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### Article

Progressive Review and Analytical Approach for Optimal Solution of Stochastic Transportation Problems (STP) Involving Multi-Choice Cost

1Department of Mathematics & Statistics, School of Science & Technology, The University of Fiji, Fiji Islands

2Vision Institute of Technology, U.P. Technical University, India

3SUNY, Korea & Ex Vice-Chancellor, Avadh University, India

4Department of Operations Research, University of Delhi, India

5Department of Electronics & Communication Engineering Lucknow Institute of Technology, U.P. Technical University, India

American Journal of Modeling and Optimization. 2014, 2(3), 77-83
DOI: 10.12691/ajmo-2-3-3

Cite this paper:
Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Avadhesh Kumar Maurya. Progressive Review and Analytical Approach for Optimal Solution of Stochastic Transportation Problems (STP) Involving Multi-Choice Cost. American Journal of Modeling and Optimization. 2014; 2(3):77-83. doi: 10.12691/ajmo-2-3-3.

Correspondence to: Vishwa  Nath Maurya, Department of Mathematics & Statistics, School of Science & Technology, The University of Fiji, Fiji Islands. Email: prof.drvnmaurya@gmail.com

### Abstract

In this paper some general transportation models have been discussed and particularly a multi-choice cost stochastic transportation problem (STP) has been reviewed in the light of progressive research works of previous noteworthy researchers. In addition, an analytical approach for the optimal solution (OS) of the proposed stochastic transportation problem has been demonstrated. The analytical method proposed by us is not only heuristic but also a generalization in threefold. We remark here that some unnecessary complications involved previously have been removed in our proposed method. Finally, by way of demonstrating a numerical illustration some significant conclusive observations have also been drawn in order to highlight the threefold feature.

