Mathematical Aspects of Logistics

Transcription

1 Mathematical Aspects of Logistics Berlin :00 10:30 Institut für Mathematik, Technische Universität Berlin (TUB) DFG-Forschungszentrum Mathematik für Schlüsseltechnologien (MATHEON) Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

2 2 Today s program

3 3 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

4 4 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

5 5 Logistics A few pictures say more than thousand words.

6 6 Global logistics

7 7

8 8 Logistics What is logistics?

9 9 Logistics: definitions According to the Council of Logistics Management, a nonprofit organization of business personnel, logistics management is the process of planning, implementing, and controlling the efficient, effective flow and storage of goods, services, and related information from point of origin to point of consumption for the purpose of conforming to customer requirements.

10 10 A Typical Logistics Book

11 11 Buzz Words RRP Resource Requirements Planning DRP Distribution Requirements Planning MRP Materials Requirement Planning ERP Enterprise Requirement Planning JIT Just-in-Time CIM Computer Integrated Manufacturing

12 12 New Words Supply Chain Management

13 13 What is supply chain management Simchi-Levi, Kaminsky, Simchi-Levi (2004) Recall: logistics management is the process of planning, implementing, and controlling the efficient, effective flow and storage of goods, services, and related information from point of origin to point of consumption for the purpose of conforming to customer requirements.

14 14 Logistics Network

15 15 The Wal-Mart rise from Simchi-Levi, Kaminsky, Simchi-Levi (2004)

16 16 Supply Chain Management The strategic level deals with decisions that have a long-lasting effect on the firm. This includes decisions regarding the number, location, and capacity of warehouses and manufacturing plants, and the flow of material through the logistics network. The tactical level includes decisions which are typically updated anyhere between once every quarter and once every year. These include purchasing and production decisions, inventory policies, and transportation strategies including the frequency with which customers are visited. The operational level refers to day-to-day decisions such as scheduling, lead time quotations, routing, and truck loading. Hax and Candea (1984), see Bramel, Simchi-Levi (1997) and Simchi-Levi, Kaminsky, Simchi-Levi (2004)

17 17 History

18 18 Surviving Supply Chain Integration National Research Council The committee defined a supply chain as an association of customers and suppliers who, working together yet in their own best interests, buy, convert, distribute, and sell goods and services among themselves resulting in the creation of a specific end product. A supply chain includes all of the capabilities and functions required to design, fabricate, distribute, sell, support, use, and recycle or dispose of a product. An integrated supply chain can be defined as an association of customers and suppliers who work together to optimize their collective performance in the creation, distribution, and support of an end product. The objective of integration is to focus and coordinate the relevant resources of each participant on the needs of the supply chain and to optimize the overall performance of the chain.

19 19 MATHEON Project B14: Combinatorial Aspects of Logistics Task: online/offline control of logistics systems Practice: nothing like the logistics problem (specific aspects in each application) Wanted: identify and tackle core models/approaches, e.g. reoptimization for online problems Applications: vehicle dispatching, elevator control, automated transportation systems,...

20 20 MATHEON Project B14: Applications Scheduling of laser welding robots in car body manufacturing (Volkswagen): During welding each robot is fed by a laser source Goal: minimize number of required laser sources Control of destination-call elevator systems (Kollmorgen Steuerungstechnik): Passenger specifies destination already when calling an elevator Goal: small average/maximal waiting and journey times

21 21 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

22 22 Herlitz at Falkensee (Berlin)

23 23 Example: Control of the stacker cranes in a warehouse

24 24 Anwendungsschwerpunkt innerbetr. Logistik wichtige Teilprobleme Steuerung von Paletten-Förderanlagen und Hochregallager-Bediengeräten

25 25 Horizontal transport

26 26 Wrapping

27 27 Truck Loading

28 28 Truck Loading

29 29 Herlitz Logistics

30 30 Example: Elevator control

31 31 Süddeutsche Zeitung SZ, July 17, 2009: Bitte nehmen Sie Aufzug B

32 32 Siemens Werk für Arbeitsplatzsysteme Siemens/Nixdorf in Augsburg

33 PC-Production at Siemens Receiving area Automatically guided vehicles Control of warehouse (stacker cranes) Assembly Long-term endurance/fatigue test Final chek Packing Shipping

34 34 Principal Layout of the Factory

35 35 Principal Layout of the Factory

36 36 Principal Layout of the Distribution Center

37 37 The Warehouse Layout

38 38 Simulating Reality Simulating the stacker crane Simulating the factory logistics Simulation languages? Possible sources of trouble: Who has designed the factory? What is the role of the planning department?

39 39 AMSEL

40 Validation of the Simulation Modell ØRL ØSim ØDev max Dev % Dev # Ev Time

41 Minimimization of the empty moves # TT utr-p utr-o I %

42 Stacker Crane Animation (1989)

43 Printed Circuit Board Poduction (Petra Bauer) Flachbaugruppen We developed and implemented: - a detailed simulation modell - Optimization heuristics to sequence the production of the printed circuit boards - Methods to compute lower bounds for the throughput time Expectaion: Improvement of the der load from 65% to 100% of the (predicted) capacity.

