Prepared by Ece İndirkaş

1. Order Picking in an automatic warehouse: Solving online aymmetric TSPs Order picking in an automatic warehouse: Solving online asymmetric TSPs Prepared by Ece İndirkaş Prepared by Ece İndirkaş The article written by Norbert Ascheuer, Martin GroÈtschel, Atef Abdel-Aziz Abdel-Hamid

2. Outline • Automatic storage system in Siemens Nixdorf • Informastionssyteme (SNI). • Sequencing Problem; old and new method. • Related examples. • Modeling; online aspects. • Simulation Model; normal load and heavy load • conditions. • Experiments; static system and dynamic system. • Comparison of heuristics.

3. ATSP; Asymmetric Traveling Salesman Problem “a problem in discrete or combinatorial optimization. It is a prominent illustration of a class of problems in computational complexity theory which are classified as NP-hard.” If a salesman starts at point A, and if the distances between every pair of points are known, what is the shortest route which visits all points and returns to point A? Fig 1. Wikipedia The case where the distance from A to B is not equal to the distance from B to A is called asymmetric TSP.

4. Siemens Nixdorf Informastionssyteme (SNI) • Assemble • or test: • Flexible Manufacturing System: some amount of flexibility that allows the system to • react in the case of changes, whether predicted or unpredicted. bottlenecks in material flow, transportation tasks pile up, production delay, required parts not supplied. As volume

5. Automatic Storage System Warehouses with two-sided aisles and computer controlled stacker crane. Each warehouse has  upper part for storage  lower part for buffer Fig2. Ascheuer,N.,et al. (1999 pg. .502)

6. Single stacker crane traveling • between the two ends of the • aisle. • One container at a time both and • Transporting materials within • warehouse for such • purposes such as... Fig3. Ascheuer,N.,et al. (1999 pg. 503). Too many unloaded moves, long waiting times  Develop an optimization tool to minimize of unloaded travel time  “sequencing problem” 

7. Sequencing problem Currently... Pool of transportation tasks (orders from now on) If stacker crane is not idle • Details... • 6 priority classes in total. • on the average 10-15 tasks, max up to 50 • tasks under heavy load conditions. Priority rule  Long unloaded moves... First In First Out (FIFO)

8. Sequencing problem cont’d New proposition... Minimize total crane utilization time by scheduling currently available orders whenever an order is generated. Total loaded time Total unloaded time Total crane utilization time Transfer time

9. Related examples • Which pick-positions (on one tour) are visited as total time • is smallest with an only horizontal move. Special case of • TSP, solvable in polynomial time. • Single aisled, double sided AS/RS. Both horizontal and • vertical moves. Depends on the capacity of crane. Modeled • as a TSP. • Seven parallel aisles, crossovers and three stacker crane. • “Conflict-free” routing by minimizing idle movements and • waiting times. Modeled as decision tree with weight of idle • seconds shortest path.

10. Modeling Cij: cost of executing task j after task i. Cost = time traveled unloaded. Fig4. Ascheuer,N.,et al. (1999 pg. 505). Possibility to execute task j after task i. Nodes representing orders in pool. Current task or current position of stacker crane. • Asymmetric traveling salesman problem

11. Online Aspects New orders are coming!! Online  dynamic changes of the system New orders are optimized after all orders of the current pool are executed. Ignore: Update the sequence each time a new task is generated. Replan:

12. Online aspects cont’d Ignore: Replan: Shorter than the previous one (c). Fig 5. Ascheuer,N.,et al. (1999 pg. 506.)

13. Online aspects cont’d • Unpredictable arrival times of containers. • Unpredictable completion time of • manual assembly. • Decisions made without any knowledge • of future orders. ... So what type of mathematical models for online problems???

14. Simulation Model Online behaviours of different heuristics Fig 6. Ascheuer,N.,et al. (1999 pg. 508).

15. Simulation Model Cont’d 5 days recorded Fig 7. Ascheuer,N.,et al. (1999 pg. 508). # of tasks performed in a day Average task lenght produced by simulation model. Average time needed

16. Fit-in farins Greedy + 3 opt listins Greedy + 2opt Heuristics greedy randins optimal bestins shuffle random priority

17. Normal Load Conditions Priority rule vs. Optimal rule Fig 8. Ascheuer,N.,et al. (1999 pg. 511). Improvement bw 6 and 8% No large improvement without major breakdowns and large volume of production.

18. Heavy Load Conditions Artificial breakdowns  tasks pile up  modify input data Experiment 1: Static system Fig 9. Ascheuer,N.,et al. (1999 pg. 511). Improvement between30-45%

19. Heavy Load Conditions Cont’d Experiment 2: Dynamic system Fig 10. Ascheuer,N.,et al. (1999 pg. 512). Improvement between 25-45% Not as good as experiment 1.

20. Comparison of heuristics • Optimal seems the • best but not always • give the best result! • Fit-in is fastest but • Gives the worst • Results. • No difference bw • Priority and random. Fig 11. Ascheuer,N.,et al. (1999 pg. 512). Average unloaded travel time in seconds.

21. Conclusion 3 phases randins optimal Fit-in

23. Resources • Wikipedia, available at http://en.wikipedia.org/wiki/Travelling_salesman_problem • Microsoft Office Online Clip Art, • available at http://office.microsoft.com/en-us/clipart/default.aspx