, time: 3.5 ; bounds: 0.50,0.50; d: 1.0; Cl: 2

, 00; d: 1.0 ; Cl: 3.0

A. , R. , Y. F. Choong, S. B. Gershi{in, A. et al., Perf ormance of Hierarchical production Scheduling PoIicy, L984981-. tANlANTHONY'R.N.r,PlanningandcontrolSystems:AFrameworkfOr Analysis., Harvatd rlniversity, Gtaduate school-of Busjness eani-nisttation, p.965

, ControI of Large ScaIe Dynamic Systems by, IEEE Transactions on Automatic Control'

, tAoll AoKr , M. , Aggregat ion, vol.13, issue.3, 1968.

L. Aoki, A. , R. J. , A. C. Hax, K. R. Baker et al., IEEETransactionsonAutomatic ConttoT-, VoI . AC-23A Hierarchical Approach for a NavalTenderJobShopDeSign Operations Resea rch Ceitet, t"t. l . t . , Cambridge, MA.' L97 4 ' tAx]AXSÀTER'sThe Integration of Planningr scheduling, and control for Automated Manufacturing, AD Rolling Schedules VoI. 8

I. and W. J. , FABIANTIDecomposition'PI^icingfor Decentralization and External Economies, Management Science, vol.LI

B. Tbol, E. , J. M. Proth, K. N. Voyatzisi, . Centre-du-rocquencourt-'france-'l984-'tbrl et al., Aritificial Memory in ProductionManagemeûtMathematical Theory of Production Planning, L983' tBPl BENSoUSSAN' A. and J'M' Deterministic Environment : Costs. ", EuroPean Journal of Experimental Study of the Effectiveness of in Production Planning.", Decision Sciences

, InventorY Planning in a Continuous Time Model with Concave -Opirationai. Reseatch, VoI' 15, 1984' References tBxll BTTRAN, c.R. and A.c. HAx, "On the Problems with Bounded Variables, Operations Research Center, M.I.T

M. Cambridge, C. R. Bitran, A. C. Hax, I. Bitran, G. R. et al., On the Design of HierarchicaI Planning Systems Decision Sciences, VoI. 8, 19'77Hierarchical produçtieA Planning : A Single Stage SystemHierarchical Productioç Plannj-ng : A Two Stage SystemIssues of Hierarchical Planning in MuIti-sEage Production Systemsstochastic Scheduling and Set-ups in Flexiblq Manufacturing systems, Technical report No. 179r Operations Research Center proceedings of tàe 2nd oRsA/TrNs Conference on FTexible lûanufacturing Systems .. O.R. ModeLs and Applications, K. Stecke and R. Suri e-ds, 1980.

S. B. Gershhitn, A Hierarchical Framework for Discrete Event Scheduling in Manufacturing Systems.r', presented at the ffÀSÀ Workshop on Discrete Event Systems: Modeis and Applications, L987, to appear in the I . E. E. E. Proceedings, Special fssue on Dynamics of Discrete nveni. Systems, 0988.

[. Gershi-'ùin, S. B. Gershi{in, S. B. , R. Akella, and Y. F. Choong-i, nA Hierarchical Framework f or Manuf acturing Systems SchedulingShort Term Production of an Àutomated Manufacturing Faci1ity, Proceedings of the 26th r tccl

. Journal, . Research, . Devetopment, . Voi, S. 8. Gershwin et al., MTTTER, xA Control Perpective on Recent Trends in Manufacturing Systems, ïEEE ControL Systems Magazine, p.986

E. M. Goldratt, J. C. Cox-a, A. C. Hax, and J. J. Golovin, The Design of Large ScaIe Logistics Systems : A Survey and an Approach.", V{. Marlow êd., in Modern Trends in Logistics ResearchAggregate Production Planning, Handbook of Operations Research Studjes in Operations Managiement tKLl KoRNAT ' .t' and T . LTPTAK, 'rTwo LeveI planning . ,, Econometrica, 1965.

