Volume-5 , Issue-2 , Apr 2018, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Inventory Replenishment Policy with Time and Reliability Varying Demand

  N.P. Behera, P. K. Tripathy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.1-12, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.112

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  Abstract
  In real life situation, demand may be increase, decrease or constant. But, in our present study demand is assumed to be an increasing function of time which depends on reliability. Shortages are allowed and excess demand is backlogged. The economic production lot size and the reliability of the production process along with the production period are the decision variables and total cost per cycle is the objective function which is to be minimized. Further the parameters involved in the business may likely to be changed due to the fast growing marketing system. Therefore; it will be more realistic and market friendly to deal with a fuzzy model rather than a crisp model. Both crisp and fuzzy models have been proposed to determine the optimal solution. The demand, shortage cost, holding cost and deterioration rate and reliability are considered as pentagonal fuzzy numbers. Defuzzification of the total cost has been carried out by Graded Mean Representation Method and Signed Distance Method. Sensitivity analysis is also incorporated to investigate the effect of different system parameters in enhancing the cost.

  Key-Words / Index Term
  Reliability, Pentagonal Fuzzy Number, Graded Mean Representation Method, Signed Distance Method

  References
  [1] D. Dutta and P. Kumar, “Fuzzy Inventory Model Without Shortage using Trapezoidal Fuzzy Number with Sensitivity Analysis”, IOSR Journal of Mathematics, Vol.4, No. 3, pp.32-37, 2012.
  [2] D. Dutta and P. Kumar, “Optimal Ordering Policy for an Inventory Model for Deteriorating Items without Shortages by Considering Fuzziness in Demand Rate, Ordering Cost and Holding Cost”, International Journal of Advanced Innovation and Research, Vol. 2, No. 3, pp.320-325, 2012.
  [3] P. K. Tripathy, P. Tripathy, M. Pattnaik, “A fuzzy EOQ model with reliability and demand depended unit cost”, International Journal of Contemporary Mathematics Science, Vol.6, No. 30, pp.1467-1482, 2011.
  [4] H. J. Zimmermann, “Fuzzy Set Theory-and its Applications”, Springer Science + Business Media, LLC, 4th edition.
  [5] P. K. Tripathy, M. Pattnaik, “Optimal Disposal Mechanism with Fuzzy System Cost under Flexibility and Reliability Criteria in Non-random Optimization Environment”, Applied Mathematical Sciences, Vol.3, No.37, pp. 1823-1847, 2009.
  [6] P. K. Tripathy, N. P. Behera, “Fuzzy EOQ Model for Time-Deteriorating Items Using Penalty Cost”, American Journal of Operational Research, Vol.6, No.1, pp.1-8, 2016.
  [7] S. R. Singh, H. Rathor, “An Inventory Model for Deteriorating Items with Reliability Consideration and Trade Credit”, Pakistan Journal of Statistics and Operations Research, Vol. X, No. 3, pp.349-360, 2014.
  [8] C.K. Jaggi, S. Pareek, A. Sharma, Nidhi, “Fuzzy Inventory Model for Deteriorating Items with Time-Varying Demand and Shortages”, American Journal of Operational Research, Vol.2, No.6, pp.81-92, 2012.
  

  Citation
  N.P. Behera, P. K. Tripathy, "Inventory Replenishment Policy with Time and Reliability Varying Demand," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.1-12, 2018

• Open Access   Article

  An efficient dual to ratio-cum-product estimator for the population mean in stratified random sampling

  Rohini Yadav

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.13-20, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.1320

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  his paper deals with the problem of estimating the population mean of the study variable y with the help of the auxiliary variables under stratified random sampling. The estimator of dual to ratio-cum-product estimator for the population mean of the study variable has been suggested. The properties of the suggested estimator have been studied under large sample approximation. It has been shown that the suggested estimator is more efficient than other considered estimators. To judge the merits of the proposed estimator, an empirical study is given in the support of the present study.

