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*Dept of IE, State Univ. of New York at Buffalo

Integrated Scheduling of material handling and manufacturing activities for just-in-time production of complex assemblies. *Dept of IE, State Univ. of New York at Buffalo IJPR( International journals of production research ) 1998.vol 36 M.F.ANWAR* and R.NAGI*

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*Dept of IE, State Univ. of New York at Buffalo

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  1. Integrated Scheduling of material handling and manufacturing activities for just-in-time production of complex assemblies • *Dept of IE, State Univ. of New York at Buffalo • IJPR(International journals of production research) 1998.vol 36 • M.F.ANWAR* and R.NAGI* • 발표: 1998.5.26 송 태 영

  2. INTRODUCTION 1.Mfg. strategy from mass production to small batch mfg. 2.By some estimates, 5% of flow time being processed on machine 3.There is a need for better coordination scheduling of production and logistics on shop floor ; a problem of trade-off. 4. Such environments are common in heavy mechanical industry, radar antennas. 5. JIT production of complex assemblies under multple capacity constraints. and cycle times span over several month. 6. The objectives is to reduce the cumulative lead time of product schedule, min wip and material handling cost.

  3. Background 1 1. Job-shop scheduling or multi-level product Various authors including Billington(1983),Sinnamon(1992),Agrawal(1996)study the multi-stage, multi-item scheduling problem with only mfg. operations. AGVs or forklifts is essential 2. Scheduling AGVs 1)guide path network design 2) # of AGV 3) dispatching, routeing, traffic control AGV dispatching will in turn influence subsequent work-center.

  4. Background 2 3. Integrated material handling in the job-shop environment Ihsan and Hommertzheim(1992) investigated various machine and AGV scheduling rules against certain criteria. Raman(1986) study Integrated material handling in the flow-shop environment. Pundit and Palekar(1990)proposed heuristic(branch-and-bound)for the simultaneous scheduling of machines and material handling vehicles in job-shop environments But there is no considering about precedence relationship between different parts of the same end product - it’s essential in these assemblies

  5. Transportation integrated scheduling problem(TISP) Assumption 1.Machines/ AGV s are assumed to be reliable 2.A machine can perform at most one operation at a time 3.Pre-emption of operations or AGV trip is not permitted. 4. Processing time, due-date are deterministic 5.No backlogging 6. AGV do not encounter comgestions. 7. sufficient input-output buffers available at each machine and each loading/unloading station 8. AGVs in a single trip Notation Di duedate of the ith item S Start time of the planning horizon. s(j) downstream operation of j Sj Start time of j Fi Finish time of j tj batch processing time of j Kw(j)w(i) time of an empty transport travel from cell of j to cell of I &ij = 1 if oj precedes oi $jy = 1 if oj is performed on yth machine of 0 otherwise WC y 0 otherwise

  6. TISP Minimize: max{Di} - S st: Ss(j) >=Fj for j= 1,2, ... n (1) Fj = Sj + tj (2) &ij = &ji = 1 for I,j~Iy (3) Si - Fj >= (&ij+$iy+$jy-3)M (4) Fj <= Si-Kw(j)w(i) + (3-&ij-$iy-$jy)M +($ik - $jk - 1)m(5) &ij>= $jk + $iy - 1 (6) Fi<= Di I ~ E (7) S <= Sj (8) The problem is NP - hard pf) The vehicle routeing problem(Orloff 1976) and single machine scheduling are accepted Np-hard. So wlg.

  7. Problem formulation M11 M12 Input data BOM, routeing of the manufactured items, the layout structure, information of transportation operations. cell 1 cell2 cell3 cell4 Travel path Distance table

  8. A 1 make C 1 make B 2 make I 1 make F 2 Purchase E 1 make D 2 make J 1 Purchase H 3 Purchase G 2 Purchase BOMProcess time(setup + runtime of batch) Part Operation Components Processing Workcenter cell_no Required Time A A.10 C 6 WC#1 1 A.20 B,C 7 WC#2 2 . B B.10 D,E,F 6 WC#1 1 C C.10 I 3 WC#1 1 D D.10 G 7 WC#1 1 D.20 G 1 WC#2 2 E E.10 H 5 WC#1 1 E.20 H 3 WC#2 2 I I.10 J 1 WC#2 2

