2007
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The Hypergeometric Coupon Collection Problem and its Dual
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2
Suppose an urn contains M balls, of different types, which are removed from the urn in a uniform random manner. In the hypergeometric coupon collection problem, we are interested in the set of balls that have been removed at the moment when at least one ball of each type has been removed. In its dual, we are interested in the set of removed balls at the first moment that this set contains all of the balls of at least one type.
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7


Sheldon M.
Ross
Epstein Department of Industrial and Systems Engineering , University of Southern California,
Los Angeles, CA, USA
Epstein Department of Industrial and Systems
Iran
Hypergeometric
Dual
Coupon collection problem
[[1] Adler I., Oren S., Ross S. M. (2003), The coupon collector’s problem revisited; Journal of Applied##Probability, 40; 513518.##[2] ElNeweihi E., Proschan F., Sethuraman J. (1978), A simple model with applications in structural##reliability, extinction of species, inventory depletion and urn sampling; Advances in Applied Probability,##10(1); 232254.##[3] Ross S. M. (2002), Probability models for computer science, Academic Press.##[4] Ross S. M., Shahshahani, M., Weiss G. (1980), On the number of component failures in systems whose##component lives are exchangeable, Mathematics of Operations Research, 5(3); 358365##]
A Quartic Quality Loss Function and Its Properties
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2
We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions in the context of their industrial applications and use them in a mathematical programming model for the parameter design problem.
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8
22


Yahya
Fathi
1,2Department of Industrial and Systems Engineering, North Carolina State University Raleigh,
NC 276957906, USA
1,2Department of Industrial and Systems Engineerin
Iran


Chanwut
Poonthanomsook
Department of Industrial and Systems Engineering, North Carolina State University Raleigh,
NC 276957906, USA
Department of Industrial and Systems Engineering,
Iran
Quality cost
Continuous loss function
Parameter design problem
[[1] Bazaraa Mokhtar S., Shetty C.M. (1979), Nonlinear programming, theory and algorithm, Wiley.##[2] Box G.E.P. (1988), Signaltonoise ratio, performance criteria, and transformations; Technometrics 30;##[3] Evans David H. (1975), Statistical tolerancing: The state of the art part II. methods for estimating##moments; Journal of Quality Technology 7; 112.##[4] Fathi Y. (1990), Producerconsumer tolerances; Journal of Quality Technology 22; 138145.##[5] Fathi Y. (1997), A linear approximation model for the parameter design problem; European Journal of##Operational Research 97; 561570.##[6] ––––, Palko D. (2001), A mathematical model and a heuristic procedure for the robust design problem##with highlow tolerances; IIE Transactions 33; 11211127.##[7] Fowlkers William Y., Creveling Clyde M. (1997), Engineering Methods for Robust Product Design:##Using Taguchi Methods in Technology and Product Development, AddisonWesley.##[8] Leon R., Shoemaker A.C., Kackar R.N. (1987), Performance measures independent of adjustment##(with discussions); Technometrics 29; 253285.##[9] Leung Bartholomew P. K., Spiring Fred A. (2002), The inverted Beta loss function: properties and##applications; IIE Transactions 34; 11011109.##[10] Phadke Madhav S. (1989), Quality engineering using robust design, Prentice Hall.##[11] Spiring F.A. (1993), The reflected normal loss function; Canadian Journal of Statistics 21(3); 321##[12] Spiring F.A., Yeung A.S. (1998), A general class of loss functions with industrial applications; Journal##of Quality Technology 30(2); 152162.##[13] Sun F. B., Laramee J. Y., Ramberg J.S. (1996), On Spiring’s normal loss function; Canadian Journal##of Statistics 24(2); 241249.##[14] Taguchi G. (1978), Offline and online quality control system; International Conference on Quality##Control, Tokyo, Japan.##[15] ––––– (1986), Introduction to Quality Engineering, Asian Productivity Organization.##[16] –––––, Elsayed Elsayeda A., Hsiang Thomas (1989), Quality engineering in production systems,##McGrawHill.##[17] Tukey John W. (1957), Propagation of errors, fluctuations and tolerances, No. 1: Basic generalized##formulas; Technical Report No. 10, Princeton University, Princeton, NJ.##]
Development of a Set of Algorithms for the MultiProject Scheduling Problems
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In this paper, the problem of determining the best schedule for a set of projects has been modeled in the form of a generalized tardiness flowshop (GTF) problem. We develop a set of heuristic algorithms for minimizing the total tardiness of jobs in a GTF problem. In the generalized version of tardiness flowshop problems, a job is considered to be a collection of operations and there is a due date associated with the completion of each operation on each machine. Four algorithms based on the concept of “apparent tardiness cost” (ATC) are developed for solving the GTF problem. The relative effectiveness of the developed algorithms will then be evaluated through an extensive computational experiment.
