2016
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‘BALANCING AND SEQUENCING’ VERSUS ‘ONLY BALANCING’ IN MIXED MODEL ULINE ASSEMBLY SYSTEMS: AN ECONOMIC ANALYSIS
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2
With the growth in customers’ demand diversification, mixedmodel Ulines (MMUL) have acquired increasing importance in the area of assembly systems. There are generally two different approaches in the literature for balancing such systems. Some researchers believe that since the types of models can be very diverse, a balancing approach without simultaneously sequencing of models will not yield an optimum configuration. On the other hand, another group of researchers point to the high cost of balancing systems and prefer to do it only one time regardless of the models’ sequences. In this paper, we aim to compare these two approaches by introducing an economic indicator. To do so, two models as representatives of the two different viewpoints are taken from the literature. To check the validity of this methodology, it is implemented by Lingo 11.0, for small scale, and GA, for a large scale. The obtained results indicate that, from the proposed economic indicator point of view, mixedmodel Ulines balancing and sequencing (MMUL/BS) is preferred to its counterpart, mixedmodel Ulines balancing (MMULB). This paper offers economic guidelines for managers to choose between only balancing and implementing it by sequencing at the same time.
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1
17


Masoud
Rabbani
College of Engineering, University of Tehran
Iran, Islamic Republic of
Industrial Engineering
College of Engineering, University of Tehran
Iran
Iran


Zohreh
ZahedianTejenaki
School of Industrial Engineering, College of Engineering, University of Tehran
Iran, Islamic Republic of
School of Industrial Engineering, College
Iran


Farnoush
Otrody
School of Industrial Engineering, College of Engineering, University of Tehran
Iran, Islamic Republic of
School of Industrial Engineering, College
Iran