  Key-Words / Index Term
  Study variable, auxiliary variable, stratified random sampling, dual to ratio estimator, dual to product estimator, bias and mean squared error

  References
  [1] W.G. Cochran, “The estimation of the yields of cereal experiments by sampling for the ratio gain to total produce”, Jour. Agri. Soc, 30, pp. 262-275, 1940.
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  [6] L.N. Upadhyaya, H.P. Singh, S. Chatterjee and R. Yadav, “A Generalized Family of Transformed Ratio-Product Estimators of Finite Population Mean in Sample Surveys”, Model Assisted Statistics and Applications, 6, 2, pp. 137-150, 2011.
  [7] L.N. Upadhyaya, H.P. Singh, S. Chatterjee and R. Yadav, “Improved Ratio and Product Exponential type Estimators for Finite Population Mean in Sample Surveys”, Journal of Statistical Theory and Practice, 5, 2, pp. 285-302, 2011.
  [8] R. Yadav, L.N. Upadhyaya, H.P. Singh and S. Chatterjee, “Almost Unbiased Ratio and Product Type Exponential Estimators”, Statistics in Transition, 13, 3, pp. 537-550, 2012.
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  [10] S. Bandyopadhyay, “Improved ratio and product estimators”, Sankhya: Indian J. Stat., 42, pp. 45-49, 1980.
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  [12] H.P. Singh and G.K. Vishwakarma, “ A general procedure for estimating the population mean in stratified sampling using auxiliary information”, Metron, LXVII, 1, pp. 47-65, 2010.
  [13] R. Tailor and M. Chouhan, “Improved ratio-cum-product type exponential estimator of population mean in stratified random sampling”, International Journal of Scientific Research in Mathematical and Statistical Sciences, 4, 3, pp. 19-29, 2017.
  [14] R. Tailor, S. Chouhan, R. Tailor and N. Garg, “A ratio-cum-product estimator of population mean in stratified random sampling using two auxiliary variables”, Statistica, LXXII, 3, pp. 287-297, 2012.
  [15] R. Yadav, L.N. Upadhyaya, H.P. Singh and S. Chatterjee, “Improved Ratio and Product Exponential type Estimators for Finite Population Mean in Stratified Random Sampling” Communications in Statistics: Theory & Methods (Taylor & Francis), 43, 15, pp. 3269-3285, 2014.
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  [17] K.S. Kushwaha, L.N. Upadhyaya and S.P. Dubey, “A dual to ratio estimator in stratified random sampling”, Proc. Math. Soc., 6, pp. 11-15, 1990.
  [18] R. Tailor, N.K. Jatwa, R. Tailor and N. Garg, “Dual to ratio and product type exponential estimators in stratified random sampling using two auxiliary variates”, Journal of Reliability and Statistical Studies, 6, 2, pp. 115-126, 2013.
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  [20] National Horticulture Board. Available at https://www.google.co.in/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=National+Horticulture+Board]&*
  

  Citation
  Rohini Yadav, "An efficient dual to ratio-cum-product estimator for the population mean in stratified random sampling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.13-20, 2018

• Open Access   Article

  An EPQ Model under Constant Amelioration, Different Deteriorations with Exponential Demand Rate and Completely Backlogged Shortages

  P. D. Khatri, U.B.Gothi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.21-28, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.2128

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  Abstract
  In the present paper, we have developed an economic production quantity inventory model for ameliorating and deteriorating items. At the inception of production activity, the constant amelioration, two parameter Weibully distributed deterioration rate and exponential demand rate have been considered At the conclusion stage of production activity, deterioration of items has been assumed to follow Pareto Type-I distribution with the same amelioration and demand rate as at the inception stage. The time dependent inventory holding cost is assumed to be a linear function of time. Shortages are acceptable and backlogged completely. The aim of this study is to find the optimal solution for minimizing the total inventory cost. The manifest the model, a numerical illustration has been presented along with a sensitivity analysis for studying the impact of parameters on assessment variables and total cost of the model.

  Key-Words / Index Term
  Weibull distribution, Pareto type – I distribution, Amelioration rate