### References

 [1] Arsham H. and Khan A.B., A simplex-type algorithm for general transportation problems; An alternative to stepping-stone. Journal of Operational Research Society, Vol. 40(6), 1989, pp. 581-590. [2] Arsham H., Post optimality analyses of the transportation problem, Journal of the Operational Research Society, Vol. 43, 1992, pp. 121–139. [3] Balinski M.L. and Gomory R.E., A mutual primal-dual simplex method, Recent Advances in Mathematical Programming (Graves and Wolfe, eds.), McGraw- Hill, New York, 1963. [4] Beale E.M.L., An algorithm for solving the transportation problem when the shipping cost over each route is convex, Naval Research Logistics Quarterly, Vol. 6, 1959, pp. 43-56. [5] Charnes A. and Cooper W.W., The stepping-stone method for explaining linear programming: Calculation in transportation problems, Management Science, Vol. 1(1), 1954, pp. 49-69
 [6] Charnes A., Cooper W.W. and Henderson A., An Introduction to Linear Programming, Wiley, New York, 1953. [7] Cortez R.T., Stable Convex Parametric Programming and Applications, Ph. D. Thesis, McGill University, Montreal (Canada), 2000. [8] Dantzig G.B., Ford L.R. and Fulkerson D.R., A primal-dual algorithm for linear programs, in Linear Inequalities and Related Systems (Kuhn and Tucker, eds.), Annals of Mathematics Study, No. 38, Princeton University Press, Princeton, 1956. [9] Dantzig G.B., Linear Programming and Extensions, Princeton University Press, Princeton, N J, 1963. [10] Flood Merrill M., The travelling salesman problem, Operations Research, Vol. 4, 1956, pp. 61-75. [11] Ford L.R. and Fulkerson D.R., A simple algorithm for finding maximal network flows and an application to the Hitchcock problem, Canadian Journal of Mathematics, Vol. 9, 1957, pp. 210-218. [12] Fulkerson D.R., An out-of-kilter method for minimal cost flow problems, Journal of the Society for Industrial and Applied Mathematics, Vol. 9, 1961, pp. 18-27. [13] Garvin W.W., Introduction to Linear Programming, Mc-.Graw-hill New York. Hitchcock FL, 1941. [14] Garvin W.W., The distribution of a product from several sources to Numerous localities, Journal Of Mathematical Physics, Vol. 20, 1960, pp. 224-230 [15] Gass S., Linear Programming Mc-Graw-Hill New York, 1964 [16] Gleyzal A., An algorithm for solving the transportation problem, Journal of Research of the National Bureau of Standards, Vol. 54 (4), 1955, pp. 213-216 [17] Goyal S.K., Improving VAM for unbalanced transportation problem, Journal of Operational Research Society, Vol. 35(12), 1984, pp.1113-1114 [18] Grobatenko N.G. and Suvorov B.P., Model for short-time planning of production and transportation of petroleum industry, B.P. Suvorov (Editor), Mathematical Methods and Models in Petroleum Industry Planning, Nauka, Moscow (In Russian), 1967 [19] Henderson A. and Schlaifer R., Mathematical programming: Better information for better decision-making, Harvard Business Review, Vol. 32, 1954, pp. 73-100. [20] Hitchcock F.L., The distribution of a product from several sources to numerous localities, Journal of Mathematical Physics, Vol. 20, 2006, pp. 224-230 [21] Hunjet D., Milinović M., Neralić L. and Szirovicza L., Production-transportation problem and its extensions, K. Šorić, T. Hunjak and R. Scitovski (Eds.), Proceedings of the 9th International Conference on Operational Research, Croatian Operational Research Society and Department of Mathematics, University of Osijek, Osijek, 2003, pp. 73-81 [22] Ivshin Yu. F., Production-transportation model of refinery group, Control and Economy of Material-Technical Supply, No. 2, Moscow, (In Russian), 1972 [23] Kirca and Stair, A heuristic for obtaining an initial solution for the transportation problem, Journal of operational Research Society, Vol. 41(9) 1990, pp. 865-867 [24] Koopmans T.C., Optimum utilization of the transportation system, Proceeding of the International Statistical Conference, Washington D.C., 1947 [25] Koopmans T.C., Optimum utilization of transportation system, Econometrica, Supplement, Vol. 17, 1949. [26] Kuhn H.W., The Hungarian method for the assignment problem, Naval Research Logistics Quarterly, Vol. 2, 1955, pp. 83-97. [27] Kuhn H.W., Variants of the Hungarian method for assignment problem, Naval Research Logistics Quarterly, Vol. 3, 1956, pp. 253-258. [28] Mahapatra D.R., Roy S.K. and Biswal M.P., Multi-choice stochastic transportation problem involving extreme value distribution, Applied Mathematical Modelling, Vol. 37, 2013, pp. 2230-2240. [29] Maurya A.K. and Maurya V.N., A novel algorithm for optimum balancing energy consumption LEACH protocol using numerical simulation technique, International Journal of Electronics Communication and Electrical Engineering, Algeria, Vol. 3(4), 2013, pp. 1-19, ISSN: 2277-7040. [30] Maurya V.N. and Garg M.B., An alternative approach for determining an optimum assignment schedule in management systems, Acta Ciencia Indica Mathematics, Vol. 32(3), 2006, pp. 1017-1022, ISSN: 0970-0455. [31] Maurya V.N., Bathla R. K., Maurya A.K., Arora D.K and Gautam R.A., An alternate efficient sorting algorithm applicable for classification of versatile data, International Journal of Mathematical Modeling and Applied Computing, Academic & Scientific Publishing, New York, USA, Vol.1(1), 2013, pp. 1-10, ISSN: 2332-3744. [32] Maurya V.N., Computational approach to cost and profit analysis of k-out of-n repairable system integrating human error and system failure constraints, Physical Sciences Research International, Nigeria, Vol. 1 (4), 2013, pp. 133-140. [33] Maurya V.N., Investigation of probability generating function in an interdependent M/M/1:(∞;GD) queueing model with controllable arrival rates using Rouche’s theorem, Open Journal of Optimization, Scientific Research Publishing, Irvine, California, USA, Vol. 1 (2), 2012, pp. 34-38, ISSN (Print): 2325-7105, ISSN (Online): 2325-7091. [34] Maurya V.N., Mathematical modeling for performance analysis and inference of k-out of-n repairable system integrating human error and system failure constraints, American Journal of Modeling and Optimization, Science & Education Publishing, USA, Vol. 2 (1), 2014, pp. 16-24, ISSN (Print) 2333-1143, ISSN (Online) 2333-1267. [35] Maurya V.N., Mathematical modelling and performance analysis of single server two-state batch arrivals and batch service Markovian queue with multiple vacations, American Journal of Modeling and Optimization, Science & Education Publishing, USA, Vol. 2 (2), 2014, ISSN (Print) 2333-1143, ISSN (Online) 2333-1267. [36] Maurya V.N., Maximum entropy analysis of MX/(G1,G2)/1 retrial queueing model with second phase optional service and Bernoulli vacation schedule, American Journal of Operational Research, Scientific and Academic Publishing, Rosemead, California, USA, Vol. 3 (1), 2013, pp. 1-12, ISSN (Print): 2324-6537, ISSN (Online): 2324-6545. [37] Maurya V.N., Performance Analysis and Inference of Mixed Poisson Queuing Models, Scholar’s Press Publishing Co., Saarbrucken, Germany, ISBN 978-3-639-70092-3, 2013. [38] Maurya V.N., Performance analysis of MX/(G1,G2)/1 queueing model with second phase optional service and Bernoulli vacation schedule, American Journal of Modeling and Optimization, Science and Education Publishing, New York, USA, Vol. 2 (1), 2014, pp. 1-7, ISSN (Print) 2333-1143, ISSN (Online) 2333-1267. [39] Munkres and James, Algorithms for the assignment and transportation problems, Journal of the Society for Industrial and Applied Mathematics, Vol. 5, 1957, pp. 32-38. [40] Neralić L., Modified Lagrangians and optimization of costs, Ph.D. Thesis, Faculty of Economics, University of Zagreb, Zagreb. (In Croatian), 1979. [41] Neralić, L., An extended production-transportation model for oil products, Nafta, Vol. 31, 1980, pp. 267-271. [42] Pandian P. and Natarajan G., A new method for finding an optimal solution for transportation problems, International Journal of Mathematical Sciences & Engineering Applications, Vol. 4, 2010, pp. 59-65. [43] Ping Ji and Chu K.F., A dual-matrix approach to the transportation problem. Asia-Pacific Journal of Operation Research, Vol. 19(1), 2002, pp. 35-45. [44] Reinfeld N.V. and Vogel W.R., Mathematical Programming New Jersey Prentice- Hall, Englewood Cliffs, 1958. [45] Samuel A. Edward and Venkatachalapathy M., Modified Vogel’s approximation method for fuzzy transportation problems, Applied Mathematical Sciences, Vol. 28, 2011, pp. 1367-1372. [46] Sharma. J.K., Operations Research-Theory and applications, Macmillan India Ltd., New Delhi, India, 2005. [47] Shore H.H., The transportation problem and the Vogel approximation method, Decision Sciences, Vol. 1 (3-4), 1970, pp. 441-457. [48] Sudhakar V.J., Arunsankar N. and Karpagam T., A new approach for finding an optimal solution for transportation problems, European Journal of Scientific Research, Vol. 68, 2012, pp. 254-257. [49] Taha. H.A., Operations Research- Introduction, Prentice Hall of India, New Delhi, India, 2004.
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### Article

