A COMPETENT ALGORITHM TO FIND THE INITIAL BASIC FEASIBLE SOLUTION OF COST MINIMIZATION TRANSPORTATION PROBLEM


 Hester Holt
 2 years ago
 Views:
Transcription
1 BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 1, 016 Secţia AUTOMATICĂ şi CALCULATOARE A COMPETENT ALGORITHM TO FIND THE INITIAL BASIC FEASIBLE SOLUTION OF COST MINIMIZATION TRANSPORTATION PROBLEM BY AMINUR RAHMAN KHAN 1,*, ADRIAN VILCU, MD. SHARIF UDDIN 1 and FLORINA UNGUREANU 3 1 Jahangirnagar University, Dhaka134, Bangladesh. Department of Mathematics Gheorghe Asachi Technical University of Iasi, Romania, Department of Management Engineering 3 Gheorghe Asachi Technical University of Iasi, Romania, Department of Automatic Control and Computer Engineering Received: 6 July 015 Accepted for publication: 4 July 015 Abstract. In this paper, we propose a new algorithm along with MATLAB code for determining the initial basic feasible solution of Cost Minimization Transportation Problem (CMTP). Comparative study is carried out between the proposed algorithm and the other existing algorithm by means of sample examples which shows that the proposed algorithm provides better result. Key words: Cost minimization transportation problem; MATLAB; Distribution indicator; Optimum solution. 010 Mathematics Subject Classification: 90B50, 90C08. * Corresponding author;
2 Aminur Rahman Khan et al. 1. Introduction The branch of Linear Programming Problem (LPP) in which a single uniform commodity is shifted from several sources to different localities in such a way to minimize the total transportation cost while fulfilling all supply and demand limitations are CMTP. The basic CMTP was originally developed by Hitchcock (1941). Competent methods of solution derived from the simplex algorithm were developed, mainly by Dantzig (1947) and then by Charnes et al. (1953). The problem of CMTP has been studied since long and is well known by Abdur Rashid (013), Aminur Rahman Khan (011; 01; 015a; 015b), Hamdy (007), Juman & Hoque (015), Kasana & Kumar (005), M. Sharif Uddin et al. (011; 01), Md. Amirul Islam et al. (01a, 01b), Md. Ashraful Babu et al. (013; 014a; 014b), Md. Main Uddin et al. (013; 015), Mollah Mesbahuddin Ahmed et al. (014), Sayedul Anam et al. (01) and Utpal Kanti Das et al. (014a; 014b). For determining the initial basic feasible solution of TP, Reinfeld and Vogel (1958) introduced Vogel s Approximation Method (VAM) by defining penalty as the difference of lowest and next to lowest cost in each row and column of a transportation table and allocate to the minimum cost cell corresponding to the highest penalty; Kasana and Kumar (005) presented Extremum Difference Method (EDM) by calculating the penalty as the difference between the highest and lowest unit transportation cost in each row and column and allocate as like as VAM; Aminur Rahman Khan (011) proposed Highest Cost Difference Method (HCDM) by introducing pointer cost as the difference of highest and next to highest cost in each row and column of a transportation table and allocate to the minimum cost cell corresponding to the highest three pointer costs. Kirca and Satir (1990) first define the Total Opportunity Cost Matrix (TOCM) as the sum of Row Opportunity Cost Matrix (ROCM) and Column Opportunity Cost Matrix (COCM). Where, the ROCM is generated by subtracting the lowest cost of each row from the other cost elements in that row and, the COCM is generated by subtracting the lowest cost of each column from the other cost elements in that column. Kirca and Satir then essentially apply the Least Cost Method with some tiebreaking policies on the TOCM to determine the feasible solution of the transportation problem. Mathirajan and Meenakshi (004) applied VAM on the TOCM, Md. Amirul Islam et al. applied EDM (01a) and HCDM (01b) on TOCM whereas Aminur Rahman Khan (015a) calculate the pointer cost as the sum of all entries in the respective row or column of the TOCM to find the feasible solution of the transportation problem. Here, in this paper, we determine the distribution indicator for each cell of the TOCM by subtracting corresponding row and column highest element of every cell from the respective element. We then make maximum possible