  References
  [1] Ankit Bhojak and U. B. Gothi., “Inventory Models for Ameliorating and Deteriorating Items with Time Dependent Demand and IHC” International Journal of Management and Social Science Research Review, Vol.1, Issue.2, 85 – 98, 2016.
  [2] Ankit Bhojak and U.B. Gothi. “Inventory Model for Ameliorating and Deteriorating Items with Time Dependent Demand” Sankhya Vignan, (NSV 11), No.2, 31- 43, 2015.
  [3] Chun-Hsiung Lan, Yen-Chieh Yu, Robert H.-J. Lin, Cheng-Tan Tung, Chih-Pin Yen and Peter Shaohua Deng, “A Note on the Improved Algebric Method for the EPQ Model with Stochastic Lead Time,” Information and Management Sciences Vol. 18, No.1, pp. 91-96, 2007.
  [4] Devyani Chatterji, U.B.Gothi, “An EPQ Model for Two-Parameter Weibully Deteriorated Items with Exponential Demand Rate and Completely Backlogged Shortages,” International Journal of Computer Science Trends and Technology (IJCST) – Vol.3 Issue 6, Nov-Dec 2015.
  [5] Hwang, H. S. “A study on an inventory models for items with Weibull ameliorating”. Computers & Industrial Engineering 33, 701-704, 1997.
  [6] Kapil Kumar Bansal and Navin Ahalawat, “Integrated Inventory Models for Decaying Items with Exponential Demand under Inflation,” International Journal of Soft Computing and Engineering (IJSCE) Vol.2, Issue-3, 2012.
  [7] Kawale S.V. and Bansode P.B., “An EPQ model using Weibull deterioration for deterioration item with time varying holding cost,” International Journal of Science, Engineering and Technology Research, Vol.1, Issue 4, pp. 29-33, 2012.
  [8] L. Tadj, A.M. Sarhan and A. EI-Gohary, “Optimal control of an inventorysystem with ameliorating and deteriorating items.” Applied Sciences,10,243-255, 2008.
  [9] Madhu Jain, G.C. Sharma and Shalini Rathore, “Economic production quantity models with Shortage, price and stock-dependent Demand for deteriorating items,” IJE Transactions Vol. 20, No 2, pp. 159-166, 2007.
  [10] Parmar, K.C. and Gothi U. B., “An EPQ model of deteriorating items using three parameter Weibull distribution with constant production rate and time varying holding cost.” International Journal of Science, Engineering and Technology Research, Vol. 4, Issue 2, , pp. 409 – 416, 2015.
  [11] Parmar, K.C. and Gothi, U.B., “EPQ model for deteriorating items under three parameter Weibull distribution and time dependent IHC with shortages.” American Journal of Engineering Research, Vol. 4, Issue 7, pp. 246-255, 2015.
  [12] Pooja Khatri and U. B. Gothi, “An Inventory Model of Deteriorating Items under Inflation and Discount Rate with Power Demand and Time Dependent Holding Cost”, International Journal of Advanced Research in Science, Engineering and Technology, Vol. 4, Issue 3, March 2017.
  [13] R. Shamsi, A. Haji, S. Shadrokh and F. Nourbakhsh, “Economic Production Quantity in Reworkable Production Systems with Inspection Errors, Scraps and Backlogging,” Journal of Industrial and Systems Engineering Vol. 3, pp. 170-188, 2009.
  [14] S.T. Law and H.M. Wee, “An integrated production-inventory forameliorating and deteriorating items taking account of time discounting”, Mathematical and Computer Modelling , 43 , 673-685, 2006.
  [15] Srichandan Mishra, L.K.Raju, U.K.Misra & G.Misra.. “Optimal Control of An Inventory System with Variable Demand & Ameliorating / Deteriorating Items”. Asian Journal of Current Engineering and Maths, 154 – 157. 2012.
  [16] U. B. Gothi, Kareeshaa Shah and Pooja Khatri, “A two warehouse Inventory model with Weibull and Pareto Type-I deterioration and power demand, International” Journal of Research In Science & Engineering, Vol.3 Issue.3, May-June 2017.
  
  

  Citation
  P. D. Khatri, U.B.Gothi, "An EPQ Model under Constant Amelioration, Different Deteriorations with Exponential Demand Rate and Completely Backlogged Shortages," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.21-28, 2018

• Open Access   Article

  Independent Roman Domination Number of Graphs

  D.K. Thakkar, S.M. Badiyani

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.29-34, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.2934

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  Abstract
  In this manuscript we consider Independent Roman Dominating Functions for graphs. We characterize minimal Independent Roman Dominating Functions. We observed the change in the Independent Roman Domination Number of a graph when a vertex is removed from the graph. We prove a necessary and sufficient condition under which the Independent Roman Domination Number of a graph increases or decreases. We have defined a new class of graphs called Independent Roman graphs. A necessary and sufficient condition is given under which a graph is an Independent Roman graph.

  Key-Words / Index Term
  Independent Roman Dominating Function, Independent Roman Domination Number, minimal Independent Roman Dominating Function, minimum Independent Roman Dominating Function, Independent Roman graph.