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23
36


Farhad
GhassemiTari
Department of Industrial Engineering, Sharif University of Technology, Iran
Department of Industrial Engineering, Sharif
Iran


Laya
Olfat
School of Management, Tabtabaei University, Iran
School of Management, Tabtabaei University,
Iran
Generalized tardiness flowshop
Multiproject scheduling
Intermediate due date
Apparent tardiness cost
[[1] Allahverdi A. (2004), A new heuristic for mmachine flow shop scheduling problem with bicriteria##of makespan and maximum tardiness; Computers & Operations Research 31(2); 157180.##[2] Baker K.R., Bertrand J.W.M. (1982), A Dynamic priority rule for sequencing against due dates;##Journal of Operational Management 3(1); 3742.##[3] Baker K.R. (1984), Sequencing rules & due date assignments in a job shop; Management Science##30(9); 10931104.##[4] Bilge U., Kirac F., Kurtulan M., Pekgun P. (2004), A tabu search algorithm for parallel machine total##tardiness problem; Computers & Operations Research 31( 3); 397414.##[5] Carroll D.C. (1965), Heuristic sequencing of jobs with single & multiple components, Ph.D.##dissertation, Sloan School of Management, MIT, Mass.##[6] Chakravarthy K., Rajendran C. (1999), A heuristic for scheduling in a flowshop with the bicriteria of##makespan and maximum tardiness minimization; Production planning and control, 10(7); 701714.##[7] Chio S.W., Lee G.C., Kim Y.D. (2005), Minimizing total tardiness of orders with reentrant lots in a##hybrid flow shop; International Journal of Production Research, 43( 11); 21492167.##[8] Etiler O., Toklu B., Atak M., Wilson J. (2004), A generic algorithm for flow shop scheduling##problems; Journal of Operations Research Society, 55( 8); 830835.##[9] GhessmiTari F., Olfat L. (2004), Two COVERT based algorithms for solving the generalized flowshop##problems; Proceedings of the 34th International Conference on Computers and Industrial##Engineering, 2937.##[10] Gupta N.D., Kruger K., Lauff V., Werner F., Sotskov Y.N. (2002), Heuristics for hybrid flow shops##with controllable processing times and assignable due dates; Computers & Operations Research, 29(##10); 14171439.##[11] Lee G.C., Kim Y.D. (2004), A branch and bound for a two stage hybrid flow shop scheduling##problem minimizing total tardiness; International Journal of Production Research 42( 22); 4731##[12] Lee L. (2001), Artificial intelligence search methods for multimachine twostage scheduling with##due date penalty, inventory, and machining costs; Computers & Operations Research 28( 9); 835##[13] Lin H.T., Liao C.J. (2003), A case study in a twostage hybrid flow shop with setup time and##dedicated machines; International Journal of Production Economics 86(2); 133143.##[14] Linn R., Zhang W. (1999), Hybrid flowshop scheduling: a survey; Computers & Industrial##Engineering 37( 1&2); 5761,##[15] Mosheiov G. (2003), Scheduling unit processing time jobs on an mmachine flowshop; Journal of##the Operations Research Society 54( 4); 437441##[16] Olfat L. (1998), Development of a set of algorithms for flowshop tardiness problems, Ph.D.##dissertation, School of Management, University of Tehran, Tehran, Iran.##[17] Parthasarathy S., Rajendran C. (1998), Scheduling to minimize mean tardiness and weighted##tardiness in flowshop and flowlinebased manufacturing cell; Computers & Industrial Engineering##34(2); 431546.##[18] Rachamaduagu R.V., Morton T.E. (1982), Myopic heuristic for the single machine weighted##tardiness problem, working paper #388283, GsIA, Carnegie Mellon University.##[19] Rachamaduagu R.V. (1984), Myopic heuristic in open shop scheduling, modeling & simulation,##Proceedings of the 14 Annual Pittsburgh Conf., 12451250.##[20] Sapar H., Henry M.C. (1996), Combinatorial Evaluation of six dispatching rules in dynamic two##machine flowshop; International Journal of Management Science 24,( 1); 7381.##[21] Vepsalainen A.P.J., Morton T.E. (1987), Priority rules for job shops with weighted tardiness costs;##Management Science 23(8); 10351047.##[22] Yeh W., Allahverdi A. (2004), A branch and Bound algorithm for the three machine flow shop##scheduling problem with bicriteria of makespan and total flow time; International Transaction in##Operations Research 11(3); 323332.##]