Amir
FarshbafGeranmyeh
School of Industrial Engineering, College of Engineering, University of Tehran
Iran, Islamic Republic of
School of Industrial Engineering, College
Iran
Mixed model Ulines
Assembly line balancing
Assembly line balancing and Sequencing
Cost index
Genetic Algorithm
[S. Agrawal, M. Tiwari, A collaborative ant colony algorithm to stochastic mixedmodel Ushaped disassembly line balancing and sequencing problem, International Journal of Production Research, 46 (2008) 14051429. ##S. Akpınar, G. M. Bayhan, A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints, Engineering Applications of Artificial Intelligence, 24(2011) 449457. ##D. Battini, M. Faccio, A. Persona, F. Sgarbossa, Balancing–sequencing procedure for a mixed model assembly system in case of finite buffer capacity, The International Journal of Advanced Manufacturing Technology, 44(2009) 345359. ##C. Becker, A. Scholl, A survey on problems and methods in generalized assembly line balancing, European Journal of Operational Research, 168 (2006) 694715. ##N. Boysen, M. Fliedner, A. Scholl, A classification of assembly line balancing problems, European Journal of Operational Research, 183 (2007) 674693. ##G. Buxey, Assembly line balancing with multiple stations, Management science, 20(1974) 10101021. ##A. Hamzadayi, G. Yildiz, A genetic algorithm based approach for simultaneously balancing and sequencing of mixedmodel Ulines with parallel workstations and zoning constraints, Computers & Industrial Engineering, 62(2012) 206215. ##A. Hamzadayi, G. Yildiz, A simulated annealing algorithm based approach for balancing and sequencing of mixedmodel Ulines, Computers & Industrial Engineering, 66(2013) 10701084. ##R. Hwang, H. Katayama, A multidecision genetic approach for workload balancing of mixedmodel Ushaped assembly line systems, International Journal of Production Research, 47 (2009) 37973822. ##R. Hwang, H. Katayama, Integrated procedure of balancing and sequencing for mixedmodel assembly lines: a multiobjective evolutionary approach, International Journal of Production Research, 48(2010) 64176441. ##M. Kamal Uddin, M. Cavia Soto, J. L. Martinez Lastra, An integrated approach to mixedmodel assembly line balancing and sequencing, Assembly Automation, 30(2010) 164172. ##Y. Kara, U. Ozcan, A. Peker, An approach for balancing and sequencing mixedmodel JIT Ulines, The International Journal of Advanced Manufacturing Technology, 32(2007a) 12181231. ##Y. Kara, U. Ozcan, A. Peker, Balancing and sequencing mixedmodel justintime Ulines with multiple objectives, Applied Mathematics and Computation,184(2007b) 566588. ##Y. Kara, Line balancing and model sequencing to reduce work overload in mixedmodel Uline production environments, Engineering Optimization, 40(2008) 669684. ##S. Karabatı, S. Sayın, Assembly line balancing in a mixedmodel sequencing environment with synchronous transfers, European Journal of Operational Research, 149(2003) 417429. ##R. M. Karp, Reducibility among combinatorial problems: Springer, (1972) ##S. M. Kazemi, R. Ghodsi, M. Rabbani, R. TavakkoliMoghaddam, A novel twostage genetic algorithm for a mixedmodel Uline balancing problem with duplicated tasks, The International Journal of Advanced Manufacturing Technology, 55(2011) 11111122. ##Y. K. Kim, J. Y. Kim, Y. Kim, A coevolutionary algorithm for balancing and sequencing in mixed model assembly lines, Applied Intelligence, 13(2000) 247258. ##Y. K. Kim, J. Y. Kim, Y. Kim, An endosymbiotic evolutionary algorithm for the integration of balancing and sequencing in mixedmodel Ulines, European Journal of Operational Research, 168(2006) 838852. ##N. Kriengkorakot, N. Pianthong, The Uline Assembly Line Balancing Problem, KKU Engineering Journal, 34(2007) 267274. ##I. Kucukkoc, D. Z. Zhang, Simultaneous balancing and sequencing of mixedmodel parallel twosided assembly lines, International Journal of Production Research, 52(2014) 36653687. ##K. Lian, C. Zhang, L. Gao, X. Shao, A modified colonial competitive algorithm for the mixedmodel Uline balancing and sequencing problem, International Journal of Production Research, 50(2012) 51175131. ##N. Manavizadeh, M. Rabbani, F. Radmehr, A new multiobjective approach in order to balancing and sequencing Ushaped mixed model assembly line problem: a proposed heuristic algorithm, Int J Adv Manuf Technol, 36(2015) 485501. ##C. Merengo, F. Nava, A. Pozzetti, Balancing and sequencing manual mixedmodel assembly lines, International Journal of Production Research, 37(1999), 28352860. ##J. Miltenburg, Balancing and scheduling mixedmodel Ushaped production lines, International Journal of Flexible Manufacturing Systems, 14(2002) 119151. ##H. Mosadegh, M. Zandieh, S. F. Ghomi, Simultaneous solving of balancing and sequencing problems with stationdependent assembly times for mixedmodel assembly lines, Applied Soft Computing, 12(2012) 13591370. ##A. Nourmohammadi, M. Zandieh, R. TavakkoliMoghaddam, An imperialist competitive algorithm for multiobjective Utype assembly line design, Journal of Computational Science, 4(2013) 393400. ##U. Özcan, H. Çerçioğlu, H. Gökçen, B. Toklu, Balancing and sequencing of parallel mixedmodel assembly lines, International Journal of Production Research, 48(2010) 50895113. ##U. Özcan, T. Kellegöz, B. Toklu, A genetic algorithm for the stochastic mixedmodel Uline balancing and sequencing problem, International Journal of Production Research, 49(2011) 16051626. ##M. Rabbani, S. M. Kazemi, N. Manavizadeh, Mixed model Uline balancing type1 problem: A new approach, Journal of Manufacturing Systems, 31(2012) 131138. ##A. RahimiVahed, A. H. Mirzaei, A hybrid multiobjective shuffled frogleaping algorithm for a mixedmodel assembly line sequencing problem, Computers & Industrial Engineering, 53(2007) 642666. ##M. F. F. Rashid, W. Hutabarat, A. Tiwari, A review on assembly sequence planning and assembly line balancing optimisation using soft computing approaches, The International Journal of Advanced Manufacturing Technology, 59(2012) 335349. ##J. Riezebos, Order sequencing and capacity balancing in synchronous manufacturing, International Journal of Production Research, 49(2011) 531552. ##M. E. Salveson, The assembly line balancing problem, Journal of Industrial Engineering, 6(1955) 1825. ##D. Sparling, J. Miltenburg, The mixedmodel Uline balancing problem, International Journal of Production Research, 36(1998) 485501. ##H.E. Tseng, C.E. Tang, A sequential consideration for assembly sequence planning and assembly line balancing using the connector concept, International Journal of Production Research, 44(2006) 97116.##]
FIXED POINT THEOREM OF KANNANTYPE MAPPINGS IN GENERALIZED FUZZY METRIC SPACES
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2
Binayak et al in [1] proved a fixed point of generalized Kannan
typemappings in generalized Menger spaces. In this paper we extend gen
eralized Kannantype mappings in generalized fuzzy metric spaces. Then we
prove a fixed point theorem of this kind of mapping in generalized fuzzy metric
spaces. Finally we present an example of our main result.
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19
27


