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Impact of Cross Aisles in a Rectangular Warehouse: A Computational Study

Impact of Cross Aisles in a Rectangular Warehouse: A Computational Study. Gürdal Ertek Sabancı University, Istanbul, Turkey Bilge Küçük İncel Roketsan, Ankara, Turkey. Preview. Motivation Strategies for Eliminating Traveling Costs Definitions Earlier work Research Questions Model

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Impact of Cross Aisles in a Rectangular Warehouse: A Computational Study

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  1. Impact of Cross Aisles in a Rectangular Warehouse: A Computational Study Gürdal Ertek Sabancı University, Istanbul, Turkey Bilge Küçük İncel Roketsan, Ankara, Turkey

  2. Preview • Motivation • Strategies for Eliminating Traveling Costs • Definitions • Earlier work • Research Questions • Model • Algorithms • Computational Results • Insights • Conclusions • Future Work

  3. Motivation

  4. Operational Cost Receiving Shipping 10% 20% Storage 15% 55% Order Picking

  5. Order Picking Time Documentation and Other activities 15% Extracting 15% 50% Traveling 20% Searching

  6. Strategies for Eliminating Traveling Costs* • Pick from storage • Goal: Achieve forward picking rates from a reserve storage area • Ford service parts distribution centers • Contents of incoming cages are distributed to tote pans • Conveyed to one of 54 carousels, which act as reserve storage area (no replenishment in the system) • Three carousels / operator • WMS interleaves the putaway and picking tasks, which are light-directed • Need for a sophisticated logistics information system • Random storage • Intelligent slotting • Activity balancing • Dynamic wave planning * Frazelle, E. H. (2001). World-Class Warehousing and Material Handling, McGraw-Hill.

  7. Strategies for Eliminating Traveling Costs* • Pick task simplification • Strategy: Eliminate and combine order picking tasks when possible * Frazelle, E. H. (2001). World-Class Warehousing and Material Handling, McGraw-Hill.

  8. Strategies for Eliminating Traveling Costs* • Pick task simplification • When work elements cannot be eliminated, they can be combined to improve order picking productivity. • Traveling & Extracting Items • Stock-to-picker systems (carousel, miniload, etc.) keep the order pickers extracting while a mechanical device travels, bringing pick locations to order picker • Traveling & Documenting • Person-aboard machine transports the order picker, and the order picker is free to document picking transactions, sort material or pack material while machine is moving * Frazelle, E. H. (2001). World-Class Warehousing and Material Handling, McGraw-Hill.

  9. Strategies for Eliminating Traveling Costs* • Order batching • Especially effective for small (<5 lines) orders. • Advantage: Reduction in travel time per line item • Disadvantages: • Time required to sort line items into customer orders • Potential for picking errors • Sorting • Seperate containers to sort on the carts • Combine orders and then do downstream sortation * Frazelle, E. H. (2001). World-Class Warehousing and Material Handling, McGraw-Hill.

  10. Strategies for Eliminating Traveling Costs* • Zone picking • A portion of an aisle, multiple aisles, or machines assigned to an operator for picking. • The operator is dedicated to a zone and no other operator works in that zone. • Advantages: • Reduced travel time • Minimal congestion • Product-location familiarity • Operator-zone accountability • Minimizing excessive socializing • Disadvantage: • Sorting is required * Frazelle, E. H. (2001). World-Class Warehousing and Material Handling, McGraw-Hill.

  11. Strategies for EliminatingTraveling Costs* • Slotting Optimization • For each item, we determine: • Appropriate storage mode • Appropriate allocation of space in its appropriate storage mode • Appropriate storage location in its apropriate storage mode • <15% of items in a typical warehouse are slotted correctly. • Pick Sequencing (Order Picker Routing) • Sequence pick location visits to reduce travel time. • Building a Warehouse with Cross Aisles * Frazelle, E. H. (2001). World-Class Warehousing and Material Handling, McGraw-Hill.