A Multiprocessor System with NonPreemptive EarliestDeadlineFirst Scheduling Policy: A Performability Study
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This paper introduces an analytical method for approximating the performability of a firm realtime system modeled by a multiserver queue. The service discipline in the queue is earliestdeadline first (EDF), which is an optimal scheduling algorithm. Realtime jobs with exponentially distributed relative deadlines arrive according to a Poisson process. All jobs have deadlines until the end of service and are served nonpreemptively. An important performance measure to calculate is the loss probability. The performance of the system is approximated by a Markovian model in the long run. A key parameter, namely, the loss rate when there are n jobs in the system is used in the model, which is estimated by partitioning the system into two subsystems. The resulting model can then be solved analytically using standard Markovian solution techniques. The number of servers in the system may change due to failure or repair. The performability of the system is evaluated in the presence of such structural changes. The latter measure is approximated by a Markov reward model, considering the loss probability as the reward rate. Comparing numerical and simulation results, we find that the existing errors are relatively small.
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55


Mehdi
Kargahi
Department of Electrical and Computer Engineering, University of Tehran,Tehran, Iran
Department of Electrical and Computer Engineering,
Iran


Ali
Movaghar
Department of Computer Engineering, Sharif University of Technology, Tehran,Iran
Department of Computer Engineering, Sharif
Iran
Analytical methods
Earliestdeadlinefirst (EDF)
Firm realtime systems
Multiprocessor systems
Nonpreemptive scheduling
Performability modeling
[[1] AlEnavy T.A., Aydin H. (2005), Energyconstrained scheduling for weaklyhard realtime systems;##Proceedings of the 26th IEEE RealTime Systems Symposium (RTSS’05); 376385.##[2] Baccelli F., Boyer P., Hebuterne G. (1984),Singleserver queues with impatient customers; Advanced##Applied Probability 16; 887905.##[3] Barrer D.Y. (1957), Queueing with impatient customers and ordered service; Operational Research##5; 650 656.##[4] Bernat G., Burns A., Llamosi A. (2001), Weakly hard realtime systems; IEEE Transactions on##Computers 50 (4); 308321.##[5] Brandt A., Brandt M. (1999), On the M(n)/M(n)/s queue with impatient calls; Performance##Evaluation 35; 118.##[6] Brandt A., Brandt M. (2002), Asymptotic results and a Markovian approximation for the##M(n)/M(n)/s+GI system; Queueing Systems 41; 7394.##[7] Cohen J.W. (1968), Single server queue with uniformly bounded virtual waiting time; Journal of##Applied Probability 5; 93122.##[8] Daley D.J. (1965), General customer impatience in queue GI/G/1; Journal of Applied Probability 2;##[9] Deavours D.D., Clark G., Courtney T., Daly D., Derisavi S., Doyle J.M., Sanders W.H., Webster##P.G. (2002), The Mobius framework and its implementation; IEEE Transactions on Software##Engineering 28(10); 956969.##[10] Dolev S., Keizelman A. (1999), Nonpreemptive realtime scheduling of multimedia tasks; Real##Time Systems 17(1); 23–39.##[11] Doytchinov B., Lehoczky J., Shreve S. (2001), Realtime queues in heavy traffic with earliestdeadline##first queue discipline; Annals of Applied Probability 11; 332379.##[12] EN 50170 (1996), General purpose field communication system; CENELEC, In European Standard.##[13] George L., Muhlethaler P., Rivierre N. (1995), Optimality and nonpreemptive realtime scheduling##revisited; Rapport de Recherche RR2516, INRIA, Le Chesnay Cedex, France.