mHealth: A Sustainable Healthcare Model for Developing World

1Department of Biochemistry and Molecular Biology, Jahangirnagar Universtity, Savar, Dhaka, Bangladesh

2Department of Computer Science and Engineering, Jahangirnagar Universtity, Savar, Dhaka, Bangladesh

American Journal of Modeling and Optimization. 2014, 2(3), 73-76
DOI: 10.12691/ajmo-2-3-2

Cite this paper:
Sharmin Jahan, M. Mozammel Hoque Chowdhury. mHealth: A Sustainable Healthcare Model for Developing World. American Journal of Modeling and Optimization. 2014; 2(3):73-76. doi: 10.12691/ajmo-2-3-2.

Correspondence to: M.  Mozammel Hoque Chowdhury, Department of Computer Science and Engineering, Jahangirnagar Universtity, Savar, Dhaka, Bangladesh. Email: mozammel_ju@yahoo.com

### Abstract

Health is a basic requirement to improve the quality of life. Providing effective health care is an essential component towards the social and economic development of a country. A large number of people in the developing countries, particularly in rural and remote areas, remained with no or little access to health care facilities. However, recent emergence of mobile communication technologies could play in improving healthcare services. There is a great potential in using mHealth as one of the supportive systems within the healthcare sector to solve the inequalities in healthcare delivery between rural and urban hospitals. This research aims to evaluate the potentialities, issues and challenges of developing mobile healthcare system in the developing world. We have proposed a potential mHealth model based on mobile telecommunication networks. This research offers a set of guidelines to aid the implementation of a successful mobile healthcare system.