  12. Definitions • “Rectangular warehouse” • ...or... independent rectangular zones within a warehouse • Picker-to-part system • Storage blocks • Aisles between storage blocks • Cross aisles perpendicular to the main aisles

  13. Case 0: No cross aisles (N=0) Main Aisle 4 Main Aisle 5 Main Aisle 3 Main Aisle 1 Main Aisle 2 Finish Start

  14. When a cross aisle is added... Main Aisle 4 Main Aisle 5 Main Aisle 3 Main Aisle 1 Main Aisle 2 Cross aisle N Finish Start

  15. Cross Aisles: Pros and Cons • Cross aisles can bring significant savings in order picking costs, specifically due to decreased travel times. • Having too many cross aisles results in: • Lost floorspace with negligible marginal travel time benefits. • After a certain point, the additional space occupied by cross aisles even causes the travel times to increase, since the warehouse becomes larger.

  16. Case 1: Equally spaced cross-aisles B W Cross Aisle 0 Notation L M: no of main storage blocks A Cross Aisle 1 1) - N: no of interior cross aisles Main Aisle M Main Aisle 1 Main Aisle 2 Main Aisle 3 T: length of pick face on eachmain aisle Main Aisle (M L: length of each storage block L = T / (N+1) Cross Aisle N A: width of each cross aisle Cross Aisle N+1 B: width of each main aisle W: width of each storage block Start Finish

  17. Earlier Work: V&P • Vaughan, T.S. and Petersen, C.G. (1999) “The effect of warehouse cross-aisles on order picking efficiency”, International Journal of Production Research, vol. 37, no.4, p881-897 • Optimal aisle-by-aisle tour to pick items for Case 1 • Conditions under which cross aisles generate the greatest benefit

  18. Earlier Work: R&dK • Roodbergen, K.J. and De Koster, R. (2001) “Routing methods for warehouses with multiple cross aisles”, International Journal of Production Research, vol. 39, no.9, p1865-1883 • Routing algorithms for Case 1 • Two new heuristic algorithms developed • Comparison of six heuristics (four from literature, including aisle-by-aisle)

  19. Case 2: Unequally Spaced Cross Aisles NEW! Cross Aisle 0 L1 1 - M 2 M 3 A Cross Aisle 1 L2 Cross Aisle N LN+1 Cross Aisle N+1 Start Finish

  20. Research Questions • Should the cross aisles be equally spaced or not (Case 1 vs. Case 2)? In other words... Should the storage blocks have equal length or variable lengths? • How much savings do cross aisles bring? • How many cross aisles should there “ideally” be? NEW! NEW!

  21. Assumptions • Slower moving items (B&C items) • Uniformly distributed pick locations • Aisle-by-aisle picking policy • Order picker starts at the left bottom corner and ends at the right bottom corner.

  22. 1 Xm- B1m(i,j) L1 L1 i Entrance cross aisle 2 L2 L2 Cm(i,j) j 3 L3 B2m(i,j) L3 4 Xm+ L4 L4

  23. V&P Model • Xm(t): The location of an item t in main aisle m, 0 Xm(t)T, m = 1, 2, … , M,t = 1, 2, … , Km (undefined if Km = 0) • Xm+ : The location of the item with greatest (south-most) location in the main aisle m (undefined if Km = 0), Xm+ = maxt{Xm(t)} • Xm-: The location of the item with smallest (north-most) location in the main aisle m (undefined if Km = 0), Xm- = mint{Xm(t)}

  24. V&P Model • Cm(i,j) : The total vertical travel distance required to pick all the items in main aisle m, if main aisle m is entered at cross aisle i, and exited to main aisle m-1 at cross aisle j • Blockof(Xm-) : The index of storage block Li in main aisle m where Xm- is located, Li = 1, 2, … , N+1 • Blockof(Xm+) : The index of storage block Li in main aisle m where Xm+ is located, Li = 1, 2, … , N+1 NEW!