  References
  [1] C.S.Revelle, K.E.Rosing, “Defenders Imperium Romanum: a classical problem in military strategy”, Amer.Math.Monthly Vol. 107 (7), pp. 585-594, 2000.
  [2] D.K.Thakkar and S.M.Badiyani, “MINIMAL ROMAN DOMINATING FUNCTIONS”, International Journal of Mathematics and Soft Computing, Vol. 7, No. 2, pp. 63-71, 2017.
  [3] D.K.Thakkar and S.M.Badiyani, “On the Roman Domination Number of Graphs”, International Journal of Mathematical Archive, Vol. 8 (2), pp. 184-188, 2017.
  [4] E.J. Cockayne, P.M. Dreyer Jr., S.M Hedetniemi and S.T. Hedetniemi, “On Roman Domination In graphs”, Discrete Math. Vol, 278, pp. 11-22, 2004.
  [5] I. Stewart, “Defend the Roman Empire!” Sci. Amer. Vol. 281(6), pp. 136-139, 1999.
  [6] M. Adabi, E. E. Targhi, N. J. Rad and M.S. Moradi, “Properties ofIndependent Roman Dominatinon in graphs”, Australasian Journal of Combinatorics, Vol. 52, pp. 11-18, 2012.
  [7] N. J. Rad and Lutz Volkmann “Roman Domination Perfect graphs”, An. St. Univ. Ovidius Constanta, Vol. 19 (3), pp. 167-174, 2011.
  [8] P. A. Dreyer, Jr. Dissertation Director: Fred S Roberts, “Application and Variations of domination in graphs”, New Brunswick, New Jersey, October 2000.
  [9] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Fundamental of Domination In graphs”, Marcel Dekker, New York, 1998.
  [10] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Domination In graphs Advanced Topics”, New York, 1998.
  

  Citation
  D.K. Thakkar, S.M. Badiyani, "Independent Roman Domination Number of Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.29-34, 2018

• Open Access   Article

  Some Topological Indices of Carbon Nanocones [CNC_k(n)] and Nanotori [C₄C₆C₈(P, Q)]

  Keerthi G. Mirajkar, Bhagyashri R. Doddamani

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.35-39, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.3539

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  Abstract
  Chemical graph theory is a branch of graph theory which focuses on the topological indices of chemical molecular graphs, which correlate well with chemical properties of the chemical molecules. Topological indices play important role in mathematical chemistry especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this article, we compute the sum connectivity index, product connectivity index, geometric-arithmetic index and inverse sum indeg index for Carbon Nanocones [CNC_k(n)] and Nanotori [C₄C₆C₈(P, Q)].

  Key-Words / Index Term
  Sum connectivity index, Product connectivity index, Geometric-arithmetic index, Inverse sum indeg index, Carbon Nanocones [CNCk(n)] and Nanotori [C4C6C8(p,q)].

  References
  [1] F. Harary, “Graph Theory”, Addison - Wesely, Reading, 1969.
  [2] R. Todeschini, V. Consonni, “Handbook of Molecular Descriptors”, Weinheim, Wiley-VCH, 2000.
  [3] H. Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, Vol.69, pp. 17-20, 1947.
  [4] B. Zhou and N. Trinajstić, “On a Novel Connectivity Index”, Journal of Mathematical Chemistry, Vol.46, pp. 1252-1270, 2009.
  [5] M. Randić, “On Characterization of Molecular Branching”, Journal of the American Chemical Society, Vol.97, Issue.2, pp.6609-6615, 1975.
  [6] D. Vukičević, B. Furtula, “Topological Index Based on the Ratios of Geometrical and Arithmetical Means of End-Vertex Degrees of Edges”, Journal of Mathematical Chemistry, Vol.46, pp.1369-1376, 2009.
  [7] D. Vukičević and M. Gaśperov, “Bond Additive Modeling 1. Adriatic Indices”, Croatica Chemica Acta, Vol.83, pp. 243-260, 2010.
  [8] J. Gillot, W. Bollmann and B. Lux, “Cristaux De Graphite En Forme De Cigare Et A Structure Conique”, Carbon, Vol.6, Issue.3, pp.381-384, 1968.
  [9] S. Iijima, “Helical Microtubules of Graphitic Carbon”, Nature, Vol.354, pp.56-58, 1991.
  [10] M. Yudasaka, S. Iijima and V. H. Crespi, “Single-wall Carbon Nanohorns and Nanocones”, Topics in Applied Physics, Vol.111, pp.605-629, 2008.
  [11] M. V. Diudea, “Graphenes From 4-Valent Tori”, Bulletin of the Chemical Society of Japan, Vol.75, pp.487-492, 2002.
  [12] M. V. Diudea, A. Graovac, “Generation and Graph-Theoretical Properties of C4-Tori”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.44, pp.93-102, 2001.
  [13] M. V. Diudea, P. E. John, “Covering Polyhedral Tori”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.44, pp.103-116, 2001.
  [14] M. V. Diudea, M. Stefu, “Wiener Index of C4C8 Nanotube”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.50, pp.133-144, 2004.
  [15] M. Ge and K. Sattler, “Observation of Fullerence Cones”, Chemical Physics Letters, Vol.220, Issue.35, pp.192-196, 1994.
  [16] M. R. Farahani, “Computing Randi´c, Geometric-Arithmetic and Atom-Bond Connectivity indices of Circumcoronene Series of Benzenoid”, International Journal of Chemical Modelling, Vol.5, Issue.4, pp.485-493, 2013.
  [17] M. Ghorbani, M. Jalali, “The vertex PI, Szeged and Omega Polynomials of Carbon Nanocones CNC4[n]”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.62, Issue.2, pp.353-362, 2009.
  [18] M. H. Khalifeh, H. Y. Azari and A. R. ashrafi, “A Method for Computing the Wiener Index of One-Penta gonal Carbon Nanocones”, Current Nanoscience, Vol.6, Issue.2, pp.155-157, 2010.
  [19] A. Nejati and M. Alaeiyan, The Edge-Version of MEC Index of One-Pentagonal Carbon Nanocones”, Bulgerian Chemical Communications, Vol.46, Issue.3, pp.462-464, 2014.
  [20] W. Gao, M. R. Farahani, M. K. Siddiqui and M. K. Jamil, “On the First and Second Zagreb and First and Second Hyper-Zagreb Indices of Carbon Nanocones CNCk[n]”, Journal of Computation and Theoretical Nanosciences, Vol.13, pp.7475-7482, 2016.
  