##[14] George L., Rivierre N., Spuri M. (1996), Preemptive and nonpreemptive realtime uniprocessor##scheduling; Rapport de Recherche RR2966, INRIA, Le Chesnay Cedex, France.##[15] Hong J., Tan X., Towsley D. (1989), A performance analysis of minimum laxity and earliest##deadline scheduling in a realtime system; IEEE Transactions on Computers 38(12); 17361744.##[16] Hsueh M.C., Iyer R. K., Trivedi K.S. (1988), Performability modeling based on real data: A case##study; IEEE Transactions on Computers 37(4); 478484.##[17] Kargahi M., Movaghar A. (2005), Nonpreemptive earliestdeadlinefirst scheduling policy: A##performance study; Proceedings of IEEE International Symposium on Modeling, Analysis, and##Simulation of Computer and Telecommunication Systems (MASCOTS’05); 201210##[18] Kargahi M., Movaghar A. (2006), A method for performance analysis of earliestdeadlinefirst##scheduling policy; Journal of Supercomputing 37(2); 197222.##[19] Kruk L., Lehoczky J., Shreve S., Yeung S.N. (2004), Earliestdeadlinefirst service in heavytraffic##acyclic networks; Annals of Applied Probability 14(3); 13061352.##[20] Lehoczky J.P. (1996), Realtime queueing theory; Proceedings of IEEE RealTime Systems##Symposium; 186195.##[21] Lehoczky J.P. (1997), Using realtime queueing theory to control lateness in realtime systems;##Performance Evaluation Review 25(1); 158168.##[22] Liu C.L., Layland J.W. (1973). Scheduling algorithms for multiprogramming in a hard realtime##environment; Journal of Associative Computational Machinery 20; 4661.##[23] Livani M.A., Kaiser J. (1998), EDF consensus on CAN bus access for dynamic realtime##applications; Proceedings of IEEE Workshop on Parallel and Distributed Computing Systems in##conjunction with 12th International Parallel Processing Symposium / 9th Symposium on Parallel and##Distributed Processing (IPPS/SPDP'98); 10881097.##[24] Meyer J.F. (1982), Closedform solutions of performability; IEEE Transactions on Computers C##31(7); 648657.##[25] Meyer J.F. (1992), Performability: A retrospective and some pointers to the future; Performance##Evaluation 14(34); 139156.##[26] Movaghar A. (1998), On queueing with customer impatience until the beginning of service;##Queueing Systems 29; 337350.##[27] Movaghar A. (2006), On queueing with customer impatience until the end of service; Stochastic##Models 22; 149173.##[28] Palm C. (1953), Methods for judging the annoyance caused by congestion; Tele 2; 120.##[29] Panwar S.S., Towsley D., Wolf J.K. (1988), Optimal scheduling policies for a class of queues with##customer deadlines to the beginning of service; Journal of Associative Computational Machinery##35(4); 832844.##[30] Qiu Q., Wu Q., Pedram M. (2001), Dynamic power management in a mobile multimedia system##with guaranteed qualityofservice; Proceedings of the 38th Conference on Design Automation##(DAC’01); 834839.##[31] Raghunathan V., Schurgers C., Park S., Srivastava M. B. (2002), Energy aware wireless microsensor##networks; IEEE Signal Processing Magazine 19 (2); 4050.##[32] Reibman A.R., Trivedi K.S. (1988), Numerical transient analysis of Markov dependability models;##Computers and Operations Research 15; 1936.##[33] Smith R.M., Trivedi K.S., Ramesh A.V. (1988), Performability analysis: Measures, an algorithm,##and a case study; IEEE Transactions on Computers 37(4); 406417.##[34] Takacs L. (1974), A singleserver queue with limited virtual waiting time; Journal of Applied##Probability 11; 612617.##[35] Towsley D., Panwar S.S. (1990), On the optimality of minimum laxity and earliest deadline##scheduling for realtime multiprocessors; Proceedings of IEEE EUROMICRO90 Workshop on Real##Time; 1724.##[36] Towsley D., Panwar S.S. (1992), Optimality of the stochastic earliest deadline policy for the G/M/c##queue serving customers with deadlines; Second ORSA Telecommunications Conference.##[37] Trivedi K.S., Muppala J.K., Woolet S.P., Haverkort B.R. (1992), Composite performance and##dependability modeling; Performance Evaluation 14; 197215.##[38] Zhao W., Stankovic J.A. (1989), Performance analysis of FCFS and improved FCFS scheduling##algorithms for dynamic realtime computer systems; Proceedings of IEEE RealTime Systems##Symposium; 156165.##[39] CANCIA, ″CAN specification 2.0 Part B″,##http://www.cancia.org/downloads/ciaspecificatios, 1992.##[40] Sanders W.H., ″Mobius user manual″, http://www.mobius.uiuc.edu, 2005##]