Esmaeil
Feizi
BuAli Sina university
Iran, Islamic Republic of
BuAli Sina university
Iran, Islamic Republic
Iran
Generalized Fuzzy metric space
Kannantype mappings
Generalized Kannantype mappings
fixed point
[Binayak S. Choudhury and Kirshnapada Das, Fixed point of generalized Kannantype mappings in generalized menger spaces, Commun. Korean. Math. Soc., 24 (2009), No. 4,529537. ##A. Branciari, A fixed point theorem of BanachCaccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57(2000), no. 12, 3137. Kaleva[3] R. Chugh and S. Kumar, Weakly compatible maps in generalized fuzzy metric spaces, J. Analysis. 10 (2002) 6574. ##Pratulanada Das and Lakshmi Kanta Dey, A fixed point theorem in generalized metric spaces, Soochow Journal of mathematics, No., 1 (2007) 3339. ##Z. K. Deng, Fuzzy pseudometric spaces, J. Math. Anal. Appl., 86 (1982) 7495. ##C. Dibari and C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math. 13(2005) 973982. ##A. George and P. Veeramani, On some results in metric spaces, Fuzzy Set and System., 64 (1994) 395399. ##M. Grabiec, Fixed point in fuzzy metric spaces, Fuzzy Set and System., 27 (1988) 385389. ##R. Kannan, Some result on fixed points, Bull. Calcutta Math. Soc., 60 (1968) 7176. ##I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika. 11 (1975) 336344. ##K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535537. ##P. V. Subrahmanyam, Completeness and xed points, Monatsh, Math. 80(1975) 325330. ##L. A. Zadeh, Fuzzy sets, Inform and Control, 8(1965) 338353.##]
AN LPLQVERSION OF MORGAN’S THEOREM FOR THE GENERALIZED BESSEL TRANSFORM
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2
n this article, we prove An LpLqversion of Morgan’s theorem
for the generalized Bessel transform.
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29
35


Ahmed
Abouelaz
Iran


Radouan
Daher
Iran


Loualid El
Mehdi
Morocco
Morocco
Iran
Generalized Bessel transform
uncertainty principle
LpLqversion of Morgan’s theorem
INVENTORY MODEL FOR DETERIORATING ITEMS WITH REVENUE SHARING ON PRESERVATION TECHNOLOGY INVESTMENT UNDER PRICE SENSITIVE STOCK DEPENDENT DEMAND
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2
The objective of this research is to tackle the emerging problem of jointly determining theoptimal retail price, the replenishment cycle, and the cost of preservation technology investment from an integrated perspective among the supplier and the manufacturer. This paper deals an integrated singlemanufacturer singleretailer supply chain model for deteriorating items under revenue sharing on preservation technology investment. The proposed model is developed under the contract that the manufacturer offers the retailer for a percentage of revenue sharing on preservation technology investment. The market demand is assumed to be dependent on both the onhand stock and price, and the manufacturer & the retailer are in an agreement of lotforlot policy. Numerical & graphical analysis is given to illustrate the model.
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37
48


vinod kumar
Mishra
B T kumaon Institute of Technology,Dwarahat, Almora,Uttarakhand, India
India
Computer Science, Assistant Professor
B T kumaon Institute of Technology,Dwarahat,
Iran
THE REVIEW OF ALMOST PERIODIC SOLUTIONS TO A STOCHASTIC DIERENTIAL EQUATION
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2
This paper proves the existence and uniqueness of quadratic mean almost periodic mild solutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.
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49
59