  Citation
  Keerthi G. Mirajkar, Bhagyashri R. Doddamani, "Some Topological Indices of Carbon Nanocones [CNC_k(n)] and Nanotori [C₄C₆C₈(P, Q)]," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.35-39, 2018

• Open Access   Article

  Decision Support Model with Default Risk under Conditional Delay

  P.K.Tripathy, Anima Bag

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.40-45, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.4045

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  Abstract
  To establish long term relationship with the customers and survive in the business scenario the supplier frequently offers a credit period to its customers to make the payment. This attracts the new customer and hence boosts market demand. On the contrary the presence of credit period leads to default risk for the supplier. In this paper an inventory model is developed which deals with credit period dependent quadratic demand and default risk associated with sales revenue. Deterioration rate under natural environment is also incorporated with the inventory model. Seller’s optimal decision to set the permissible credit period for the customer and purchase quantity is discussed here. For profit maximization, environmental concerns of deterioration are also incorporated in to purchasing decision. A solution procedure is given for finding the optimal solution of total profit. Numerical example is given to show the effectiveness of the model. Finally sensitivity analysis is carried out to explore the managerial implications.

  Key-Words / Index Term
  Inventory, Environment, Trade Credit, Default Risk, Deterioration

  References
  [1] S. K. Goyal, “Economic order quantity under conditions of permissible delay in payments”, Journal of the Operational Research Society 36(4), pp.335-338, 1985.
  [2]F. Raafat., “Survey of literature on continuously deteriorating inventory models”, Journal of the Operational Research Society 40, pp. 27-37, 1991.
  [3] H. M. Wee, “ Economic production lot size model for deteriorating items with partial back ordering”, Computers & Industrial Engineering 24, pp. 449-458, 1993.
  [4] S. K. Goyal and B. C. Giri, “Recent trend in modeling of deteriorating inventory”, European Journal of the Operational Research Society 134, pp.1-16, 2001.
  [5] C. K. Jaggi, S. K. Goyal, and S. K. Goel, “Retailer’s optimal replenishment decisions with credit-linked demand under permissible delay in payments”, European Journal of Operational Research 190(1), pp.130-135, 2008.
  [6] Nita H.Shah, P.Pandey, “Optimal ordering policy for the time dependent deterioration with associated salvage value when delay in payments is permissible”,Revista Investigacion Operacional,Vol.2, No.2, pp.117-129, 2008.
  [7] N. H. Shah, K. T. Shukla and B. J. Shah,“Deteriorating inventory model for two-level credit linked demand under permissible delay in payments”, Australian Society of Operations Research Bulletin 28(4), pp. 27-36, 2009.
  [8] N. H Shah, H. N. Soni, and C. K. Jaggi, “Inventory model and trade credit: Review, Control and Cybernetics”, 39(3), pp. 867-884, 2010.
  [9] C.K.Tripathy and L.M. Pradhan,“An EOQ model for three parameter weibull deterioration with permissible delay in payments and associated salvage value”, International Journal of Industrial Engineering Computations, 2011.
  [10] M. Bakker, J. Riezebos and R. H.Teunter, “Review of inventory systems with deterioration since 2001”, European Journal of Operational Research 221, pp. 125-138, 2012.
  [11] K. R. Lou and W.C. Wang,“Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk”, Journal of the Operational Research Society 64, pp.1551-1556, 2013.
  [12] C.K.Tripathy and L.M. Pradhan,“An EOQ Model for weibull deteriorating item with ramp type demand and salvage value under trade credit system”, Log Forum 10(1), 61-72, 2014.
  [13] B. Sarkar, S. Saren,“An inventory model with trade credit policy and variable deterioration for fixed lifetime products”. Annals of Operation Research, June 2015, volume 229, issue 1, pp 677-702. , June 2015.
  [14] Nita H. Shah, Digeshkumar B. Shah and Dushyantkumar G. Patel, “An EOQ Model for perishable inventory under credit period dependent quadratic demand”, Mexican Journal of Operations Research, Vol. 3, No. 1, pp. 2-12. ISSN: 2007-5138. , Jan-Jun 2014.
  [15] J. Sujatha, P. Parvathi, “Fuzzy EOQ Model For Deteriorating Items With Weibull Demand And Partial Backlogging Under Trade Credit”, International Journal of Informative and Futuristic Research(IJIFR),Vol.3, Issue-2, October 2015.
  [16] P.K. Tripathy & Bhabani S. Mohanty, “Fuzzy Inventory Model for Deteriorating Items with Exponentially Decreasing Demand under Fuzzified Cost and Partial Backlogging”, International Journal of Mathematics Trends and Technology (IJMTT), Vol. 51, No. 3, 2017.
  [17] P.K. Tripathy & Sujata Sukla: “Decision Support in a Credit Environment with Fuzzy behaviour of Cost”, International Journal of Statistical Sciences, Bangladesh, Vol.15, pp-37-54, 2017.
  

