SCHEDULING AND ROUTING

Transcription

1 SCHEDULING AND ROUTING

2 I. Scheduling and routing coordination 2 communities Scheduling community Routing community Scheduling community Scheduling with transportation Example : Job-Shop with transport Routing community No Scheduling Pick up and deliveries are available 2

3 I. Scheduling and routing coordination scheduling routing Scheduling + transport 3

4 I. Scheduling and routing coordination Current works Collaboration with LIMOS/LAAS Disjunctive Scheduling update the graphe PhD Thesis (M. Vinot) Scheduling with extra constraints -Collaboration LIMOS/Bologna 4

5 I. Scheduling and routing coordination Questions How researchers in scheduling include transportation in the problems? How Supply chain optimization is achieved? 5

6 II. Scheduling and transport Example : job-shop J1 : M1(1) M2(1) M3(1) J2 : M2(4) M1(3) M3(1) J3 : M3(2) M2(5) M3(1) 6

7 II. Scheduling and transport Example : job-shop Non oriented disjunctive graph J1 : M1(1) M2(1) M3(1) J2 : M2(4) M1(3) M3(1) J3 : M3(2) M2(5) M3(1) Time lag max 1 4 m1 m2 m m2 4 m1 2 m3 1 * m3 m2 m1 7

8 II. Scheduling and transport Scheduling? A disjunction between operation J1 : M1(1) M2(1) M3(1) J2 : M2(4) M1(3) M3(1) J3 : M3(2) M2(5) M3(1) m1 m2 m3 m3 m m2 m1 m3 m m1 m2 m m2 m1 m3 * m3 m2 m

9 II. Scheduling and transport Scheduling? A solution : an evaluation of the graph J1 : M1(1) M2(1) M3(1) J2 : M2(4) M1(3) M3(1) J3 : M3(2) M2(5) M3(1) m1 m2 m m2 m1 m3 * m3 m2 m

10 II. Scheduling and transport Scheduling? Example : job-shop J1 : M1(1) M2(1) M3(1) J2 : M2(4) M1(3) M3(1) J3 : M3(2) M2(5) M3(1) P3 P1 P2 P2 P1 P3 P1 P2 P Time lag min O11 O22 1

11 II. Scheduling and transport Scheduling? And the transport? Mohand Larabi. «Le problème de job-shop avec transport : modélisation et optimisation». PhD Thesis. Clermont Ferrand University. 15 dec 21. Johann Hurink, Sigrid Knust. Tabu search algorithms for jobshop problems with a single transport robot. European Journal of Operational Research, Volume 162, Issue 1, 1 April 25, Pages

12 II. Scheduling and transport What does it mean? 12

13 II. Scheduling and transport 1 robot with capacity 1 mi Duration of operation on machine i t ij Transportation time from machine i to machine j m j Transportation time from i to j + Transportation time for j to u m u Duration of operation on machine u + Empty trip duration from machine j to u t uv Transportation time from machine u to machine v m v 13

14 II. Scheduling and transport 1 robot with capacity 1 14

15 II. Scheduling and transport 1 robot with capacity = 1 15

16 II. Scheduling and transport 2 robots : a solution for the routing m1 1 1 m2 1 1 m m2 2 m m3 * m3 2 2 m2 2 2 m1 2 16

17 II. Scheduling and transport A solution for the routing and the scheduling m1 1 1 m2 1 1 m m2 2 m m3 * m3 2 2 m2 2 2 m P3 P2 P1 P1 P2 34 P2 44 P1 48 P3 P

18 II. Scheduling and transport Remarks It is possible No specific algorithms for the routing Why? Semi active solutions Feasibility check! 18

19 II. Scheduling and transport Instances Hurink J. and Knust S. (25). Tabu search algorithms for job-shop problems with a single transport robot, European Journal of Operational Research, Vol. 162, No 1, pp Bilge U and Ulusoy. A time windows appoach to simulteneous scheduling of machines and material handling system in a FMS. Operations Research. 43(6). Pp Ulusoy U., F. Sivrikay-eSrifoglu and Bilge U. A genetic algorithm approach to the simultaneous scheduling of machines and automated guided vehicles. Computers and Operations Research. 24(4). pp Last publications Houssem Eddine Nouri, Olfa Belkahla Driss, Khaled Ghédira. Simultaneous scheduling of machines and transport robots in flexible job shopenvironment using hybrid metaheuristics based on clustered holonic multiagent model. Computers & Industrial Engineering, In Press, Corrected Proof, March