### References

 [1] Akter, S., D’Ambra, J., Ray, P. (2010) User perceived services quality of mHealth Services around the world. 18 th European Conference on Information Systems, Pretoria, South Africa. [2] Kuhn, K. A.. Wurst, S. H. R, Bott., O. J., Giuse, D. A. (2006), Expanding the scope of health information systems: challenges and developments. IMIA yearbook of Medical Informatics 2006. [3] UN foundation & Vodafone foundation (2009), “mHealth for Development: The opportunity of mobile technology for healthcare in developing world”, available from: http://www.vitalwaveconsulting.com/insights/mHealth.htm last logged in April 03, 2009. [4] Istepanian, Robert; Laxminarayan, Swamy; Pattichis, Constantinos S., eds. (2005). M-Health: Emerging Mobile Health Systems. Springer. ISBN 978-0-387-26558-2. [5] Torgan, Carol (November 6, 2009). "The mHealth Summit: Local & Global Converge". caroltorgan. com. Retrieved July 29, 2011.
 [6] World Helath Organization (WHO). The world health report. Primary healthcare- now more than ever, Geneva, 2008. [7] Istepanian, R. and J. Lacal (2003). “Emerging Mobile Communication Technologies for Health: Some Imperative notes on mHealth.” Paper presented at the 25th International Conference of the IEEE Engineering in Medicine and Biology Society, Cancun, Mexico. [8] Mechael, P (2009), “The case for mHealth in developing countries”, Innovations, MIT press. [9] Per-Gunnar Svensson, “eHealth Applications in Health Care Management”, EHealth International, 2002; 1:5, pp. 1-2. [10] Saroj Mishra and Indra Pratap S, "mHealth: A Developing Country Perspective", Making the eHealth connection, Bellagio, Italy, July 13- August 8, 2008. [11] Mechael, P. “WHO mHealth Review: Towards the Development of an mHealth Strategy”. August 2007. [12] Vital Wave Consulting, mHealth for Development: The Opportunity of Mobile Technology for Healthcare in the Developing World. United Nations Foundation, Vodafone Foundation. p. 9. February 2009. [13] Andaleeb, S. S. Service quality perceptions and patient satisfaction: a study of hospitals in a developing country. Social Science & Medicine, 2001. 52 (9), 1359-1370. [14] Brown, K., “Developing countries must plan road map for e-health”, Conference Interview by Africa. Bellagio, Italy, 2008. [15] Mechael, P. The case for mHealth in developing countries, Innovations: Technology, Governance, Globalization, MIT Press Journal (online), 2009, 4 (1). [16] International Telecommunication Union (ITU), Geneva, Switzerland, The World in 2013: ICT Facts and Figures, http:\\www.itu.int/ict (visited on May 30, 2014).
Show Less References

### Article

A Robust De-Noising Model for Image Enhancement with Adaptive Median Filtering

1Department of Computer Science and Engineering, Jahangirnagar University, Dhaka, Bangladesh

American Journal of Modeling and Optimization. 2014, 2(3), 69-72
DOI: 10.12691/ajmo-2-3-1

Cite this paper:
M. Mozammel Hoque Chowdhury. A Robust De-Noising Model for Image Enhancement with Adaptive Median Filtering. American Journal of Modeling and Optimization. 2014; 2(3):69-72. doi: 10.12691/ajmo-2-3-1.

Correspondence to: M.  Mozammel Hoque Chowdhury, Department of Computer Science and Engineering, Jahangirnagar University, Dhaka, Bangladesh. Email: mozammel_ju@yahoo.com

### Abstract

This paper presents a robust de-noising model for image enhancement using adaptive median filtering. In this approach image noise is detected with a standard median filter using an adaptive window. Within the window, the original value of the center pixel is changed to a newer that is closer to or same as the standard median. A comparison has been arranged among the proposed method, the standard median (SM) filter and the center weighted median (CWM) filter, which proves the superiority of the proposed filtering method.

### References

 [1] A. Polesel, G. Ramponi, and V. J. Mathews, “Image enhancement via adaptive unsharp masking,” IEEE Trans. Image Processing, vol. 9, pp. 505-510, Mar. 2000. [2] B. Singh, R. Singh and H. Singh, “Removal of High Density Salt & Pepper Noise in Noisy color Images using Proposed Median Filter”, International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE, Vol. 2, Issue 2, pp. 253-256, 2013 [3] T. Loupas, W. N. McDicken, and P. L. Allan, “An adaptive weighted median filter for speckle suppression in medical ultrasonic images,” IEEE Transactions on Circuits and Systems, Vol. 36, Jan. 1989. [4] S. J. Ko and Y.H Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Transactions on Circuits and Systems, Vol. 38, pp. 984-993, 1991. [5] T. C. Chen, K. K. Ma and L. H. Chen, “Tri-state median filter for image de-noising,” IEEE Transactions on Image Processing, Vol. 8, No. 12, pp. 1834-1838, Dec. 1999.