iosr-Jm   Volume-4 ~ Issue-4

Abstract: In this paper, we have developed an economic production models with finite production rate and fuzzy deterioration rate. In the development of the model, lost of production quantity due to faulty machine aged machine, manufacturing defect etc. from the actual production quantity have also been taken into account. We developed the corresponding fuzzy model. The solution form minimizing the fuzzy cost function have been derived The sensitivity of the optimal solution with respect to the changes in the different parameter values is also discussed. all the inventory models have been developed under the assumption that the deterioration rate is constant or it is dependent on time.

[1] Ghare P.M. and Schrader G.F. An inventory model for exponentially deteriorating items. Journal of industrial Engineering.,14: 238-243,(1963).
[2] Ghare P.M. and Schrader, G.P.,"A model for exponentially decaying inventory", Journal of Industrial Engineering ,14: 238-243, (1963)
[3] Convert R.P. and Philip G.C., An EOQ model for items with Weibull distribution deterioration. AIIE Trans, 5: 323-326, (1973).
[4] Covert, R.P. and Philip, G.C.,An EOQ model items with weibull distribution deterioration" A.I.T.E. Transactions, 5:323- 326, (1973).
[5] Misra R.B. : Optimum production lot-size model for a system with deteriorating inventory. International Journal of Production Research,13:495-505. (1976).
[6] Cohen, M.A.: Joint pricing and ordering policy for exponentially decaying inventory with known demand. Naval Research Logistics Quarterly, 24: 257-268, (1977).
[7] Kang. S. and Kim. I: "A study on the price and production level of the deteriorating inventory system". International Journal Production Research,21:449-460, (1983).
[8] Aggarwal S.P. and Jaggi C.K."Ordering policies of deteriorating items under permissible delay in payments", Journal of operation research society, 46:658-662, (1995).
[9] Aggrawal S.P. and Jaggi C.K.: Ordering policy for decaying inventory". International Journal of system of system Sciences, 20:151-155, (1989).
[10] Wee, Hui-Ming : "A replenishment policy for items with a price dependent demand and varying rate of deterioration". Production Planning and Control. 8:No. 5, 494-499, (1997).

Abstract:Gracefulness of nc4 merging with paths

[1] R. L. Graham and N. J. A. Sloane, On additive bases and harmonious graph, SIAM J. Alg. Discrete Math., 1 (1980) 382 – 404.
[2] A. Rosa, On certain valuation of the vertices of a graph, Theory of graphs (International
[3] Synposium,Rome,July 1966),Gordon and Breach, N.Y.and Dunod Paris (1967), 349-355.
[4] A.Solairaju and K.Chitra Edge-odd graceful labeling of some graphs, Electronics Notes in Discrete Mathematics Volume 33,April 2009,Pages 1.
[5] A. Solairaju and P.Muruganantham, even-edge gracefulness of ladder, The Global Journal of Applied Mathematics & Mathematical Sciences(GJ-AMMS). Vol.1.No.2, (July-December-2008):pp.149-153.
[6] A. Solairaju and P.Sarangapani, even-edge gracefulness of Pn O nC5, Preprint (Accepted for publication in Serials Publishers, New Delhi).
[7] A.Solairaju, A.Sasikala, C.Vimala Gracefulness of a spanning tree of the graph of product of Pm and Cn, The Global Journal of Pure and Applied Mathematics of Mathematical Sciences, Vol. 1, No-2 (July-Dec 2008): pp 133-136.
[8] A.Solairaju, A.Sasikala, C.Vimala, Edge-odd Gracefulness of a spanning tree of Cartesian product of P2 and Cn, The Global Journal of Pure and Applied Mathematics of Mathematical Sciences, (Preprint).
[9] A. Solairaju, C.Vimala,A.Sasikala Gracefulness of a spanning tree of the graph of Cartesian product of Sm and Sn, The Global Journal of Pure and Applied Mathematics of Mathematical Sciences, Vol. 1, No-2 (July-Dec 2008): pp117-120.
[10] A.Solairaju, C.Vimala, A.Sasikala , Even Edge Gracefulness of the Graphs,

Abstract:Harmonious colouring is a proper vertex colouring such that no two edges share the same colour pair. The harmonious Chromatic number (G) h  of a graph is the least number of colours in such a colouring. In this paper we give some new properties of harmonious colouring graphs and its applications.

Keywords: Harmonious Colouring, Harmonious chromatic Number ,Upper bound , Lower bound.