Product Development Decision Support System CustomerBased
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Quality Function Deployment (QFD) has been traditionally used as a planning tool primarily for product development and quality improvement. In this context, many people have used QFD for making decisions on how to prioritize critical product areas from a customer perspective. However, it is the position of the author that the QFD process can be viewed as a decision support system that would encompass multiple facets of information to enhance the quality and output of the decision making process in the course of product development. In this paper, the author submits the QFD process in combination with other engineering decision making tools such as the Pugh concept selection and the KepnerTregoe analysis technique as a decision making and modeling process that is as old as management science itself. Specifically, the attempt is made to illustrate how QFD provides an iterative sequence of steps involved in decision making, from the initial problem identification to a proposal for the actual implementation plan. To make this position more applicable to the reader, the subject has been approached from an actual business environment.
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Kioumars
Paryani
College of Management, Lawrence Technological University, Southfield, MI, USA
General Motors Corporation, R & D and Strategic Planning Technical Fellow Retiree, Warren, MI,
USA
College of Management, Lawrence Technological
Iran
Quality Function Deployment (QFD)
Voice of the Customer (VOC)
Decision making process
Customerdriven decision making process
KepnerTregoe analysis
Pugh concept selection
Models
[[1] Altshuller G. (1996), And suddenly the inventor appeared: TRIZ, the theory of inventive problem##solving (TIPS); 2nd ed., Technical Innovation Center, Inc.##[2] Chowdhury S. (2002), Design for six sigma: The revolutionary process for achieving extraordinary##profits; 1st ed., Dearborn Trade, Kaplan Professional Company.##[3] Howard R. A. (1980), An assessment of decision analysis; Operations Research 28(1); 427.##[4] KepnerTregoe Inc. (1977), Problem solving, decision making, and planning. Training Manual,##Transportation Hardware, Inc. (THINC), Toledo, Ohio.##[5] Pugh S. (1991), Total design: Integrated methods for successful product engineering, Addison##Wesley Publishing Company Inc.; Reading, MA.##[6] Simon H. (1977), The new science of management decisions. Revised edition, PrenticeHall;##Englewood Cliffs, NJ.##[7] Turban E. (1990). Decision support and expert systems: Management support systems. Second##edition, Macmillan Publishing Co.; New York, NY.##]
A Project Scheduling Method Based on Fuzzy Theory
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In this paper a new method based on fuzzy theory is developed to solve the project scheduling problem under fuzzy environment. Assuming that the duration of activities are trapezoidal fuzzy numbers (TFN), in this method we compute several project characteristics such as earliest times, latest times, and, slack times in term of TFN. In this method, we introduce a new approach which we call modified backward pass (MBP). This approach, based on a linear programming (LP) problem, removes negative and infeasible solutions which can be generated by other methods in the backward pass calculation. We drive the general form of the optimal solution of the LP problem which enables practitioners to obtain the optimal solution by a simple recursive relation without solving any LP problem. Through a numerical example, calculation steps in this method and the results are illustrated.