  9. E10 5 T12 5 E20 3 T21 3 B10 6 . T12 5 T21 3 D20 1 T12 5 A20 7 D10 7 T12 5 A10 6 C10 3 Given BOM of final product, routeing of manufactured part , we can propose a network and insert transportation operations. T21 3 I 10 1

  10. Transportation integrated problem scheduling algorithm Backward scheduling manner similar to MRP - last operation is scheduled first, and the remaining operations are scheduled backwards in subsequent step. Input : The delivery schedule, product structures, routeing data(network) and transportation time step1 Define the set of feasible operations as F={oj; s(j) = zero set j = 1... n} step2 While the feasible list has entry 1. Select the operation from the list F that has largest value 2. Set tentative finish time Fj I) earliest start time s(j) II) if j is last operation then due date 3. each machine or AGV include the required WC 3.1 Set tentative latest starting time for Oj as sj = Fj - tj 3.2 if machine or AGV is available during [Sj, Fj] then ideal time else select MAX{Sj} 3,3 Schedule Oj at latest available starting time Sj 3.4 delete oj from the network. Step6. compute the make span of the resulting reschedule Step7. Compute cost of production combining material, labour, WIP

  11. Steps of TIPSA for scheduling of product A E10 5 T12 5 E20 3 T21 3 Iteration Oj EF Oj Tentative Sj, Fj W.c Feasible # from F selected finish selected list 1 A20 34 a20 50 43,50 2 {T12(B10), T12(A10)} 2 T12(B10) 27 T12(B10) 43 38,43 AGV {B10, T12 (A10)} T12(A10) 18 3. B10 22 b10 38 32,38 1 {T12(A10), T21(D20)} T12(A10) 18 {T21(E20)} B10 6 T12 5 T21 3 A20 7 T12 5 D10 7 D20 1 T12 5 A10 6 I 10 1 T21 3 C10 3

  12. . E10 5 T12 5 E20 3 T21 3 Iteration Oj EF Oj Tentative Sj, Fj W.c Feasible # from F selected finish selected list 4 T12(A10) 18 T.12(A10) 43 30, 35 AGV {A10,T21(D20),T21(E20)} T21(E20) 16 T21(D20) 16 5 T21(E20) 16* T21(E10) 32 27,30 AGV {A10, T21(D20), E20} T21(D10) 16 A10 13 B10 6 T12 5 T21 3 A20 7 T12 5 D10 7 D20 1 T12 5 A10 6 I 10 1 T21 3 C10 3

  13. WC#2 II D20 E20 A20 WC#1 C10 E10 D10 A10 B10 Transportation integrated Scheduling heuristic1. Critical path concept LETSA(1996 Agrawal) SLIPSA(1997 Anwar and Nagi) AGV T21 T12 t21 T12 T21 t12 T21 T12 t21 T12 WC#2 I D E20 A20 WC#1 E10 D10 C10 A10 B10 0 4 8 12 16 20 24 28 32 35 Gantt chart by simple network 0 4 8 12 16 20 24 28 32 36 40 44 48 50 Gantt chart considering transportation 0 4 8 12 16 20 24 28 32 36 40 44 48 50 54 57 Gantt chart of sequential schedule AGV T21 T12 t21 T12 T21 t12 T21 T12 t21 T12 WC#2 I D E20 A20 WC#1 C10 E10 D10 A10 B10

  14. Result and discussion Compare NP-hard, sequential Scheduling NP-hard optimal results are possible with only small ex. and limited interest. Sequential Scheduling use LETSA and FCFS AGV services sometimes use 3.4 methods rather than random vehicle assignment. The result is makespan is that 7days is short in TIPSA Because TIPSA threat vehicle as a operation.

  15. Conclusion TIPSA result in considerable improvement compared with popular LETSA and mathematical programming. The performance is measured by makespan and cost This method is also useful in determining the optimal # of AGV- fleet sizing and other purpose. Further research could be directed to system to include lot-sizing and to account for conflict-free routeing of AGVs on the travel paths

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