3 Bul. Inst. Polit. Iaşi, t. LIX (LXIII), f. 1, allocation to the cell having the smallest distribution indicator. The proposed method is also illustrated with several numerical examples. Comparative study shows that the proposed algorithm gives better result in comparison to the other existing heuristics available in the text. We also coded the presented algorithm by using MATLAB and it is utilized via many randomly generated problems of different order in order to prove the exactness of the code. Based on the results we conclude that the coded algorithm for solving the transportation problem is accurate.. Formulation of Cost Minimization Transportation Problem A general cost minimization transportation problem is represented by the network in the following Fig. 1. S 1 Source 1 C : X Locality 1 D 1 Units of Supply S D Units of Demand S m m C mn : X mn n D n Fig. 1 Network representation of Cost Minimization Transportation Problem There are m sources and n destinations, each represented by a node. The arrows joining the sources and the localities represent the route through which the commodity is shifted. Suppose S i denotes the amount of supply at source i (i = 1,,, m), D j represents the amount of demand at destination j (j=1,,, n), C denotes the unit transportation cost from sources i to destination j, X represents the amount transported from sources i to destination j. Then the LPP model of the balanced cost minimization transportation problem is m n Min. Z = i = j = C X 1 1 n s/t, =1 X = i ; i=1,,,m j S
4 Aminur Rahman Khan et al. m i =1 X = D j ; j=1,,,n X 0 for all i, j. (1) 3. Algorithm of Proposed Method The proposed algorithm for determining the initial basic feasible solution consists of the following steps: Step 1 Step Step 3 : Subtract the smallest entry of every row from each of the element of the subsequent row of the transportation table and place them on the righttop of the corresponding elements. C C ik C, where C ( C, C,, C ) ik = min i1 i in, i = 1,,......, m : Apply the same operation on each of the column and place them on the leftbottom of the corresponding elements. C C kj C, where C kj = min ( C 1 j, C j,, C mj ), j = 1,,......,n : Form the TOCM whose entries are the summation of righttop and leftbottom elements of Steps 1 and. C = C C + C C ( ) ( ) Step 4 : For each cell (i, j), calculate the distribution indicator, Δ = c  ū i  ē j, where, ū i =largest unit time in the ith row and ē j = largest unit time in the jth column. Step 5 : Make maximum possible allocation to the cell having the smallest value of Δ. If tie occurs in the distribution indicator, select any one of them arbitrarily. Step 6 Step 7 Step 8 : No further deliberation is required for the row or column which is satisfied. If both the row and column are satisfied at a time, delete both of them assigning an extra zero supply (or demand) to any one cell of the satisfied row or column. : Calculate fresh distribution indicators for the remaining submatrix as in Step 4 and allocate following the procedure of Steps 5 and 6. : Continue the process until all rows and columns are satisfied. ik kj
5 Bul. Inst. Polit. Iaşi, t. LIX (LXIII), f. 1, Step 9 : Finally compute the total transportation cost as the sum of the product of original transportation cost and corresponding allocation obtained in step The Novelty of our algorithm Although we have used TOCM of Kirca and Satir in our proposed algorithm; we calculate the distribution indicator (in step 4) for each cell of the TOCM by subtracting corresponding row and column highest element of every cell from the respective element. Whereas Mathirajan and Meenakshi calculate the penalty as the difference of lowest and next to lowest entries of the TOCM; Md. Amirul Islam et al. calculate distribution indicator as the difference of highest and lowest entries of the TOCM and Aminur Rahman Khan et al. calculate pointer cost as the sum of all entries in the respective row or column of the TOCM. 5. Material and Methods Table 1, 10 and 11 shows three sample cost minimizing transportation problem, selected at random to solve by using proposed algorithm and the existing algorithms. Example 1: Table 1 Cost Matrix for the Numerical example Destination Demand Factory Step 1: 3 is the minimum element of the first row, so we subtract 3 from each element of the first row. Similarly, we subtract 1 and 3 from each element of the nd and 3 rd row respectively and place all the differences on the righttop of the corresponding elements in Table. Step : In a similar fashion, we subtract 3, 1, and 4 from each element of the 1 st, nd, 3 rd and 4 th column respectively and place the result on the leftbottom of the corresponding elements in Table.