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45 Results (1) Span between best and worst heuristic solution ~ 20 % (2) Provable span ~ 30 % (3) Solutions used in practice ~ in the middle of the span (4) Random solution ~ in the middle of the span (5) Best heuristic solution ~ 7 % better than practice, but unstable The project was unsuccessful. We could prove that the layout of the system was not well-suited for the current demand (types of printed circuit boards to be produced).

46 49 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

47 50 Greeting Cards

48 51 Commissioning of greeting cards Theory Simulation Practice

49 52

50 53 Online Bin Coloring Given: sequence of colored items Bins with capacity B Task: Pack items into bins such that there are always at most q open bins and Max. #colors in a bin is minimized 1

51 54 Order Picking Project Norbert Ascheuer,, Nicola Kamin, Jörg Rambau Combinatorial online optimization in practice OPTIMA, 57 (1998) 1-6 Kamin, Nicola: On-Line Optimization of Order Picking in an Automated Warehouse PhD Thesis, TU Berlin, 1998

52 55 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

53 56 Optimization of Botany Bay a Container Terminal in Sydney, Australia

54 57 Port Botany existing Terminal layout

55 58 Routing AGVs in a container terminal in Hamburg Harbor (AG Rolf Möhring) Cooperation with Rolf Möhring

56 59 Details of AGV routing (AG Rolf Möhring) Simple grid-like graph Complex turns of AGVs Rolf Möhring

57 60 Issue: Flows over Time (AG Rolf Möhring) Combining time and congestion New theoretical challenges Flow problems become provably harder Approximation algorithms so far only for special cases Rolf Möhring

58 61 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

59 62 Delivery: Vehicle Routing Film and photo processing Repair services

60 63 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

61 64 Allgemeiner Deutscher AutomobilClub

62 65 Unit of the service fleet: Yellow Angel gelber Engel

63 66 Service vehicle planning at ADAC Help center Wireless data transmission Yellow Angel Dispatch: human operator

64 67 The Mathematics of Yellow Angels See the next lecture by Benjamin Hiller

65 68 Contents 1. What is logistics? 2. Stacker cranes, elevators, AGVs and the like 3. Greeting cards commissioning and assembly lines 4. Harbour optimization 5. Delivery 6. Yellow angels 7. What is online optimization?

66 69 What is online? Mathematical theorems usually start with Suppose the following... is given, then. And, as a rule, it is required that algorithms start working only when all data is available. When we deal with online problems, however, we have to make decisions before all information is on hand. Sometimes fast decisions are necessary; in this case we speak of real-time problems. IHK Aufzug

67 70 Real time

68 71 Again: What is online? An online algorithm is a method making a decision as soon as new pieces of information become known. Any decision made is irrevocable. Remarks: The running time is irrelevant: The key issue is the difficulty arising through the lack of data. If running time is important: real-time algorithms! Models of analysis: sequence model, time-stamp model,... Variants: limited intermediate storage, repacking,...

69 72 DFG priority program Online optimization of large scale systems Book:, Sven O. Krumke, Jörg Rambau (Editors) Online Optimization of Large Scale Systems Springer, 2001, 803 pages

70 73 Competitiveness (again) Let ALG be an online algorithm (majority decision of the audience). Let s be a request sequence for the bin packing problem (generated by me). ALG(s) denotes the value ALG produced, whereas OPT(s) denotes the optimal solution of the offline adversary. Let c 1. We say that ALG is c-competitive, if ALG(s) c OPT(s) is valid for all request sequences s. Is there a lower bound on c for bin packing?

71 74 Competitiveness of bin packing Online solution: 3 bins 2 bins are optimal

72 75 Competitivity of bin packing My request sequence yields: 1.5 x OPT(s) ALG(s) From this follows a general lower bound: c 1.5 for online bin packing. Best lower bound known: c = (van Vliet)

73 76 Bin packing algorithms Next Fit First Fit First Fit Decreasing (offline) Best Fit Harmonic Fit (many variants)...

74 77 Bin packing algorithms Simple proofs for: Next Fit is 2-competitive. First Fit is 2-competitive. Upper bounds on the bin packing competitiveness Algorithm Competitivity Next Fit 2 Best Fit 1.7 First Fit 1.7 Revised Harmonic Fit Harmonic (Seiden 01)

75 78 Bin packing with repacking It is permitted to keep k containers open and to repack among them. As soon as another container is opened, one of the k containers must be closed forever. Lee & Lee c (for arbitrary k) Galambos & Wöginger c (for k = 3) One example for optimal competitiveness

76 79 Online Optimization This was just a warm-up. More on this topic in the next talk

77 80 Final Remarks on Logistics

78 Mathematical Aspects of Logistics Berlin :00 10:30 Institut für Mathematik, Technische Universität Berlin (TUB) DFG-Forschungszentrum Mathematik für Schlüsseltechnologien (MATHEON) Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)