20 II. Scheduling and transport Station 2 Station 3 Station 4 Station 5 vehicle guided network Load station Unload station Station 1 2

21 III. First trend : disjunctive. Classical scheduling approaches Extensions.???? 2 kinds of extensions New definition of Earliest Starting Times New definition of routing considering some specific scheduling approaches 21

22 D D 1 2 III. First trend : disjunctive. Disjunctive modelisation 1 m1 1 4 A+ A- m2 C m2 2 2 m m m B

23 III. First trend : disjunctive. Challenging problems? 23

24 IV. Second trend : specific problems. Scheduling with specific approach. RCPSP Scheduling + resource management Resource management => flot problem High quality specific methods Under study with Marina Vinot (LIMOS) 24

25 IV. Second trend : specific problems. Data : R set of resources, limited constant availability B k for k R, A set of activities (tasks), duration p i, i A, resource requirement b ik, k R, E set of precedence constraints i, j, avec i, j A, i < j T time interval (scheduling horizon) Constraints : S i S j S j + p i, with i, j E Precedence constraints start time of activity i b ik B k j A(t), with t T, k R Resource constraints 25

26 IV. Third trend : divide to conquer. Scheduling with specific approach. Transport routing Under study with Caroline Prodhon, Ren Libo and Daniele Vigo. 26

27 IV. Third trend : divide to conquer. $ $ Step 1 Step 2 Step 3 $ Step 4 $ LAST STEP Supplier FIRM C Manufacturer FIRM A Manufacturer FIRM B Manufacturer FIRM C Routing 1 Retailer FIRM A Retailer FIRM B Customer Routing 1 Customer Retailer FIRM A Retailer FIRM B Distribution Center FIRM C Warehouse FIRM A Warehouse FIRM C Supplier FIRM C Routing 2 Manufacturer FIRM A Manufacturer FIRM B Supplier Firm C Manufacturer FIRM C Retailer FIRM B Customer Routing 3 27

28 IV. Third trend : divide to conquer. A job : number of parts batched together (ni) (Adacher and Cassandras, 214) Lot size : Processing time of batch : 28

29 IV. Third trend : divide to conquer. 29

30 IV. Third trend : divide to conquer. Time windows to unload the job Delivery time Waiting time Sub-operation on machine (i+1) Sub-operation on machine i Waiting time Time windows to load the job Departure time 3

31 I. The problem description : batch job-shop 3 jobs, 3 machines, 2 vehicles 31

32 I. The problem description : batch job-shop A two parts solution 32

33 IV. Third trend : divide to conquer. A two parts solution 33

34 IV. Third trend : divide to conquer. Non Oriented Disjunctive graph G Generation of a permutation job list + TL TL Oriented Disjunctive Graph (Job-Shop only) 1 5 m m2 m m2 4 m1 2 m3 1 * m3 2 m2 5 m1 TL 5 55 Oriented Disjunctive Graph + Time Lags Critical path analysis Time Windows Violation : analysis Makespan and critical path Longest Path Computation PDPTW resolution 34

35 IV. Third trend : divide to conquer. 35

36 IV. Third trend : divide to conquer. 36

37 IV. Third trend : divide to conquer m3 m3 m3 m2 m3 m1 m M2 M1 5 M2 3 M3 M1 5 M2 3 M3 3 M2 15 M1 5 M3 15 M2 15 M1 5 M3 M3 5 M2 1 M M2 M2 M1 5 3 M2 M M1 5 3 M2 M M2 M1 M M2 15 M1 5 M M3 M2 1 M1 1 3 M2 94 M3 5 1 M2 M M3 5 1 M2 M1 8 M3 5 M2 1 M1 M3 5 M2 1 M M3 5 M2 1 M M3 5 M2 1 M1 37

38 IV. Third trend : divide to conquer. 38

39 IV. Third trend : divide to conquer. Resolution of the PDPTW Trip 1 Trip 2 See (Cordeau and Laporte, 25) 39

40 IV. Third trend : divide to conquer M2 M1 5 3 M2 M M1 5 3 M2 M M M1 M M M1 M M3 M2 M M M3 5 1 M2 M M3 5 1 M2 M M3 5 1 M2 M1 Use the longest path in 2 ways. 4

41 IV. Third trend : divide to conquer. Resolution of the PDPTW 41

42 IV. Third trend : divide to conquer. 42

43 Conclusion scheduling routing Scheduling + transport Scheduling with transport Scheduling with routing 43