1. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Scheduling Automated Manufacturing Systems with Transportation and Storage Constraints Yazid MATI Ecole des Mines de Nantes yazid.mati@emn.fr Xiaolan XIE INRIA / MACSI Team & LGIPM / AGIP Team Ile du Saulcy, 57045 Metz, France xie@loria.fr

2. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 1.Scope of the scheduling model 2.A case study in which new features really count 3.Backgrounds 4.A generic scheduling model 5.Solving the scheduling model 6.Numerical performances 7.Extensions PLAN

3. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 The new scheduling model includes most existing production scheduling models as special cases: Job-shop and flow-shop models Robotic cell Production line with intermediate buffers Hybrid flow shops Flow shop without intermediate buffers Flexible manufacturing systems with AGVs. Scope of the scheduling model

4. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Algorithms developed in our research have been selected and are being implemented for the production planning of : A French company that produces large and heavy parts for the aerospace industry Plant: Plant layout arranged in line 6 types of workstations : 2 idem workstations for 2 types A single transportation device No buffer area Case study in which new features really count

5. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Characteristics of the demand: Around 10 part types (25 to 60 units per year) Manufacturing processes : 8 to 13 operations (re-entrance) An operation needs a machine, a tool and an operator Processing times range from 1 to 23 hours Additional constraints: Transportation device cannot held workpieces and wait Workpieces are loaded on palettes (high prices) Case study in which new features really count

6. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Main objective (realized): Determine the minimum number of palettes Determine a schedule that minimizes the completion time Second step (realized): Any workstation can serve as a buffer Scheduling model with resources flexibility Future work : Operational software that takes into account the work-in- process Case study in which new features really count

7. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 High productivity of automated manufacturing systems is achieved through use of modern production resources for machining, transportation and storage. Economic pressure requires high utilization of all resources and makes all resources nearly critical. There is a need to coordinate the use of all resources for efficient production planning/scheduling. Background

8. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Mainstream literature in production scheduling only considers machining resources, treats other resources as “secondary resources” and focuses on oversimplified models such as job- shop, flow-shop models. Practical approach to deal with this problem is to (i) first derive a production plan with machining resources and then (ii) adjust the planning by taking into account the availability of other resources. This approach is unsatisfactory if the so-called “secondary resources” are nearly critical. Background

9. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 The system is composed of m resources {R 1, R 2, …, R m } and has n jobs (or customer orders) {J 1, J 2, …, J n } Each job J i requires a sequence of operations O i1 O i2 …O iN(i). The processing time p ik of each operation O ik is given. The goal is to complete all jobs in the minimum time. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB)

10. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Resource availability: Each resource is available in several units. Resource requirement of an operation: Each operation might require simultaneously more than one resource and more than one unit of each resource. Example: O ik = (2OP+TR, 10 min) corresponds to an operation performed by 2 operators OP with one transportation device TR during 10 minutes. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB)

11. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Resource release after an operation : At the completion of an operation O ik, its resources are held and cannot be released till resources needed for the next operation of the same job are available. This constraint is called Hold-While-Wait constraint. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB)

12. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 A production line without intermediate buffer where M1 is blocked during one hour after the completion of J1 on it. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB) J1 (1h)J2 (2h) M1M2 A job-shop without intermediate buffer where M1 and M2 are deadlocked after the completion at time 1. J1 (1h)J2 (1h) M1M2

13. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 One remarkable feature of our scheduling model is its flexible modeling granularity of resource requirements of operations thanks to multi-resources operations and the hold-while-wait constraint. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB) Example : Operation with machine requirement only : O ij = (M, p ij ). Machine+operator + tools, O ij = (M+O+T, p ij ). If the operator is only needed to mount the tool and to load the product, then O ij = (M+O+T,  ij ) (M+T, p ij ).

14. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Some common operations can be modeled as follows special MJSB operations: waiting in a buffer of unlimited capacity as O ij = ( , 0), waiting in a buffer B of size n as O ij = (B, 0) transportation delay  on a conveyor as O ij = ( ,  ) transportation with an AGV as O ij = (AGV,  ) transportation with a robot R as O ij = (R,  ). A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB)

15. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Solving the scheduling model : two-job case Geometric method Representation in the plane Successors The resulting network J 1 = (M 1 M 4, 1), (M 2, 2), (M 3, 1), J 2 = (M 3, 2), (M 2, 1), (M 1, 2),

16. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 FJobs are scheduled one after another according to a job sequence, geometric approach FThe two first jobs are scheduled using a geometric approach, combined job FJobs already scheduled are grouped into a combined job, the geometric approach. FA new job and the combined job are scheduled by the geometric approach. Solving the scheduling model :general case A Greedy algorithm Job sequence : J 1 J 2 J 3 … J N-1 J N J com J3J3 Geometric approach geometric approach between J com and J 3

17. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 FDetermine the Gantt diagram of the resulting schedule, F Decompose [0, makespan] into sub-intervals according to the finishing time of operations, FProcessing time : the length of the sub-interval, F The required machines are machines occupied in the corresponding sub-interval. Solving the scheduling model :general case Construction of the combined job J com = M 1  M 3 (1) M 2  M 3 (1) M 2 (1) M 3  M 2 (1) M 1 (2)

18. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 F The performance of the greedy algorithm strongly depends on the order, called job sequence, in which jobs are scheduled. FA taboo search is used to identify the job sequence with which the greedy algorithm leads to the shortest makespan, i.e. Min Cmax(J [1] J [2] …J [n] ) where Cmax is the makespan of the schedule given by the greedy algorithm with job sequence J [1] J [2] …J [n]. Solving the scheduling model :general case Improving the greedy algorithm

19. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Numerical performances Benchmark test  There is no test problems in the literature with features of our scheduling model.  For existing benchmarks (over 100 test cases) for the job shop problem, the proposed approach is in general very competitive with best known heuristics.

20. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 Numerical performances Test on special cases Robotic cell (Ramaswamy & Joshi [1996]) : 4 jobs, 3 machines, one robot under various buffer size constraints at machines. Optimal solutions Computation time Computation time : 0.1 CPUs Randomly generated examples (Damasceno et Xie [1999]) best 9 best solutions overs 9 instances Computation time Computation time : 8 CPUs Robot chargement/déchargement M4M4 M3M3 M2M2 M1M1 PiPiPiPi PjPjPjPj

21. Yazid Mati & Xiaolan Xie CRF Club, 04/07/2004 EXTENSIONS The proposed approach has been extended to the following cases: 1.operations with alternative resource requirements 2.products with multiple manufacturing processes Future extensions include: 3.assembly/disassembly operations 4.jobs with no-wait operations 5.jobs with limited-wait operations.