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Scheduling Automated Manufacturing Systems with Transportation and Storage Constraints Yazid MATI Ecole des Mines de

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 . PLAN. Scope of the scheduling model

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Scheduling Automated Manufacturing Systems with Transportation and Storage Constraints Yazid MATI Ecole des Mines de

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  1. 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 CRF Club, 04/07/2004

  2. PLAN • Scope of the scheduling model • A case study in which new features really count • Backgrounds • A generic scheduling model • Solving the scheduling model • Numerical performances • Extensions CRF Club, 04/07/2004

  3. Scope of the scheduling model • 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. CRF Club, 04/07/2004

  4. Case study in which new features really count • 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 CRF Club, 04/07/2004

  5. Case study in which new features really count • 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) CRF Club, 04/07/2004

  6. Case study in which new features really count • 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 CRF Club, 04/07/2004

  7. Background 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. CRF Club, 04/07/2004

  8. Background 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. CRF Club, 04/07/2004

  9. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB) The system is composed of m resources {R1, R2, …, Rm} and has n jobs (or customer orders) {J1, J2, …, Jn} Each job Ji requires a sequence of operations Oi1Oi2…OiN(i). The processing time pik of each operation Oik is given. The goal is to complete all jobs in the minimum time. CRF Club, 04/07/2004

  10. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB) 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: Oik = (2OP+TR, 10 min) corresponds to an operation performed by 2 operators OP with one transportation device TR during 10 minutes. CRF Club, 04/07/2004

  11. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB) Resource release after an operation : At the completion of an operation Oik, 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. CRF Club, 04/07/2004

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

  13. A generic scheduling model Multi-resource Job-Shop with Blocking (MJSB) 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. • Example : • Operation with machine requirement only : Oij = (M, pij). • Machine+operator + tools, Oij = (M+O+T, pij). • If the operator is only needed to mount the tool and to load the product, then Oij = (M+O+T, Dij) (M+T, pij). CRF Club, 04/07/2004

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

  15. Solving the scheduling model : two-job case Geometric method J1 = (M1M4, 1), (M2, 2), (M3, 1), J2 = (M3, 2), (M2, 1), (M1, 2), Successors Representation in the plane The resulting network CRF Club, 04/07/2004

  16. Solving the scheduling model :general case A Greedy algorithm • Jobs are scheduled one after another according to a job sequence, • The two first jobs are scheduled using a geometric approach, • Jobs already scheduled are grouped into a combined job, • A new job and the combined job are scheduled bythe geometric approach. Job sequence : J1 J2 J3 … JN-1 JN geometric approach between Jcom and J3 Jcom J3 Geometric approach CRF Club, 04/07/2004

  17. Solving the scheduling model :general case Construction of the combined job • Determine the Gantt diagram of the resulting schedule, • Decompose [0, makespan] into sub-intervals according to the finishing time of operations, • Processing time : the length of the sub-interval, • The required machines are machines occupied in the corresponding sub-interval. Jcom = M1 M3 (1) M2 M3 (1) M2 (1) M3 M2 (1) M1 (2) CRF Club, 04/07/2004

  18. Solving the scheduling model :general case Improving the greedy algorithm • The performance of the greedy algorithm strongly depends on the order, called job sequence, in which jobs are scheduled. • A 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]. CRF Club, 04/07/2004

  19. 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. CRF Club, 04/07/2004

  20. Numerical performances Test on special cases Pj M3 M2 Pi Robot M4 M1 chargement/déchargement • Robotic cell (Ramaswamy & Joshi [1996]) : 4 jobs, 3 machines, one robot under various buffer size constraints at machines. • Optimal solutions • Computation time : 0.1 CPUs • Randomly generated examples (Damasceno et Xie [1999]) • 9 best solutions overs 9 instances • Computation time : 8 CPUs CRF Club, 04/07/2004

  21. EXTENSIONS • The proposed approach has been extended to the following cases: • operations with alternative resource requirements • products with multiple manufacturing processes • Future extensions include: • assembly/disassembly operations • jobs with no-wait operations • jobs with limited-wait operations. CRF Club, 04/07/2004

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