6 Aminur Rahman Khan et al. Table Formation of Total Opportunity Cost Matrix Destination Demand Factory Step 3: We add the righttop and leftbottom entry of each element of the transportation table obtained in Iteration 1 and Iteration and formed the TOCM as in Table 3. Table 3 Total Opportunity Cost Matrix (TOCM) Destination Demand Factory Step 4: We determine the distribution indicator for each cell of the TOCM by subtracting corresponding row and column highest element of every cell from the respective element. Here, c 11 =0, highest entry in the first row is 11 and in the first column is 8, so distribution indicator, Δ 11 =0811=19. Do the same for each entry and place them in the righttop of every cell of the cost matrix. Table 4 Determination of distribution indicator after Step Demand
7 Bul. Inst. Polit. Iaşi, t. LIX (LXIII), f. 1, Step 5: Here, smallest value of Δ =  corresponding to the cell (3, 3). So we allocate 13 units (minimum of 17 and 13) to the cell (3, 3). We adjust the supply and demand requirements corresponding to the cell (3, 3) and since the demand for the cell (3, 3) is satisfied, we delete the third column and calculate the distribution indicator again for the resulting reduced transportation table. Table 5 Determination of distribution indicator after Step Demand Step 6: Here, smallest value of Δ = 0 corresponding to the cell (, ). So we allocate 19 units (minimum of 8 and 19) to the cell (, ). We adjust the supply and demand requirements corresponding to the cell (, ) and since the demand for the cell (, ) is satisfied, we delete the third column and calculate the distribution indicator again for the resulting reduced transportation table. Table 6 Determination of distribution indicator after Step Demand
8 Aminur Rahman Khan et al. Step 7: Here, smallest value of Δ = 14 corresponding to the cell (, 4). So we allocate 9 units (minimum of 9 and 18) to the cell (, 4). We adjust the supply and demand requirements corresponding to the cell (, 4) and since the supply for the cell (, 4) is satisfied, we delete the second row and calculate the distribution indicator again for the resulting reduced transportation table. Table 7 Determination of distribution indicator after Step Demand Step 8: Here, smallest value of Δ = 11 corresponding to the cell (1, 4), (3, 1) and (3, 4). So we allocate 9 units (minimum of 0 and 9) to the cell (1, 4). We adjust the supply and demand requirements corresponding to the cell (1, 4) and since the demand for the cell (1, 4) is satisfied, we delete the fourth column and calculate the distribution indicator again for the resulting reduced transportation table. Table 8 Determination of distribution indicator after Step Demand Step 9: Since only the first column is remaining with two unallocated cell in this case, we allocate 11 units (minimum of 11 and 15) to the cell (1, 1) and 4 units (minimum of 4 and 4) to the cell (3, 1).