[. Ievùski, L. J. , L. P. , and K. , Disaggregation in Manufacturing and service organizatj-ons : survey of probrems and Research Ig77Hierarchicar Decomposit j-on of Linear Economic Models, Decision ScjencesA1 LASDON' L.s., "Duarity and Decomposition in Mathematical Programting tl-r LAsDoN, L. s . and R. c. TERJUNG,An Ef f icient Argorithm for Multi-item scheduring.", operations Research, 1969.

J. 8. Lasserre, J. P. Martin, and F. Roubellat, Aggregate Mode] and Decomposition for Mid-term Production planning

S. R. Lavùrence and T. E. Morton, patriarch: Hierarchical Productj-on_ Schedul1n9l, {:f :S. SpeciaJ publication 724, R, 1993.

. Tl-el, M. Lefkowttz-'r, K. , and J. M. Proth, MurtiLevel Approach Applied to controt-system Designscheduling in Large Scal-e production Systems: a Medium Term Production Management Model, Proc. of t.he 2nd International Conference on Production Systems

M. M. Tmcl, D. Màcko, and Y. Takahara, Theory of MuTtilevel Hierarchical Systems

M. E. and T. L. , SMUNT, nA Planning and Scheduling SyBtem for Flexibl-e Manuf acturing, FLexibl-e Mauf acturing Systems.r Iûethods and Studies, 1986.

I. Nevùson and E. F. , Multi-rtem Lot Size Scheduling by HeurisÇic Part r : with Fixed ResourcesMulti-rtem Lot Size Scheduling by Heuristic Part rr : with variabre Resources, I975. tNE2l NEhISoN

G. , P. J. , U. Menon-olson, C. D. Papas, P. N. Pendrock et al., A Hierarchy of rntelrigent Scheduling and Control for Automated Manufacturing SystemsA Prototype system f or Hierarchicar prodllct ion PIànning Speci a J tPNl PARNABY' J.t "Concept of a Manufacturing SystemA Hierarchicat Approach to rntegrated Production and Distribution Planning, unpublished M.s. thesis, M.I.T., References tsHl SHAW, M., trA Two-r,ever planning and scheduring Approach for Computer Integrated Manufacturing.", N.B.S. SpeciaT publication 724, 1975.

R. J. Tsol-shoenberger and J. , Some observations Implementation fssues of Just-in-Time Journal-of Operatjons Management, VoI. 3, on the Advantages and Production Systems Interact ion between Aggregate Scheduling in a Job Shop, tS! SINGH' M.G. Dynamical HierarchicaL Control, 1972.

M. G. Stngh, S. A. Dreht, and J. F. Coalest, ,comparison of Practical Hierarchical Control Methods for rnterconnected Dynamical Systems, Automatica, vol.LL, 1975.

'. M. Tstl-sfngh and A. Titli, Closed Loop Hierarchical Control-for Non-linear Systems Using QuasilinearisationAn Introduction to Hierarchical Systems Theory, Automatica, VoI, vol.11, 1975.

A. Tvcl-vrlla, E. Canuto, and . Rossetto, A Hierarchicar part Routing control scheme for Frexible Manufacturing systemsD.R.-rtary on Ad.vances in rnformational-Àspects of rndustrial Automation, Berlin, 19g5. vrLLA' A. ' A. coNTr ' F. LOMBARDT and s. RossETTo, "A Hierarchical Approach Moder and control_ Manufacturing systems, Proc. of the 3rd BiJ-ateral Meeting G Materiar F7ow, speciaT rssue on Materiar Handling -in Fl-exibl_e Manufacturing Systems

R. Vi\, G. Mosca, and . Muràrr, Expert control Theory : a Key ryol for Solving Production planning and Manufacturing Control Problems in Flexible IEEE Conf. on Robotic and tvRl vrLLA' A. and s. RossETToTowards a Hierarchicar Production planning and Control in Flexible Systems Structure for Manufacturing Manufacturing, Proc. oî the j-9A6 Automation ModeTing and Design of Flexible Systems, 1986.

H. M. Iwwj-hiagner and T. M. Hihrtrn, Dynamic version of the Economic Lot Size Problem, Management Seience, vol.5

L. A. Twll-i-'ùashrngton and A. H. Levts, Ef fectiveness Ànalysis of Flexible Manufacturing Systems, Proc. of the j-986 IEEE Conf. on Robotic and Automation