[1] A.Chaudhary and Vishwanathan, "Approximation Algorithms for the Achromatic Number, Journal of Algorithms 41, 404–416 (2001)
[2] Colin Mc Diarmid Luo Xinhua , "Upper Bounds for Harmonious Colourings Journal of Graph Theory". Vol 15, No.6, 629-636 (1991).
[3] Donald G. Beare Norman L.Biggs Brain J.Wilson "The Growth rate of the Harmonious Chromatic Number" Journal of Graph theory Vol 13, No.3 291-299 (1989)
[4] F.Harary, S.Hedetniemi, and G.Prins, "An interpolation theorem for graphical Homomorphism‟ Portugal,Math., Vol.26,pp 453-462,1967.
[5] F.Hughes and G.MacGillivray, " The achromatic number of graphs : a survey and some new results, Bill. Inst. Combin. Appl. 19 (1997),pp27-56.
[6] Krasikov ,Y.Roditty " Bounds for the Harmonious chromatic Number of a Graph" Journal of graph theory Vol -18, No.2, 205-209 (1994).
[7] J. Hopcroft and M.S. Krishnomoorthy, "On the harmonious colouring of graphs" , SIAM J.Algebraic Discrete methods 4(1983) 306-311.
[8] K.J.Edwards, "The harmonious chromatic number and the achromatic number of graphs", Surveys in combinatorics, London,1997,pp.13-47.
[9] K.Thilagavathi And A.Sangeetha devi, "Harmonious colouring of C[B(Kn,Kn)] And C[F2,k],Proceedings of the international conference on mathematics and computer science-2009.
[10] K.Thilagavathi and J.V.Vivin, "Harmonious chromatic number of line graph of central graph. Proceedings of the international conference on mathematics and computer science-2006.

Abstract:In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favourably with the exact solution

Keywords:Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order

[1] S.O. Fatunla, Block Method for Second Order Initial Value Problem. International Journal of Computer Mathematics, England. Vol. 4, 1991, pp 55 – 63.

[2] S.O. Fatunla, Higher Order parallel Methods for Second Order ODEs. Proceedings of the fifth international conference on scientific computing, 1994, pp 61 –67.

[3] J.D.Lambert, Computational Methods in Ordinary Differential Equations (John Willey and Sons, New York, USA, 1973)

[4] P. Onumanyi, D.O. Awoyemi, S.N. Jator and U.W. Sirisena, New linear Multistep with Continuous Coefficient for first order initial value problems. Journal of Mathematical Society, 13, 1994, pp 37 – 51.

[5] D.O. Awoyemi, A class of Continuous Stormer – Cowell Type Methods for Special Second Order Ordinary Differential Equations. Journal of Nigerian Mathematical Society Vol. 5, Nos. 1 & 2, 1998, pp100 – 108.

[6] Y.A. Yahaya and Z.A. Adegboye, A family of 4 – step Block Methods for Special Second Order in Ordinary Differential Equations. Proceedings Mathematical Association of Nigeria, 2008, pp 23 – 32.

[7] I. Fudziah L. K. Yap. and O. Mohammad, Explicit and Implicit 3 – point Block Methods for Solving Special Second Order Ordinary Differential Equations Directly. International Journal of math. Analysis, Vol. 3, 2009, pp 239 – 254.

[8] K.R. Adeboye , A superconvergent H2 – Galerkin method for the solution of Boundary Value Problems. Proceedings National Mathematical Centre, Abuja, Nigeria. Vol. 1 no.1, 2000, pp 118 – 124, ISBN 978 – 35488 – 0 – 2

[9] R. Taparki and M.R. Odekunle, An Implicit Runge – Kutta Method for Second Order Initial Value Problem in Ordinary Differential Equations. International Journal Num. Mathematics, Vol. 5 No. 2, 2010, pp 222 - 234

[10] P. Henrici, Discrete Variable Methods for ODEs. (John Willey New York U.S.A, 1962).

Abstract:In this paper we turn our attention to the sBB algorithm itself and its computer implementation in a form that can be used as a component within larger software systems such as process modeling tools. We start with an overview of the common structure of most sBB algorithms. We then provide a more detailed description of Smith's sBB algorithm which forms the basis for our work and propose some algorithmic improvements to improve its performance. Lastly, we describe ooOPS (object-oriented Optimization System), a general software framework for defining and solving optimization problems, and the implementation of our algorithm within this framework.

Keywords:spatial branch and bound algorithm, object oriented optimization system.