Siavosh
Ahmadi
Tehran north branchAzad Universityiran
Iran, Islamic Republic of
I'm an Assistant Professor of Applied Mathematics at the University of Azad university. I received my doctorate in Fluid mechanics fro pune University. My recent publication
Tehran north branchAzad Universityiran
Iran,
Iran
Stochastic dierential equations
quadratic mean almost periodic
analytic semigroups of linear operators
[Acquistapace, P., Terreni, B.: A unied approach to abstract linear nonautonomous parabolic equa ##tions. Rend. Sem. Mat. Univ. Padova 78, 47107 (1987) ##Bezandry, P., Diagana, T.: Existence of almost periodic solutions to some stochastic dierential equa ##tions. Appl. Anal. 86, 819827 (2007) ##Bezandry, P., Diagana, T.: Squaremean almost periodic solutions nonautonomous stochastic dier ##ential equations. Electron. J. Dier. Equ. 2007, 110 (2007) ##REFERENCES 11 ##Bezandry, P.: Existence of almost periodic solutions to some functional integro dierential stochastic ##evolution equations. Stat. Probab. Lett. 78, 2844 2849 (2008) ##Bezandry, P., Diagana, T.: Existence of S2almost periodic solutions to a class of nonautonomous ##stochastic evolution equations, Electron. J. Qual. Theory Dier. Equ. 35, 119 (2008) ##Bezandry, P., Diagana, T.: Existence of quadraticmean almost periodic solutions to some stochastic ##hyperbolic dierential equations. Electron. J. Dier. Equ. 2009, 114 (2009) 13 ##Cao, J., Yang, Q., Huang, Z., Liu, Q.: Asymptotically almost periodic solutions of stochastic functional ##dierential equations. Appl. Math. Comput. 218, 1499 1511 (2011) ##Corduneanu, C.: Almost Periodic Functions, 2nd edn. Chelsea, New York (1989) ##Da Prato, G., Zabczyk, J.: Stochastic Equations in Innite Dimensions. Cambridge University Press, ##Cambridge (1992) ##Dorogovtsev, A.Ya., Ortega, O.A.: On the existence of periodic solutions of a stochastic equation in ##a Hilbert space. Visnik Kiiv. Univ. Ser. Mat. Mekh. 115, 2130 (1988) ##Hernandez E.M., Pelicer, M.L., dos Santos J.P.C.: Asymptotically almost periodic and almost periodic ##solutions for a class of evolution equations. Electron. J. Dier. Equ. 2004 115 (2004) ##Hernandez, E., Pelicer, H.L.: Asymptotically almost periodic and almost periodic solutions for partial ##neutral dierential equations. Appl. Math. Lett. 18, 1265 1272 (2005) ##Ichikawa, A.: Stability of semilinear stochastic evolution equations. J. Math. Anal. Appl. 90, 1244 ##Kannan, D., BharuchaReid, D.: On a stochastic integrodierential evolution of volterra type. J. ##Integral Equ. 10, 351379 (1985) ##Lunardi, A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems, PNLDE, vol. 16. ##Birkhauser, Basel (1995) ##N'Guerekata, G.M.: Almost Automorphic Functions and Almost Periodic Functions in Abstract ##Spaces. Kluwer Academic Plenum Publishers, New York (2001) 13 Vol. 63 (2013) Almost Periodic ##Solutions to a Stochastic Dierential Equation 449 ##Pazy, A.: Semigroups of Linear Operators and Applications to Partial Equations, in: Applied Math ##ematical Sciences, Vol. 44. Springer, New York (1983) ##Ren, Y., Xia, N.: Existence, uniqueness and stability of the solutions to neutral stochastic functional ##dierential equations with innite delay. Appl. Math. Comput. 210, 7279 (2009) ##Sakthivel, R., Kim, J.H., Mahmudov, N.I.: On controllability of nonlinear stochastic systems. Rep. ##Math. Phys. 58, 433443 (2006) ##Sakthivel, R., Luo, J.: Asymptotic stability of impulsive stochastic partial dierential equations with ##innite delays. J. Math. Anal. Appl. 356, 16 (2009) ##Sakthivel, R., Luo, J.: Asymptotic stability of nonlinear impulsive stochastic dierential equations. ##Stat. Probab. Lett. 79, 12191223 (2009) ##Tudor, C.: Almost periodic solutions of ane stochastic evolutions equations. Stoch. Stoch. Rep. 38, ##266 (1992) ##Xie, B.: Stochastic dierential equations with nonlopschitz coecients in Hilbert spaces. Stoch. Anal. ##Appl. 26, 408433 (2008) ##Zhao, Z.H., Chang, Y.K., Li, W.S.: Asymptotically almost periodic, almost periodic and pseudo ##almost periodic mild solutions for neutral dierential equations. Nonlinear Anal. RWA 11, 30373044##]
PENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH COULOMB’S FRICTION FOR LOCKING MATERIAL
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2
In this work, we study a unilateral contact problem with non local friction of Coulombbetween a locking material and a rigid foundation. In the first step , we present the mathematicalmodel for a static process, we establish the variational formulation in the form of a variationalinequality and we prove the existence and uniqueness of the solution. In the second step, usingthe penalty method we introduce the penalized problem numerical in the form of variationalequality where we replace the law behavior and the law contact of Sigorini . The we show theconvergence of the continuous penalty solution as the penalty parameter n tends towards infinity.Then, the analysis of the finite element discretized penalty method is carried out.
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61
81