9 Bul. Inst. Polit. Iaşi, t. LIX (LXIII), f. 1, We adjust the supply and demand requirements again and we see that all supply and demand values are exhausted. Table 9 Determination of distribution indicator after Step Demand Step 10: Since all the rim conditions are satisfied and total number of allocation is 6. Therefore, the solution for the given problem is x =11, 9 11 x 14=, x = 19, x 9 4 =, x = 31 4 and x = for a flow of 65 units with the total transportation cost Example : z = = 00 Table 10 Cost Matrix for the Numerical example Destination 1 3 Supply Demand Factory Example 3: Fac tory Table 11 Cost Matrix for the Numerical example Destination
10 Aminur Rahman Khan et al Demand Result Table 1 shows a comparison among the solutions obtained by our Proposed Approach and the other existing methods and also with the optimal solution by means of the above three sample examples and it is seen that our proposed method gives better results. Table 1 A comparative study of different solutions Solution obtained by Total Transportation Cost Ex. 1 Ex. Ex. 3 North West Corner Method Row Minimum Method Column Minimum Method Least Cost Method Vogel s Approximation Method Extremum Difference Method Highest Cost Difference Method TOCMMMM Approach TOCMVAM Approach TOCMEDM Approach TOCMHCDM Approach TOCMSUM Approach Average Cost Method Proposed Approach Optimum Solution We also solve randomly selected transportation problem of order 3 3, 3 4, 3 5, 4 3, 4 4, 4 5, 4 6, 6 6 and see that the MATLAB code presented by us gives identical result as the manual solution which proves the correctness of our code. 7. Conclusion A new algorithm along with MATLAB code for finding an initial basic feasible solution of cost minimization transportation problem is introduced. We also illustrate this algorithm numerically to test the efficiency of
11 Bul. Inst. Polit. Iaşi, t. LIX (LXIII), f. 1, the proposed method. Comparative study among the solution obtained by proposed method and the other existing methods by means of sample examples show that our proposed method gives better result. Acknowledgement The first author acknowledges the financial support provided by the EU Erasmus Mundus ProjectcLINK, Grant Agreement No: 1645/ EM, Action. REFERENCES Abdur Rashid, Syed Sabbir Ahmed, Md. Sharif Uddin, Development of a New Heuristic for Improvement of Initial Basic feasible solution of a Balanced Transportation Problem, Jahangirnagar University Journal of Mathematics and Mathematical Sciences, 8, , 013. Aminur Rahman Khan, A Resolution of the Transportation Problem: An Algorithmic Approach, Jahangirnagar University Journal of Science, 34,, 496, 011. Aminur Rahman Khan, Analysis and Resolution of the Transportation Problem: An Algorithmic Approach, M. Phil. Thesis, Dept. of Mathematics, Jahangirnagar University, 01. Aminur Rahman Khan, Adrian Vilcu, Nahid Sultana, Syed Sabbir Ahmed, Determination of Initial Basic Feasible Solution of a Transportation Problem: A TOCMSUM Approach, Buletinul Institutului Politehnic Din Iasi, Romania, Secţia Automatica si Calculatoare, LXI (LXV), 1, 3949, 015a. Aminur Rahman Khan, Avishek Banerjee, Nahid Sultana, M Nazrul Islam, Solution Analysis of a Transportation Problem: A Comparative Study of Different Algorithms accepted for publication in the Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile. Leathership, in issue of 015b. Charnes A., Cooper W.W, Henderson A., An Introduction to Linear Programming, John Wiley & Sons, New York, Dantzig G.B., Linear Programming and Extentions, Princeton University Press, Princeton, N J, Hamdy A.T., Operations Research: An Introduction, 8 th Edition, Pearson Prentice Hall, Upper Saddle River, New Jersey 07458, 007. Hitchcock F.L., The distribution of a Product from Several Sources to Numerous Localities, Journal of Mathematics and Physics, 0, 430, Juman Z.A.M.S., Hoque M.A., An Efficient heuristic to obtain a Better Initial Feasible Solution to the Transportation Problem, Applied Soft Computing, 34, , 015. Kasana H.S., Kumar K.D., Introductory Operations Research: Theory and Applications, Springer International Edition, New Delhi, 005. Koopmans T.C., Optimum Utilization of the Transportation System, Econometrica, 17, 34, 1947.
