the travel distance. The remainder of this paper is structured as follows. The problem is briefly described in Section 2. The proposed approach including the introduction of encoding of a chromosome and genetic operations is illustrated in Section 3. Then results and discussion are presented in Section 4. As a final point, conclusions are drawn and some suggestions are given for further studies in the future in Section The Problem Let M= {1, 2,, m} be a set of customer orders and let N = {1, 2,, n} be a set of picking locations in a DC, where m is the total number of customer orders and n is the total number of picking locations in a time period. To simplify the problem, the following main assumptions are made: (1) All the positions of items are known and fixed. (2) The positions of the entrance and exit of the packing area are known and fixed. The worker responsible for picking start picking from the exit of the packing area and return from the entrance. (3) The distances between two different locations of items are fixed. After the main assumptions were made, the problem to be deal with can be described as follows. To construct batches, customer orders need to be aggregated first. The order-location matrix after aggregation and before clustering is illustrated in Fig. 1. A 1 in a cell means that the picking location should be visited to pick the items requested by an order. Otherwise, a 0 is designated. 2

3 Proceedings of the Third European Academic Research Conference on Global Business, Economics, Figure 1: An Order-Location Matrix after Order Aggregation and before Clustering Location n Order m The orders can be clustered into some clusters according to the requirement of the management. The order-location matrix after clustering is illustrated in Fig. 2. Figure 2: An Order-Location Matrix after Clustering Location n 6 4 Order m The route optimization problem can be formulated as follows. Objective function: Constraints: n n n n Minimize D total = D ij p ij i=0 j=0 p ij = n b,r + 1, i j, i = 0,1, n; j = 0,1, n; r = 1,2,3,, m b (2) i=0 j=0 (1) 3

4 p ij {0,1}, i j, i = 0,1, n; j = 0,1, n (3) Equation (1) states that the total picking travel distance of a batch is minimized, where both i = 0 and j = 0 stand for the origin (the packing area). Equation (2) states that the number of total paths traveled is equal to n b,r + 1. The value of decision variable p ij should be either 1 or 0, as indicated in Eq. (3). Note that the distance D ij between two locations of item is known. It is the actual distance between two picking points. Racks may exist between two item locations. Therefore, the actual travel distance may be different from the line distance between two locations. As the number of picking locations becomes large, finding the shortest travel distance grows into a complex problem. The problem to be dealt with is like a travelling salesman problem (TSP) [5-7], which is NP-hard. Heuristic approximate algorithms which can provide feasible solutions within a short period of run time, therefore, might be more appropriate than exact ones. GA [8-16] is one of the most effective approximate algorithms to solve the TSP problem. Consequently, in this paper GA is employed to find solutions. 3. The Approach The orders are clustered by using a ROC scheme [4]. Given a binary order-locations n- by-m matrix b ij, Rank Order Clustering is an algorithm characterized by the following steps [4]: m (1) For each row i compute the number j=1 b ij 2 m j (2) Order rows according to descending numbers which are computed previously n (3) For each column j compute the number i=1 b ij 2 n i (4) Order columns according to descending numbers which are computed previously (5) If on steps 2 and 4 no reordering happened, go to step 6. Otherwise, go to step 1 (6) Stop The encoding for route optimization is illustrated in Fig. 3. Since there are n picking locations, the number of genes is equal to n. Each gene is given an integer which stands for the picking location. For instance, the value of the first genes is 10, means the 1 st location to pick items is the 10 th location. Figure 3: Representation of A Chromosome for Route Optimization. Priority Location n 10 5 n

5 4. Results and Discussion Experiments were carried out by running the GA program to evaluate the performance of the proposed approach. To validate the GA program, the exhaustion method (EM) which can obtain the optimal solutions was also run and its results on some small cases were compared with those from GA. The results from the tests show that the GA can obtain the same optimal solutions as those from EM. To investigate the performance of GA on solving the problem, a base case was constructed. The layout of the DC is shown in Fig. 4. Totally, there are 50 picking locations of items. A picker starts picking from the exit of the packing area. After completion of the picking operation, the picker is back to the packing area. Figure 4: Illustration of Picking Locations for the DC Figure 5 and figure 6 display two typical results. In these figures, the picking route can be effortlessly observed. Pickers in the DC can easily pick items in the DC even they are new in this company. Furthermore, the picking time can be significantly reduced since a shortest route has been suggested. Figure 5. A Typical Output for 14 Picking Locations. 5. Conclusions and Recommendations Figure 6. A Typical Output for 21 Picking Locations. To make more profits, some companies implement on-demand delivery service, which provides consumers quick online ordering and express delivery. However, this model did not work very well for some companies since the operation of order fulfillment is inefficient, 5

6 which is mainly caused by much picking time relating to travel. Picking orders without a suitable approach in a DC can be quite cumbersome in terms of efficiency and indirect cost. In this paper we have employed a genetic algorithm (GA) as an aid to help decide a best picking route with the shortest travel distance. This paper proposes a systematic approach to shorten the picking distances for DCs. A two-stage mechanism is employed. At the first stage, a ranked order clustering (ROC) is employed to cluster the customer orders into batches. At the second stage, a GA is used to minimize the total travel distance of picking. Experimental results show that the proposed approach is highly feasible and very potential in dealing with the present problem. References Battarra M, Erdogan G, Laporte G, Vigo D. The Travelling Salesman Problem with Pickups, Deliveries and Handling Costs. Transportation Science, Vol. 44, Issue 3, Bellmore M, Nemhauser GL. The Travelling Salesman Problem: A Survey, Operations Research, Vol. 16, No. 3, pp , Chen RC, Huang MJ, Chung RG, Hsu CJ. Allocation of Short-Term Jobs to Unemployed Citizens amid the Global Economic Downturn Using Genetic Algorithm, Expert Systems with Applications, Vol.38, pp , Chen RC. Grouping Optimization Based on Social Relationships, Mathematical Problems in Engineering, Vol. 2012, Article ID , pp Coley DA. An Introduction to Genetic Algorithms for Scientists and Engineers. Singapore: World Scientific Press; Flood MM. The Travelling Salesman Problem, Operations Research, Vol. 4, pp.61-75, Gangopadhyay A. Managing Business with Electronic Commerce: Issues and Trends, Idea Group Publishing, Gen M, Cheng R. Genetic Algorithms and Engineering Design. New York: Wiley; Gen M, Cheng R. Genetic Algorithms and Engineering Optimization. New York: John Wiley & Sons; Goldberg DE. Genetic Algorithm in Search, Optimization, and Machine Learning. Massachusetts: Addison Wesley; Holland JH, Adaptation in Natural and Artificial Systems, Ann Arbor: University of Michigan Press; King, J. R., Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm, International Journal of Production Research, Vol Mitchell M. An introduction to Genetic Algorithms, MIT Press, Cambridge, Oncan, T. A Genetic Algorithm for the Order Batching Problem in Low-Level Picker-to-Part Warehouse Systems, Proceedings of the International MultiConference of Engineers and Computer Scientists, Vol. I, pp , Turban E, King D, Lee J, Liang TP, Turban D. Electronic Commerce: A Managerial and Social Networks Perspective, 7th Edition, Pearson Edition, Winter G, Periaux J, Galan M. Genetic Algorithms in Engineering and Computer Science. New York: Wiley;