Decision Support For Packing In Warehouses

1. Decision Support For Packing In Warehouses Gürdal Ertek &Kemal Kılıç

2. Introduction Packing problems • Loading of a set of items (objects) into a set of boxes (containers) • Optimize a performancecriterion under various constraints. • Becoming more popular • barcode and RFID technologies • investments in IT infrastructures • companies now have accessto the necessary data for improving packingprocesses.

3. Introduction Our Study • Beam search algorithm to solve a real world packing problem • 3D-MBSBPP (Multiple Bin Sized Bin PackingProblem) • not analyzed in literaturebefore • comparison of cost and computationaltime to • a greedy algorithm • a tree search enumerationalgorithm

4. Motivation • A major automobile manufacturer located in Bursa, Turkey • Urgent order packaging • Everyday... • >80 service dealers submit their urgent orders. • orders pooled in an information system until3:00pm. • workers start picking the requested items and packing them into adequatelysized boxes. • by 5:00 p.m., trucks of a 3rdparty logistics firm collect the boxesto deliver them to their destinations.

5. Motivation • Selection of appropriate boxes • 3:00pm: two experienced foremen spend ~20 minutes on a PC. • decide on and record the choice of boxes for each order. • goal: minimize the posterior extra work of reallocating the items betweenboxes • Goal of Warehouse Managers • developmentand implementation of a decision support system • help the foremenin their decision making toeliminate item reallocation

6. Decision Support System • Metaheuristicalgorithm to make the decisions • how many boxes are used of each box type • how each item is placed in its box • Objective: • minimization of thetotal cost of the boxes used • Operatein real-time • Our Study • proposal of three alternative algorithmsthat can serve as the solution engine • their comparison with respect to solution and running time performance

7. Problem Definition • A set of rectangular objects (items) each with height , width , and depth • Packed into a set of larger rectangular objects (boxes) each with height , width , and depth and cost

8. Problem Definition • Objective: • Minimize the total cost of boxes that are used • Allocating all theitems into boxes without overlap • Decisions • types of boxes to be used • number of boxes of each type • boxes that each item will go into • position of each item in each box • Assumptions • Only orthogonal arrangements ofitems • Allow items to be rotated around all three axis

9. Theoretical Contributions • Presenting the 3D-MBSBPP problem within a real world context • typology by Wäscher et al. (2006) • Developing and implementing solution algorithms for the problem • Presenting computational results to compare the algorithms

10. Practical Contributions • Reducing cost of boxes • Eliminating posterior reallocation of items into boxes, i.e. labor savings • Eliminating dependency on experienced foremen • Pilot study for the much larger problem of packing regular orders • Enable the computation of “best” box types and dimensions based on historical data • reduce box costs further • reduce the number of types of boxes • save warehouse space and reduce inventory costs

11. Relevant Literature • Cutting and packing problems • Wide range of applications in industry • Supply chain logistics • cutting metal sheets, loading containers with boxes • Computer science • memory allocation of processors • Finance • capital budgeting • NP-hard problems • Diversity of real world problems • Even smallnuances in the objective function or the packing/cutting constraints result innew problem structures

12. Relevant Literature • Over a thousand papers published on related problems • Dyckhoff and Finke (1992) • review of 308 papers prior to 1992 • Wäscher et al. (2006) • improved typology • review of 413 papers between 1994-2004 • Related Studies • Ivancic et al. (1989) • assuming few number of possible items • few preassigned patterns • Brunetta and Grégoire (2005) • only 15 items • packing at a biscuit factory • Martello et al. (2000)

13. Methodology • Greedy Algorithm (G) • Filtered Beam Search Algorithm (BS) • Tree Search based implicit enumeration algorithm (TS) (depth-first)

14. Greedy Algorithm (G) • While there are objects that are not packed into a box... • A single sized bin container loading problem (SSBCLP) is solved independently foreach different box size (Pisinger), and the best box is selected according to a performanceindex • Objects that are assigned to a box aredeleted from the waiting list. Filling ratio Cost per volume of boxj

15. Beam Search Algorithm (BS) • At each level of the branch & bound search tree • A single sized bin container loading problem (SSBCLP) is solved independently foreach different box size (Pisinger), and the best fsolutions (box selections)arefiltered according to a local evaluation function • From among these f boxes, best b are selected according to a global evaluation function

16. Beam Search Algorithm (BS) f = 3 b = 2 Greedy Greedy Greedy

17. Beam Search Algorithm (BS) • Global Evalution Function: • The total cost of the boxes of the solutionthat is obtained by applying the greedy algorithm to the non-pruned nodes

18. Experimental Results • Algorithms coded with C • MS Visual Studio .NET environment • Experiments run on a PC • Intel Centrino1700 Mhz processor and 512 MB of RAM • Subroutine of our program • C implementation of Prof. David Pisinger's algorithm for container loading(CLA) • Item sizes generated randomly within given bounds • Box costs:

19. =================================== ... AND THE FINAL SOLUTION IS ..... =================================== ************ Order with seed no 2 and 40 items ************** no dx dy dz x y z binType binNo isAlloc? 1 19 39 23 30 0 38 0 0 1 2 28 36 32 0 0 34 0 1 1 3 38 26 21 0 32 35 3 0 1 4 15 15 23 30 32 13 0 0 1 5 30 11 31 0 39 0 0 1 1 6 18 10 32 30 39 0 0 1 1 7 30 35 24 0 0 76 0 0 1 8 22 35 32 28 0 34 0 1 1 9 34 11 22 0 38 76 0 0 1 10 15 37 25 0 0 54 4 0 1 ... ... ... ... 36 40 31 35 0 0 0 3 0 1 37 10 22 23 36 25 66 0 1 1 38 20 25 32 0 0 66 0 1 1 39 18 29 35 0 31 0 3 0 1 40 40 11 37 0 39 38 0 0 1 Cost of this allocation for the order is: 8.83 The 4 bins allocated for the order are of the following types 0 3 0 4 **********************************************************

21. Experimental Results • 10 orders for each scenario • Execution terminated after 5min. 15-30 cm 20-35 cm 10-25 cm

22. Thank You!