  Citation
  P.K.Tripathy, Anima Bag, "Decision Support Model with Default Risk under Conditional Delay," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.40-45, 2018

• Open Access   Article

  A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model

  Sachin Kumar Agrawal, B.K. Singh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.46-56, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.4656

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  Abstract
  In the present article, a queuing model having three servers connected in parallel in a tri-cum biserial way has been presented. Statistical tools, generating function technique and the law of calculus have been implemented to compute the various queuing characteristics such as Queue length, variance, average waiting time and probabilities. The arrival and service pattern is supposed to follow the Poisson law. Generic mathematical formulation of queuing model has been presented to ensure the implementation of the presented model in various problems occurred in real-time domain. The presented model is easy to understand and also deliver an important tool for the decision makers dealing with multi-tasking problems.

  Key-Words / Index Term
  Queue length, variance, average waiting time, probabilities

  References
  [1] I. Adan, J. Resing, “Queuing theory department of mathematics and computing science”, Eindhoren University of Technology Eindhoren, 1–123, 2002.
  [2] P.L. Maggu, “Phase type service queues with two servers in biseries”, Journal of Operational Research Society of Japan, 13(1), 1-6, 1970.
  [3] P.L. Maggu and G. Das, “Equivalent jobs for job block in job sequencing”, Opsearch, 14(4), 277-281, 1977.
  [4] Singh, Man, “Steady state behaviour of serial queuing processes with impatient customers", Math, Operations forsch. U. statist. Ser. 15(2),289-298, 1984.
  [5] D. Gupta, S. Sharma, and S. Sharma, “On linkage of a flowshop scheduling model including job block criteria with a parallel biserial queue network”, Computer Engineering and Intelligent System, 3(2), 17-28, 2012.
  [6] R.R.P. Jackson, “Queuing systems with phase-type service”, Operational Research Quarterly, 5, 109-120, 1954.
  [7] S.K. Agrawal, and B.K. Singh, “Computation of various queue characteristics using tri-cum biserial queuing model connected with a common server”, International Journal of Mathematics Trends and Technology (IJMTT) – Volume 56 Number 1, 81-90, 2018. doi: 10.14445/22315373/IJMTT-V56P510.
  

  Citation
  Sachin Kumar Agrawal, B.K. Singh , "A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.46-56, 2018

• Open Access   Article

  On Discrete Wrapped Exponential Distribution- Characteristics

  G.V.L.N. Srihari, S.V.S.Girija, A.V. Dattatreya Rao

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.57-64, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.5764

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  Abstract
  Here an attempt is made to propose new discrete circular model by employing the method of discretization of existing continuous circular model. Here considering the Wrapped Exponential model we discretized it to make it discrete Wrapped Exponential distribution. The probability mass function, distribution function and characteristic function of the new discrete circular model are obtained and population characteristics are studied .