12 Aminur Rahman Khan et al. M. Sharif Uddin, Sayedul Anam, Abdur Rashid, Aminur R. Khan, Minimization of Transportation Cost by Developing an Efficient Network Model, Jahangirnagar Journal of Mathematics & Mathematical Sciences, 6, , 011. M. Sharif Uddin, Transportation Time Minimization: An Algorithmic Approach, Journal of Physical Sciences, Vidyasagar University, 16, 5964, 01. Mathirajan M., Meenakshi B., Experimental Analysis of Some Variants of Vogel s Approximation Method, AsiaPacific Journal of Operational Research, 1, 4, , 004. Md. Amirul Islam, Md. Masudul Haque, Md. Sharif Uddin, Extremum Difference Formula on Total Opportunity Cost: A Transportation Cost Minimization Technique, Prime University Journal of Multidisciplinary Quest, 6, 1, , 01a. Md. Amirul Islam, Aminur Rahman Khan, M. Sharif Uddin, M. Abdul Malek, Determination of Basic Feasible Solution of Transportation Problem: A New Approach, Jahangirnagar University Journal of Science, 35, 1, , 01b. Md. Ashraful Babu, Md. Abu Helal, Mohammad Sazzad Hasan, Utpal Kanti Das, Lowest Allocation Method (LAM): A New Approach to Obtain Feasible Solution of Transportation Model, International Journal of Scientific and Engineering Research, 4, 11, , 013. Md. Ashraful Babu, Md. Abu Helal, Mohammad Sazzad Hasan, Utpal Kanti Das, Implied Cost Method (ICM): An Alternative Approach to Find the Feasible Solution of Transportation Problem, Global Journal of Science Frontier ResearchF: Mathematics and Decision Sciences, 14, 1, 513, 014a. Md. Ashraful Babu, Utpal Kanti Das, Aminur Rahman Khan, Md. Sharif Uddin, A Simple Experimental Analysis on Transportation Problem: A New Approach to Allocate Zero Supply or Demand for All Transportation Algorithm, International Journal of Engineering Research & Applications (IJERA), 4, 1, 4184, 014b. Md. Main Uddin, Md. Azizur Rahaman, Faruque Ahmed, M. Sharif Uddin, Md. Rashed Kabir, Minimization of Transportation Cost on the basis of Time Allocation : An Algorithmic Approach, Jahangirnagar Journal of Mathematics & Mathematical Sciences, 8, 4753, 013. Md. Main Uddin, Aminur Rahman Khan, Sushanta Kumer Roy, Md. Sharif Uddin, A New Approach for Solving Unbalanced Transportation Problem due to Additional Supply, accepted for publication in the Bulletin of the Polytechnic Institute of Iasi, Romania, Section Textile. Leathership, in issue of 015. Mollah Mesbahuddin Ahmed, Abu Sadat Muhammad Tanvir, Shirin Sultana, Sultan Mahmud, Md. Sharif Uddin, An Effective Modification to Solve Transportation Problems: A Cost Minimization Approach, Annals of Pure and Applied Mathematics, 6,, , 014a. Mollah Mesbahuddin Ahmed, Algorithmic Approach to Solve Transportation Problems: Minimization of Cost and Time, M. Phil. Thesis, Dept. of Mathematics, Jahangirnagar University, 014b. Omer Kirca, Ahmet Satir, A heuristic for obtaining an initial solution for the transportation problem, Journal of the Operational Research Society, 41, , 1990.
13 Bul. Inst. Polit. Iaşi, t. LIX (LXIII), f. 1, Reinfeld N. V., Vogel W. R., Mathematical Programming, Englewood Cliffs, NJ: PrenticeHall, Sayedul Anam, Aminur Rahman Khan, Md. Minarul Haque, Reza Shahbaz Hadi, The Impact of Transportation Cost on Potato Price: A Case Study of Potato Distribution in Bangladesh, The International Journal of Management, 1, 3, 11, 01. Utpal Kanti Das, Md. Ashraful Babu, Aminur Rahman Khan, Md. Abu Helal, Md. Sharif Uddin, Logical Development of Vogel s Approximation Method (LD VAM): An Approach to Find Basic Feasible Solution of Transportation Problem, International Journal of Scientific & Technology Research (IJSTR), 3,, 448, 014a. Utpal Kanti Das, Md. Ashraful Babu, Aminur Rahman Khan, Md. Sharif Uddin, Advanced Vogel s Approximation Method (AVAM): A New Approach to Determine Penalty Cost for Better Feasible Solution of Transportation Problem, International Journal of Engineering Research & Technology (IJERT), 3, 1, , 014b. ALGORITM PENTRU DETERMINAREA SOLUȚIEI INIȚIALE ÎN CAZUL MINIMIZĂRII COSTULUI PROBLEMEI DE TRANSPORT (Rezumat) Lucrarea propune un nou algoritm pentru determinarea unei soluții inițiale pentru o problemă clasică de transport bazată pe cost. Se prezintă problema, este descrisă metoda, se aplică algoritmul pe un exemplu numeric și se compară, pe trei instante, rezultatele algoritmului propus cu cele furnizate de alți algoritmi citați în literatura de specialitate.
