Math-based Decision Making in Logistics and Operations

1. Math-based Decision Making in Logistics and Operations

2. Where we are? UPM

3. Math-based Decision Making in Logistics and Operations Math-based Decision Making in Logistic and Operations Grupo Inv INGOR MbDMLO UD Organización de la Producción UD Administración Empresas UD Economía UD Proyectos UD Estadística Grupo InvOS Dep. Ingeniería de Organización, Adm. de Empresas y Estadística Lab IOL ETSII UPM UPM

4. The team Miguel Ortega Mier Álvaro García Sánchez Javier Diego Daniel Herrero Natalia Ibáñez Raúl Pulido JingShao Tamara Borreguero Others. UPM

5. Techniques and technologies UPM

6. The inventory routing problem for the Mixed Car Model Assembly Line UPM

7. Relevance A high inventory level in the assembly line is a big cost contributor. Some of the car manufacturer’s objectives are keeping low stock levels, performing the replenishment of the production line, and providing the required components at the right time (Monden, 1983). UPM

8. Abstract A car assembly line usually produces hundreds of cars every day; each workstation in the assembly line needs car components to perform their task. The replenishment of the components is a critical issue for the proper operation of the assembly line. In a multi-model assembly line, this task becomes more complicated than in a single model assembly line. A lack of inventory could cause some problems in the production line; excess inventory could also create it. UPM

9. Problem description In this problem, the assembly line already exists and the production plan, for the planning period, is already known. Each model has a set of characteristics, such as types of wheels and tires, radio, sunroof, car seat, and so on. In every workstation, a kit of components is installed; these components can have different trim levels. It is assumed that each component needed for the planning horizon is available in a single warehouse from where all the routes depart. UPM

10. Problem description The early arrival of the component causes space problems with the buffers of the production lines. The late arrival causes several problems in the production line. Dispatch only with a just-in-time policy increases the transportation cost and the green impact of the production line. It is necessary to select the route and the amount of required components to get the lower cost. UPM

11. Problem description UPM

12. MIP min. • A MIP has been developed. • Transportation Cost • Transportation Vehicle Used Cost • Holding Cos • Violation Cost • There is a conflict of interest among the objectives. • Right now it is being presented in the CIO 2013 by one of the authors. UPM

13. Two types of Ants • Total Production Rule Violations • Sequence(i) • Class (i) Sequencing • Initial Data • Number of Cars • Number of Car Classes • Number of Stations • Capacity of Stations • Requirements per Station by each class • Distance • Number of Vehicles Routing • Visited Stations • Total Cost • Vehicle (k) • Tour (n) • Tour Length • Time Visited (n) UPM

14. Pheromones & Heuristic info structure • Pheromone 1 (number of vehicles, number of vehicles) • MAX-MIN approach. • The best ant of the cycle deposit pheromone at the end. • Represent the learnt of desirability of scheduling Cj after Ci. • Pheromone 2 (number of classes, number of classes) • Initialize in the lower bound • Each time no more cars can be scheduled without violation some pheromones are added. • Represent the difficult to sequence this class without violating rules. UPM

15. Pheromones & Heuristic info structure 2 • Pheromone 3 (number of stations, number of stations) • The best ant of the cycle deposit pheromone at the end. • Represents the learnt of desirability of visiting Sj after Si. • Dynamic Heuristic info(number of stations, number of stations) • Different options using the stock at determinate time, Traveling time, distance, and so on. UPM

16. Simplified Algorithm • Pheromones trails are initialized. • For the maximum iteration allowed to do • The sequence ants construct a sequence. • Calculate the demand over the time. • Each route ant constructs a full route. • Each route ant construct a full route using one less vehicle. • Evaluate the solution using the global function. • Update the pheromone trails with their respective pheromone and rules. UPM

17. Probability UPM

18. WH T2 S1 S2 S3 S4 S5 T1 T3

19. RANDOM WH T2 S1 S2 S3 S4 S5 T1 T3

20. WH T2 S1 S2 S3 S4 S5 T1 T3

21. WH T2 S1 S2 S3 S4 S5 T1 T3

22. WH T2 S1 S2 S3 S4 S5 T1 T3

23. WH T2 S1 S2 S3 S4 S5 T1 T3

24. WH T2 S1 S2 S3 S4 S5 T1 T3

25. WH T2 S1 S2 S3 S4 S5 T1 T3

26. WH T2 S1 S2 S3 S4 S5 T1 T3

27. WH T2 S1 S2 S3 S4 S5 T1 T3

28. WH T2 S1 S2 S3 S4 S5 T1 T3

29. WH T2 S1 S2 S3 S4 S5 T1 T3

30. Other Ant WH T2 S1 S2 S3 S4 S5 T1 T3

31. We keep doing for the total number of ants WH T2 S1 S2 S3 S4 S5 T1 T3

32. For the best ant Evaporate T1 WH T2 S1 S2 S3 S4 S5 T1 T3

33. Best Ant WH T2 S1 S2 S3 S4 S5 T1 T3

34. Iterate

35. Routing WH T2 S1 S2 S3 S4 S5 T1 T3

36. Routing WH T2 S1 S3 S4 S5 T1 T3

37. Routing WH T2 S1 S3 S5 T1 T3

38. Routing WH T2 S3 S5 T1 T3

39. Routing WH T2 S5 T1 T3

40. Routing WH T2 T1 T3

41. Routing T2 T1 T3

42. Iterate

43. One vehicle less WH T2 S1 S2 S3 S4 S5 T1 T3

44. One vehicle less WH T2 S1 S2 S3 S4 S5 T1 T3

45. One vehicle less WH T2 T1 T3

46. Update the best ant WH T2 S1 S2 S3 S4 S5 T1 T3

47. Update the best ant WH T2 S1 S2 S3 S4 S5 T1 T3

48. Iterate

49. Repeat the entire process

50. We keep working Which heuristic information is better for the problem. Time to be out stock, time to arrive, distance, and so on. Type of filling, series or parallel Other updates of pheromones UPM