  Key-Words / Index Term
  Characteristic function, Distribution function, Trigonometric moments

  References
  [1]. A.J.V.Radhika,“Mathematical Tools in the Construction of New Circular Models”, unpublished thesis submitted to AcharyaNagarjuna University for the award of Ph.D,2014.
  [2]. A.J.V Radhika, S.V.S.Girija, and A.V DattatreyaRao,”On Univariate Offset Pearson Type II Model – Application To Live Data”,International Journal of Mathematics and Statistics Studies, Vol.1, No. 1, pp.1-9,2013.
  [3]. A.Pewsey, “A Wrapped Skew-Normal Distribution on the circle,” Communication in Statistics: Theory and Methods, Vol.29, No.11, pp.2459-2472,2000.
  [4]. A.V. DattatreyaRao, I. RamabhadraSarma and S.V.S Girija, “On Wrapped Version of Some Life Testing Models,”Communication in Statistics: Theory and Methods, 36, issue # 11, pp.2027-2035,2007.
  [5]. A.W. Kemp, “Characterization of a Discrete Normal Distribution,” Journal of Statistical Planning and Inference, Vol.63, No.2, pp.223-229,1997.
  [6]. Ch.V.Sastry, “On l – Axial Models”, unpublished thesis submitted to Acharya Nagarjuna University for the award of Ph.D,2016.
  [7]. K.V. Mardia, and P.E.Jupp, “Directional Statistics” 2nd Edition , Wiley, New York 2001.
  [8]. M.K. Abramowitz, I.A Stegun, “Handbook of Mathematical Functions” Dover, New York, 1965
  [9]. Min – Zhen Wang and Kunio Shimizu, “Discrete Cardioid Distribution”, presented in Conference on Advances and Applications in Distribution Theory, The Institute of Statistical Mathematics, Tokyo, Japan,2014.
  [10]. S. Inusah and T.J.Kozubowski, “A Discrete Analogue of the Laplace Distribution,” Journal of Statistical Planning and Inference, Vol.136, No.3,pp.1090-1102,2006.
  [11]. S.RaoJammalamadaka and A.Sen Gupta, “Topics in Circular Statistics, World Scientific Press”, Singapore,2014.
  [12]. S.RaoJammalamadaka and J.Tomasz Kozubowski , “New Families of Wrapped Distributions for Modeling Skew Circular Data”, Communications in Statistics - Theory and Methods, Vol .33, No. 9, pp.2059-2074,2004.
  [13]. S.V.S Girija,”Construction of New Circular Models”,VDM VERLAG, Germany. ISBN 978-3-639-27939-9, 2010.
  [14]. S.V.S Girija, A.V.DattatreyaRao and G.V.L.N.Srihari ,“On Wrapped Binomial Model Characteristics”, Horizon Research PublicationsVolume2(7),pp.231-234,2014(a).
  [15]. S.V.S Girija, A.V.DattatreyaRao and G.V.L.N.Srihari, “On Characteristic Function of Wrapped Poisson Distribution”, International Journal of Mathamatical archive Volume5(5),pp.168-173,2014(b).
  [16]. S.V.S Girija, A.V.DattatreyaRao and Y.Phani, “On Stereographic Lognormal Distribution”, International Journal of Advances in Applied Sciences (IJAAS),Vol. 2 No.3, pp.125-132,2013(a).
  [17]. Y.Phani, “On Stereographic Circular and Semicircular Models”, unpublished thesis submitted to AcharyaNagarjuna University for the award of Ph.D,2013.
  

  Citation
  G.V.L.N. Srihari, S.V.S.Girija, A.V. Dattatreya Rao, "On Discrete Wrapped Exponential Distribution- Characteristics," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.57-64, 2018

• Open Access   Article

  Efficient Hierarchic Multivariate Product-Based Estimator

  K.B.Panda, P.Das

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.65-69, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.6569

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  Abstract
  We, in this paper, have proposed a multivariate product estimator using multi-auxiliary information. The performance of the proposed multivariate product-based estimator of order k, both under one-phase and two-phase sampling, is compared against the customary multivariate product estimator and the simple mean under conditions which hold good in practice very often. Moreover, the estimator is shown to be more efficient than the competing estimators invariably when k is determined optimally. The superiority of the estimator has been numerically illustrated by considering data from two real populations.