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70
80


Ahmad
Soltani
Sharif University of Technology and Engineering Research Institute, Ministry of
Agricultural Jahad, P. O. Box: 13445754, Tehran, Iran
Sharif University of Technology and Engineering
Iran


Rasoul
Haji
Department of Industrial Engineering, Sharif University of Technology, P. O Box:
113659414, Tehran, Iran
Department of Industrial Engineering, Sharif
Iran
Project scheduling
Fuzzy theory
Modified backward pass (MBP)
Trapezoidal fuzzy number (TFN)
Linear programming (LP)
[[1] Chanas S., Kamburowski J. (1981), The use of fuzzy variables in PERT; Fuzzy Sets and Systems 5(1);##[2] Chanas S., Zielinski P. (2001), Critical path analysis in the network with fuzzy activity times; Fuzzy##Sets and Systems 122; 195204.##[3] Chang S., Tsujimura Y., Tazawa T. (1995), An efficient approach for large scale project planning##based on fuzzy delphi method; Fuzzy Sets and Systems 76; 277288.##[4] Chen S. J., Hwang C. L. (1992), Fuzzy multiple attribute decision making: methods and applications;##Lecture notes in economics and mathematical systems, SpringerVerlag; Berlin, Germany.##[5] Dubois D., Prade H. (1988), Possibility theory: an approach to computerized processing of uncertainly;##Plenum Press; New York.##[6] Gazdik I. (1983), Fuzzynetwork planningFNET; IEEE Transactions Reliability 32(2); 304–313.##[7] Kaufmann A., Gupta M. (1985), Introduction to fuzzy arithmetic theory and applications; Van##Nostrand Reinhold; New York.##[8] Kuchta D. (2001), Use of fuzzy numbers in project risk (criticality) assessment; International Journal##of Project Management 19; 305310.##[9] Lin F.T., Yao J.S. (2003), Fuzzy critical path method based on signeddistance ranking and statistical##confidenceinterval estimates; Journal of Supercomputing 24(3); 305325.##[10] Lorterapong P., Moselhi O. (1996), Projectnetwork analysis using fuzzy sets theory; Journal of##Construction Engineering and Management 122(4); 308318.##[11] McCahon C.S. (1993), Using PERT as an approximation of fuzzy projectnetwork analysis; IEEE##Transactions on Engineering Management 40(2); 146153.##[12] Nasution S.H. (1994), Fuzzy critical path method; IEEE Transactions on Systems, MAN, AND##Cybernetics 41(1); 4857.##[13] Oliveros A., Robinson A. (2005), Fuzzy logic approach for activity delay analysis and schedule##updating; J. Constr. Engrg. and Mgmt. 131(1); 4251.##[14] Yao J.S., Lin F.T. (2000), Fuzzy critical path method based on signed distance ranking of fuzzy##numbers; IEEE Transactions on Systems, MAN, AND Cybernetics 30(1); 7682.##[15] Zimermann H.J. (1996), Fuzzy set theoryand its applications; Third Edition, Kluwer Academic##Publishers; Boston.##]
Layout Design of a Furniture Production Line Using Formal Methods
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This paper experiments application of different heuristic approaches to a real facility layout problem at a furniture manufacturing company. All the models are compared using AHP, where a number of parameters of interest are employed. The experiment shows that formal layout modelling approaches can be effectively used real problems faced in industry, leading to significant improvements.
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81
96


Pinto
Wilsten J.
Faculty of Engineering, Swinburne University of Technology, Hawthorn, Victoria, Australia
Faculty of Engineering, Swinburne University
Iran


E.