Salah
Bourichi
University Hassan I, FSTS, Department of Mathematics and Informatics
Morocco
University Hassan I, FSTS, Department of
Iran


El
Essoufi
Iran
Locking material
Unilateral contact
Coulomb’s friction
variational inequality
penalty method
finite element
[F.Demengel and P.Suquet; On Locking materials Acta Applicandae Mathematicae 6 ##(1986), 18521 I. 185 1986 by D. Reidel Publishing Company. ##F.Demengel; Displacements bounded deformation and measures stress, published in annals ##of superior school of Pise (1972). ##F. Demengel; Relaxation and existence for locking materials problems , to be published in ##W.Prager; On Ideal Locking Materials, Trans. Soc. Rheology 1 (1957) 169175. ##W.Prager; Unilateral Constraints in Mechanics of Continua , Estratto dagli atti del Simposio ##Lagrangiano. Accademia delle Science di Torino, 1964, pp. 111. ##W.Prager; Elastic Solids of Limited Compressibility, Proc. 9th Int. Congress AppL Mech., ##Vol. 5, Brussels, 1958, pp. 205211. ##P. G. Ciarlet;The finite element method for elliptic problems, NorthHolland, Amsterdam, ##G. Duvaut, J.L. Lions; Les in´equations en m´ecanique et en physique, Dunod, Paris, 1972. ##R. Glowinski; Numerical Methods for Nonlinear Variational Problems. Springer, ##NewYork, 1984. Contact problems in elasticity: a study of variational inequalities and ##finite element methods, volume 8 of SIAM Studies in Applied Mathematics, Society for ##Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1988. ##J. Neˇcas and I. Hlav´aˇcek; Mathematical Theory of Elastic and ElasticoPlastic Bodies: ##An Introduction, Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York, ##G. Strang, G. Fix; An Analysis of the Finite Element Method, PrenticeHall, Englewood ##Cliffs, NJ 1973. ##R. Temam; Probl`eme math´ematiques en plasticit´e, GauthierVillars, Paris (1983). ##A.Ern, J.L.Guermound; ##Theory and Pratice of finite element, Appl.Math.Sci,vol.159.SpringerVerlag New York, ##P.Hild Y.Renard An improved a priori error analysis for finite element approximations of ##Signorin’s, SIAM J. Numer. Anal. 50(2012)24002419 ##R.Temam, NavierStokes Equations, NorthHolland, Amsterdam, 1979. ##R.Temam, R. and G.Strang; Duality and Relaxation in the Variational Problems of Plasticity, ##J. Mecanique. 19 (1980) 493528.##]
AN APPLICATION OF FUZZY NUMBERS TO THE ASSESSMENT OF MATHEMATICAL MODELLING SKILLS
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In this paper we use the Triangular and Trapezoidal Fuzzy Numbers as tools for assessing student Mathematical Modelling (MM) skills. Fuzzy Numbers play a fundamental role in fuzzy mathematics analogous to the role played by the ordinary numbers in classical mathematics, On the other hand, MM appears today as a dynamic tool for teaching and learning mathematics, because it connects mathematics with our everyday life giving the possibility to students to understand its usefulness in practice thus increasing their interest about mathematics. Therefore the subject of the present paper appears to be of great interest. Our results are illustrated by three examkples, through which the effectiveness of our new fuzzy assessment approach is validated compared to already established by the present authors in earlier works assessment methods of the classical (calculation of the means, GPA index) and the fuzzy logic (Trapezoidal Model).
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83
103


Michael Gr.
Voskoglou
Graduate T.E.I. of Western Greece
Professor Emeritus of Mathematical Sciences
School of Technological Applications
Graduate T.E.I. of Western Greece
Professor
Iran


Igor Ya.
Subbotin
Iran
Mathematical Modelling
Trapezoidal Fuzzy Assessment Model
Fuzzy numbers
[Klir, J. G. and Folger, T. A., Fuzzy Sets, Uncertainty and Information, , PrenticeHall, London, 1988 ##]