  Key-Words / Index Term
  Hierarchic multivariate product-based estimator, auxiliary information, predictive estimation

  References
  [1] M.C. Agrawal, K.B. Panda- Multivariate Product Estimators, Jour. Ind. Soc. Ag. Statistics, 45(3), 359-371, 1993.
  [2] M.C. Agrawal, A. B. Sthapit- Hierarchic predictive ratio-based & product-based estimators and their efficiencies. Journal of Applied Statistics, Vol. 24, No. 1, 97- 104. 1997.
  [3] D. Basu- An essay on the logical foundations of statistical inference, Part I, Foundations of Statistical Inference, Ed. By V.P. Godambe and D.A. Sportt, New York, 203-233, 1971.
  [4] K.B. Panda- Some contributions to the Theory of Survey Sampling. Ph.D. thesis submitted to University of Delhi,Delhi-11007, 1994.
  [4] T.M.F. Smith- The foundations of survey sampling, a review, Jour. R. Statist. -Soc., Series A, 139, 183-204, 1976.
  [5] G.K. Vishwakarma, M. Kumar- An improved class of chain ratio-product type estimators in two-phase sampling using two auxiliary variables, Jour. of Prob. and Stat., Vol. 2014
  [6] S. Weisberg,- Applied Linear Regression, John Wiley & Sons, Inc., New York, 1980.
  

  Citation
  K.B.Panda, P.Das, "Efficient Hierarchic Multivariate Product-Based Estimator," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.65-69, 2018

• Open Access   Article

  On the Tribonacci fractals

  T. Sellami

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.2 , pp.70-74, Apr-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.7074

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  Abstract
  We consider the two tribonacci substitutions, a → ab, b → ac, c → a and a → ab, b → ca, c → a. In this paper we give some properties for the Tribonacci fractals, and its associated intersection fractal. We show in more details intersections of subtiles.

  Key-Words / Index Term
  Rauzy fractals, Substitution dynamical systems, balanced pairs algorithm

  References
  [1] P. Arnoux and S. Ito "Pisot substitutions and Rauzy fractals" Bull. Belg. Math. Soc. Simon Stevin 8: 181--207 (2001).
  [2] M.Barge and B.Diamond. "Coincidence for substitutions of Pisot Type". Bell.Soc.Math. France, 130:619-626, 2002.
  [3] Marcy Barge and Jarek Kwapisz, "Geometric theory of unimodular Pisot substitutions". American journal of mathematics(Print) 128:55, 1219-1282.
  [4] Vicent Canterini and Anne Siegel : {"Automate des préfixes-suffixes associé une substitution primitive".J. Théor. Nombres Bordeaux 13, no. 2, 353--369, 2001.
  [5] Amara Chandoul : {"On the continued fraction of fixed period in finite filds", Canadian mathematical bulletin.}.
  [6] Amara Chandoul : {"The Pell Equation", Advances in Pure Mathematics..}
  [7] Amara Chandoul : {"On the continued fraction over the filds of formal power series" , Canadian mathematical bulletin.}
  [8] Amara Chandoul : {"On Polynomials solutions of quadratic Diophantine Equations.", Advances in Pure Mathematics..}
  [9] F. M. Dekking, recurrent sets, Adv. in Math. 44 (1982), no. 1, 78-104. MR 84 : 52023.
  [10] P. Fogg, "Substitutions in dynamics, arithmetics and combinatorics" (Lecture Botes in Mathematics, Vol. 1794).
  [11] J. M. Luck, C. Godrѐche and A. Janner and T. Janssen, "The nature of the atomic surfaces of quasiperiodic self similar structures", J. Phys. A : Math. Gen. 26 : 1951-1999 (1993).
  [12] A. Messaoudi: "Propriétés arithmétiques et dynamiques du fractal de Rauzy", journal de Théorie des nombres de bordeaux, 10, 1998, 135-162.
  [13] G. Rauzy: "Nombre algébrique et substitution", Bull.Soc.Math. France 110 (1982), 147-178.
  [14] M. Queffelec, "Substitution dynamical system", Spectra analysis, lecture note in mathematics, 1294, Springer-Verlag, Berlin, 1987.
  [15] Anne Siegel: "Autour des fractals de Rauzy", Journées Femmes et Mathématiques, Paris (03/2002).
  [16] Anne Siegel and Jorg M.Thuswaldner: "Topological proprieties of Rauzy fractal", Mémoires de la SMF.
  [17] Victor F.Sirvent: "The common dynamics of the tribonacci substitutions", Bull. Belg.Math..Soc. 7 (2000), 571-582.
  [18] B. Sing and V. Sirvent: "Geometry of the common dynamics of flipped Pisot substitution", Monatshefte für Mathematik, 155 (2008), 431-448.
  [19] Victor Sirvent and yang Sirvent, "Self affine tiling via substitution dynamical systems and Rauzy fractal". Pacific journal of mathematics Vol 206, N 2, 2002.
  

  Citation
  T. Sellami, "On the Tribonacci fractals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.70-74, 2018