Shayan
Faculty of Engineering, Swinburne University of Technology, Hawthorn, Victoria, Australia
Faculty of Engineering, Swinburne University
Iran
Facilities layout design
Layout algorithms
Optimisation
Production lines
[[1] Banerjee P., Zhou Y. (1995), Facilities layout design optimization with single loop material flow##path configuration; Int. Journal of Production Research 33(1); 183204.##[2] Banerjee P., Zhou Y., Montreuil B. (1997),Genetically assisted optimization of cell layout and##material flow path skeleton; IIE Trans 29(4); 277292.##[3] Bozer Y.A, Meller R.D., Erlebacher S.J. (1994), An improvement type layout algorithm;##International Journal of Production Research 1; 16751692.##[4] Buffa E.S., Armour G.C., Vollman T.E. (1964), Allocating facilities with CRAFT; Harvard Business##Review 42; 136159.##[5] DeAlvarenga A.G., Gomes N.J., Mestria M. (2000), Metaheuristic methods for a class of the facility##layout problems; Journal of Intelligent Manufacturing 11; 421430.##[6] Domschke W., Drexl A. (1985), Location and layout planning, An international bibliography;##Springer Verlag, Berlin.##[7] Foulds L.R., Robinson D.F. (1976), A strategy for solving the plant layout problem; Operational##Research Quarterly 27; 845855.##[8] Francis R.L., McGinnis Jr. L.F., White J.A. (1992), 2nd Ed, Facility layout and location, An##analytical approach; Prentice Hall; Englewood Cliffs, NJ.##[9] Fu M.C., Kaku B.K. (1997), Minimizing work in progress and material handling in the facilities##layout problem; IIE Trans 29; 2936.##[10] Giffin J.W., Foulds L.R. Cameron D.C. (1984), Drawing a block plan from a REL chart with graph##theory and microcomputer; Computers & Industrial Engineering 10; 109116.##[11] Green R.H., AlHakim L. (1985), A heuristic for facilities layout planning; OMEGA, International##Journal of Management Science 13; 469474.##[12] Hassan M.M.D., Hogg G.L. (1991), On constructing a block layout by graph theory;##International Journal of Production Research 29; 12631278.##[13] Heragu S.S. (2007), 2nd Ed, Facilities Design; iUniverse Inc., NY.##[14] Hicks P.E., Lowan T.E. (1976), CRAFTM for layout rearrangement; Industrial Engineering 8(5);##[15] Houshyar A., White B. (1993), Exact optimal solution for facility layout – deciding which pairs of##locations should be adjacent; Computers and Industrial Engineering 24(2); 287290.##[16] Kim J.Y., Kim Y.D. (1985), Graphic theoretic for unequal sized facility layout problems; OMEGA,##International Journal of Management Science 23; 391401.##[17] Koopmans T.C., Beckmann M. (1957), Assignment problems and the location of Economic##Activities; Econometrica 25(1), 5376.##[18] Leung J.A. (1992), A new graph theoretic heuristic for facility layout, Management Science 38; 554##[19] Meller R.D., Narayanan V., Vance P.H. (1998), Optimal facility layout design; Operation Research##Letters 23;117127.##[20] Muther R. (1955), Practical plant layout; McGrawHill; New York, NY.##[21] Otten R.H.J.M. (1982), Automatic floor plan design; Proceedings of the 19th ACMIEEE##DesignAutomation Conference; 261267.##[22] Palekar V.S., Batta R., Bosch R.M., Elhence S. (1992), Modeling uncertainties in plant layout##problems; European Journal of Operations Research 63(2); 347359.##[23] Rosenblatt M.J. (1986), The dynamics of plant layout; Management Science 32(1); 7686.##[24] Satty T.L. (1980), Analytical hierarchic process; McGraw Hill; New York.##[25] Shang J.S. (1993), Multicriteria facility layout problem An integrated approach; European Journal##of Operational Research; 66(3); 291304 .##[26] Shayan E., AlHakim L., 1999. "Cloning in layout design problem: A genetic algorithm approach."##Proceedings of the 15th International Conference on Production Research; Hillery, M., Lewis, H.##Eds.), University of Limerick, Ireland; 787792.##[27] Shayan E., Chittilappilly A.(2004) , Genetic algorithm for facilities layout problems based on slicing##tree structure; Int. J Production Research; 42(19); 4055–4067.##[28] Tam K.Y., Chan S.K. (1998), Solving facility layout problems with geometric constraints using##parallel genetic algorithms: experimentation and findings; International Journal of Production##Research 36(12); 34113423.##[29] Tam K.Y., Li S.L. (1991), A hierarchal approach to facility layout problem; International Journal##Production Research, 29; 165184.##[30] Tompkins J.A., White J.A. (1984), Facilities planning; John Wiley & Sons, NY##]