[1]. C. Adjiman, S. Dallwig, C. Floudas, and A. Neumaier. A global optimization method, αBB, for general twice-differentiable constrained NLPs: I. Theoretical advances. Computers & Chemical Engineering, 22:1137–1158, 1998.
[2]. C. Adjiman, S. Dallwig, C. Floudas, and A. Neumaier. A global optimization method, αBB, for general twice-differentiable constrained NLPs: I. Theoretical advances. Computers & Chemical Engineering, 22:1137–1158, 1998.
[3]. C. Adjiman, I. Androulakis, and C. Floudas. A global optimization method, αBB, for general twice-differentiable constrained NLPs: II. Implementation and computational results. Computers & Chemical Engineering, 22:1159–1179, 1998.
[4]. C. Adjiman, I. Androulakis, C. Maranas, and C. Floudas. A global optimization method, αBB, for process design. Computers & Chemical Engineering, 20:S419–S424, 1996.
[5]. I. Androulakis, C. Maranas, and C. Floudas. α BB: A global optimization method for general constrained non-convex problems. Journal of Global Optimization, 7:337–363, 1995.
[6]. A. Brook, D. Kendrick, and A. Meeraus. Gams, a user's guide. ACM SIGNUM Newsletter, 23:10–11, 1988.
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[8]. T. Epperly. Global Optimization of Nonconvex Nonlinear Programs using Parallel Branch and Bound. PhD thesis, University of Winsconsin – Madison, 1995.
[9]. T. Epperly and E. Pistikopoulos. A reduced space branch and bound algorithm for global optimization. Journal of Global Optimization, 11:287:311, 1997.
[10]. P.Gill. User's Guide for SNOPT 5.3. Systems Optimization Laboratory, Department of EESOR, Stanford University, California, 1999.

Abstract:The concept of soft set is one of the recent topics developed for dealing with the uncertainties present in most of our real life situations. In this paper, we have applied the notion of similarity between two fuzzy soft sets based on distance, to obtain the solution of a medical problem in an imprecise environment

Keywords:Soft set, Fuzzy soft set, Similarity measure

[1] D.A.Molodstov,"Soft set theory-first result", Computers and Mathematics with Applications ,37,1999,19-31.
[2] P.K.Maji,R.Biswas andA.R.Roy,"Fuzzy Soft Sets", Journal of Fuzzy Mathematics,9(3) 2001, 589-602.
[3] P. Majumder and S.K. Samantha,"On Similarity Measure of Fuzzy Soft Sets",Int.J.Advance Soft Comput.Appl.,vol.3,No.2,July 2011.
[4] B.Ahmad and Athar Kharal,"On Fuzzy Soft Sets", Advances in Fuzzy Systems,2009.
[5] Dusmanta Kumar Sut,"An Application of Similarity of Fuzzy Soft sets in Decision Making"Int.J.Computer Technology & Applications,Vol3(2),742-745.

Abstract:In this paper, an order level inventory unit production system for deteriorating items with a quadratic demand is developed. It is assumed that shortages in inventory are permitted and are completely backlogged. The finite production rate is proportional to the time dependent demand rate and deterioration rate is time proportional. The unit production cost is taken to be inversely related to the demand rate. Sensitivity of the decision variable to changes in the parameter values is examined and numerical example is presented to illustrate the model is developed.

Keywords: Deterioration; Inventory model; Quadratic demand rate; Shortage;

[1] Bahari-Kashani H. (1989). Replenishment schedule for deteriorating items with time proportional demand. Journal of the Operational Research Society 40, 75-81.
[2] Covert R. P. and Philip G.C. (1973). An EOQ model for items with waybills distribution deterioration. AIIE Transactions 5, 323-326.
[3] Dave U. (1986). An order level inventory model for deteriorating items with variable instantaneous demand and discrete opportunities for replenishment. Opsearch 23, 244-249.
[4] Dave U. and Patel L.K. (1981). ( , ) i T S Policy inventory model for deteriorating items with time proportional demand. Journal of the Operational Research Society 32, 137-142.
[5] Deb M. and Chaudhuri K.S. (1986). An EOQ model for items with finite rate of production and variable rate of deterioration. Opsearch 23, 175-181.
[6] Donaldson W.A. (1977). Inventory replenishment policy for a linear trend in demand –an analytical solution. Operational Research Quarterly 28, 663-670.
[7] Ghare P.M. and Schrader G.F. (1963). An inventory model for exponentially deteriorating items. Journal of Industrial Engineering 14, 238-243.
[8] Mishra R.B. (1975). Optimum production lot-size model for a system with deteriorating inventory. International Journal of Production Research Society 13, 495-505.
[9] Nahmias S. (1982). Perishable inventory theory-a review. Operational Research 30, 680-708.

[10] Philip G.C. (1974). A generalized EOQ model for items with Weibull distribution deterioration. AIIE Transactions 6, 159-162.

Abstract:We define the primal and dual linear programming problems involving interval numbers as the way of traditional linear programming problems. We discuss the solution concepts of primal and dual linear programming problems involving interval numbers without converting them to classical linear programming problems. By introducing new arithmetic operations between interval numbers, we prove the weak and strong duality theorems. Complementary slackness theorem is also proved. A numerical example is provided to illustrate the theory developed in this paper.

Keywords: Interval Numbers, Interval arithmetic, Linear Programming, weak duality, strong duality, Complementary slackness.

[1]. G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press, New York 1983.
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[3]. Atanu Sengupta, Tapan Kumar Pal and Debjani Chakraborty, Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy Sets and Systems, 119 (2001) 129-138.
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Abstract:In this paper we will describe the "An Algorithm for Linear Programming".

Keywords: Active Set, inactive Set & karush kuhn tucker (KKT) conditions.

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