1. 1 A PERFORMANCE ANALYSIS MODEL OF ORDER PICKING WAREHOUSE DESIGN for TRANSPORTERS Kainan University 黃 興 錫 (Heung Suk Hwang) Department of Business Management, Kainan University, Taiwan e-mail : hshwang@mail.knu.edu.tw 2005. 10. 29. 2005’ 倉儲系統與物料搬運研討會 逢甲大學工業工程與系統管理學系

2. 2 Contents 1. INTRODUCTION 2. ORDER PICKING WAREHOUSE SYSTEM 3. SIMULATION MODEL FOR ORDER PICKING WAREHOUSE SYSTEM ANALYIS 4. SUMMARY AND CONCLUSIONS ☞ Demonstrate a Hyundai W-Car Problem Kainan University

3. 3 1. Introduction ☞ Developed a performance evaluation model for order picking warehouse in supply center(SC) by reducing the travel distance of transporters ☞ We developed a two-step approach : - a mathematical model - a simulation model using AutoMod simulator ☞ Also we developed computer program and demonstrated the pro posed methods, ☞ Then we carryout numerical studies to compare the system performance improvement over the number of transporter in order picking warehouse. Kainan University

4. 4 ☞ The major functions of the freight terminal system are : 1) Pickup and arrival, 2) Auto-sensing the freight information, 3) Auto-sorting, and 4) Delivery. Kainan University

5. 5 Figure 1. Operating Cost Ratio of. General Warehouse Kainan University

6. 6 Figure 2. Two-Step Approach of Order Picking Warehouse System Kainan University

7. 7 2. Order Picking Warehouse System Figure 1. Freight Flow in Freight Terminal Kainan University

8. 8

9. 9 Figure 4. General Layout of Picking Warehouse Kainan University

10. 10 2.1 Probabilistic Picking in Warehouse -We assumed that an item found in the i th aisle has the probability, This is proportional to the average of the turn over rate of all items found in a aisle or the number or racks for an item. Notations used : M : number of freight of an item, : number of item stored in the ware house : probability of picking item m : number of item stored in the ware house = number of item 1 n : number of picking of order or : number of picking of each items per an order picking, Kainan University

11. 11 Prob ( picking n items in the warehouse where stored k items) = ( 1) where, means the probability of picking item in a picking. All the cases of picking of item k when a transporter repeats n times of picking with the probability, is given by, ( 2) Kainan University

12. 12 The expected number of picking by a transporter : (3) -By the assuming that the probability that a pick comes from a randomly selected zone is 1/p where p is number of transporters or number of zones. -Thus the expected number of picks in pf a transporter or zone during a particular time period can be approximated using the binomial distribution -The upper limit of picking UL(the number of items retrieved by a transporter) can be determined by using the normal distribution to approximate the binomial distribution. as following The binomial distribution B(n, p) can be approximate as N(np, np(1-p)) Kainan University

13. 13 Thus, = Kainan University

14. 14 2.2 Optimal Size of Unit Rack Notations : AW : width of unit aisle(ft) AL : length of unit aisle(ft) LW : width of unit rack(ft) LL : length of unit aisle(ft) LH : width of unit aisle(ft) WM : number of aisle R : required through put( unit/hr or day) C : total length of rack(ft) TA : available space of system, VHV: horizontal speed of transporter(ft/hr) VVV : vertical speed of transporter(ft/hr) T : scale parameter of unit rack T: LL/VHV= LH/VVV

15. 15 We formulate this problem as following : Min. WM St 2·LW·LH·WM = C (1) (AW + AL) ·((LW + LL) · WM + 1) = TA where, TU is given by following Eq. (2) (2) By Eq. 1 and 2, (3) and by Eq, 2 and 3, where, Kainan University

16. 16 The algorithm to find WM is given by following 5 steps : step 1 : step 2 : if, go to step -4 Otherwise, go to step-3 step-3 :, go to step-2 step-4 : stop, WM = minimum number of aisle, Kainan University

17. 17 We could find optimal size of aisle and the system performance as following : - number of aisle : WM - height of rack : - length of rack : - expected travel time(min) : - system utilization rate(%): utilization rate Kainan University

18. 18 Numerical example to find WM and system utilization rate : S =, R = 294 picks n = 5 picks/trip, p = 0.25 Min/pick hv = 150 m/min, vv = 30 m/min k = 1.25 min/trip Number of aisle = 3 Height of rack = 4.1m Length of rack = 20.6m Expected Travel Time = 2.83 System Performance = 92.52% Kainan University

19. 19 2.3 Travel Time Analysis Assumptions : - one picker in each zone, - each type of item in stored in one location, - sufficient supply of items in at each location, - items are picked along one side of an aisle at a time, - there are two sides to each aisle, - transporters travels through all the aisles, - items are randomly assigned to storage location within a facility, The total processing time : 1) The picking time is given by following equation : where, TN : number of transporter, : time for a transporter to pickup an item : number of all the items picked up by transporter, Kainan University

20. 20 2) Traveling time : 3) Stop time for picking : Total process time per travel of transporter) = (picking time) + (traveling time) + (Stop time for each SHU Kainan University

21. 21 4) Determining of the optimal number of transporters - dependent on total process time, number of aisle, its length and number of required amount to be retrieved. - It is very complicated problem Thus, we used a simulation method based on AutoMod simulator. Kainan University

22. 22 3.Simulation Model for Order Picking Warehouse System Analysis - We modeled the same order picking warehouse system using AutoMod simulator. -We have run the simulation for 1000hours with following design parameters : Number of aisle = 3, height of rack = 4.1m, length of rack = 20.6m, C = 539 m 2, R = 294 picks, n = 5 picks/trip, p = 0.25 Min/pick, vhv = 150 m/min, vvv = 30 m/min, k = 1.25 min/trip Kainan University

23. 23 Case 1 : Number Transporter = 1 Kainan University

24. 24 Case 2 : Number Transporter = 2 Kainan University

25. 25 Alter. of Trans DeliveringRetrieving Parking Per. of Total time Trips Made Averag e time sec/trip Per. of total time Trips made Av. time /trip Per. of Total time 150.0%34.6552.250%34.6552.20 253.5%31.3461.846.5%31.3453.40 360.9%26.2783.439.1%26.2753.40 466.4%19.61121.833.6%19.6161.80 528.1%28.82350.471.9%28.84893.40 634.7%5.852139.665.3%5.8840080 Table 1. Transporter Performance

26. 26 Table 2. Material handling flows(Amount of throughput) Kainan University Alter. of Transporter (No. of Transporter) Total ThroughputWarehouse Utilization (%) 1138.355.2 2250.359 3311.861.3 4311.161.2 557.152.4 613.750.1

27. 27 Figure 4. Total Throughput per Alternative of Transporter Kainan University

28. 28 Sample problem of order picking systems - The picking utilization obtained from mathematical model is a little greater than that from simulation (92.52 > 61.3) - the optimal number of transporter : 3 - total throughput : 311.8. - There should be a minimum two line spaces between tables and - text. Kainan University

29. 29 4. Conclusion - In this paper, we have presented an analysis for order picking systems by two-step approaches in this paper, mathematical and simulation model using AutoMod. - An algorithm for end-of-aisle is developed. - We have developed a computer program for the analytical method. - Computational results are presented on the relative performance of each type of methods. - These approaches have been compared with each other in terms of utilization of pickers, total throughput and handling time. Kainan University

30. 30 Kainan University, Taiwan Prof. Heung-Suk Hwnag Thank You Kainan University