  25. Costs at Each Stage(V&P Modified)

  26. Dynamic Programming Equations for Each Stage (V&P) The desired shortest path-picking route is determined by evaluating:

  27. Algorithms NEW!  = {1,...., N+1}, O = {1,...., } GRID_SEARCH_ALGORITHM (warehouse, orders, noOfGrids) G = T/noOfGrids for eachgridsForL, /* s.t. gridsForL[i] noOfGrids, i */ sumOfGrids = gridsForL[i] if( sumOfGrids = = noOfGrids && ARRAY_CONTAINS_NOZERO(gridsForL)) L[i] = gridsForL[i] * G, i  warehouse.setL(L) orders[o].setWarehouse(warehouse), o  O simulationStatistics = CALCULATE_SIMULATION_STATISTICS(orders) travelDistance = simulationStatistics.getAverage() if (travelDistance < bestTravelDistance) bestL = L bestTravelDistance = travelDistance returnbestL

  28. CALCULATE_SIMULATION_STATISTICS (orders)travelDistance[o] = getOptimalTravelDistance( orders[o] ), o  O return statistics for travelDistance data

  29. N = 1 • = {1,2} T = 200 • noOfGrids = 8 • G = 200/8 = 25 1 1 G gridsForL[1] = 2 L[1] = 50 2 2 3 3 4 4 gridsForL[2] = 6 L[2] = 150 T 5 5 6 6 The performances of all feasible L vectors are evaluated and compared. The bestL is selected. 7 7 8 8

  30. Algorithms REFINED_GRID_SEARCH_ALGORITHM(warehouse, orders, noOfGrids, resolution)

  31. At the next step, the following L vectors are generated and compared. The bestL is selected. Then the algorithm advances to a finer resolution: 1 G 2 3 G 4 5 6 7 8

  32. NEW! Experimental Settings 396 scenarios

  33. 1 Computational Results - 1 • Should the cross aisles be equally spaced or not (Case 1 vs. Case 2)? In other words... Should the storage blocks have equal length or variable lengths? • How much savings do cross aisles bring? • How many cross aisles should there “ideally” be?

  34. 1 Computational Results – 1.1Savings in Case 2 against Case 1 % Space Saving % Travel Time Saving

  35. Color = Pick Density

  36. c b a d Color = T

  37. Color = M

  38. 1 Computational Results – 1.2Savings in Case 2 against Case 1 M T

  39. M a b T Color = % Travel Time Saving

  40. M T Color = % Space Saving

  41. 1 Insights - 1 • Should the cross aisles be equally spaced or not (Case 1 vs. Case 2)? • Having unequally spaced cross aisles does not bring significant savings in travel time, especially for larger warehouses. • However, it brings the most significant savings in warehouse space for larger warehouses. So if there is a priority of saving warehouse space using approximately the same labor, then Case 2 can be preferred. • How much savings do cross aisles bring? • How many cross aisles should there “ideally” be?

  42. 2 Computational Results - 2 • Should the cross aisles be equally spaced or not (Case 1 vs. Case 2)? • How much savings do cross aisles bring? • How many cross aisles should there “ideally” be?

  43. 2 Computational Results – 2% Travel Time Savings in Case 1 Pick Density T M

  44. Pick Density T M Color = % Savings in Travel Time, N=1

  45. Pick Density T M Color = % Savings in Travel Time, N=5

  46. 2 Insights - 2 • Should the cross aisles be equally spaced or not (Case 1 vs. Case 2)? • How much savings do cross aisles bring? • Depends on T, M and Pick Density. • Savings up to 36%. • How many cross aisles should there “ideally” be?

  47. 2 Computational Results - 3 • Should the cross aisles be equally spaced or not (Case 1 vs. Case 2)? • How much savings do cross aisles bring? • How many cross aisles should there “ideally” be?

  48. 3 Computational Results – 3.1“Best” No of Cross Aisles in Case 1 Pick Density T M

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