A COMPETENT ALGORITHM TO FIND THE INITIAL BASIC FEASIBLE SOLUTION OF COST MINIMIZATION TRANSPORTATION PROBLEM
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LXI (LXV), Fasc., 05 SecŃia AUTOMATICĂ şi CALCULATOARE A COMPETENT ALGORITHM TO FIND THE INITIAL
More informationDETERMINATION OF INITIAL BASIC FEASIBLE SOLUTION OF A TRANSPORTATION PROBLEM: A TOCMSUM APPROACH
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LXI (LXV), Fasc. 1, 2015 SecŃia AUTOMATICĂ şi CALCULATOARE DETERMINATION OF INITIAL BASIC FEASIBLE
More informationA New approach for Solving Transportation Problem
Journal for Research Volume 03 Issue 01 March 2017 ISSN: 23957549 A New approach for Solving Transportation Problem Manamohan Maharana Lecturer Department of Mathematics M.P.C. (Jr.) College, Baripada,
More informationSolving the Linear Transportation Problem by Modified Vogel Method
Solving the Linear Transportation Problem by Modified Vogel Method D. Almaatani, S.G. Diagne, Y. Gningue and P. M. Takouda Abstract In this chapter, we propose a modification of the Vogel Approximation
More informationThe MOMC Method: a New Methodology to Find. Initial Solution for Transportation Problems
Applied Mathematical Sciences, Vol. 9, 2015, no. 19, 901914 HIKARI Ltd, www.mhikari.com http://dx.doi.org/10.12988/ams.2015.4121013 The MOMC Method: a New Methodology to Find Initial Solution for Transportation
More informationAdvanced Approximation Method for Finding an Optimal Solution of Unbalanced Fuzzy Transportation Problems
Global Journal of Pure and Applied Mathematics. ISSN 09731768 Volume 13, Number 9 (2017), pp. 53075315 Research India Publications http://www.ripublication.com Advanced Approximation Method for Finding
More informationLecture notes on Transportation and Assignment Problem (BBE (H) QTM paper of Delhi University)
Transportation and Assignment Problems The transportation model is a special class of linear programs. It received this name because many of its applications involve determining how to optimally transport
More informationA Comparative study on Algorithms for ShortestRoute Problem and Some Extensions
International Journal of Basic & Applied Sciences IJBASIJENS Vol: No: 0 A Comparative study on Algorithms for ShortestRoute Problem and Some Extensions Sohana Jahan, Md. Sazib Hasan Abstract The shortestroute
More informationZero Average Method to Finding an Optimal Solution of Fuzzy Transportation Problems
IOSR Journal of Mathematics (IOSRJM) eissn: 2278728, pissn: 231976X. Volume 13, Issue 6 Ver. I (Nov.  Dec. 2017), PP 663 www.iosrjournals.org Zero verage Method to Finding an Optimal Solution of
More informationABOUT MANUFACTURING PROCESSES CAPABILITY ANALYSIS
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 4, 013 Secţia CONSTRUCŢII DE MAŞINI ABOUT MANUFACTURING PROCESSES CAPABILITY
More informationA NOVEL SYSTOLIC ALGORITHM FOR 2D DISCRETE SINE TRANSFORM
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 3, 2013 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ A NOVEL SYSTOLIC ALGORITHM
More informationNew Methodology to Find Initial Solution for. Transportation Problems: a Case Study with Fuzzy Parameters
Applied Mathematical Sciences, Vol. 9, 2015, no. 19, 915927 HIKARI Ltd, www.mhikari.com http://dx.doi.org/10.12988/ams.2015.4121018 New Methodology to Find Initial Solution for Transportation Problems:
More informationAvailable online through ISSN
International Research Journal of Pure Algebra 4(4), 2014, 509513 Available online through www.rjpa.info ISSN 2248 9037 A STUDY OF UNBALANCED TRANSPORTATION PROBLEM AND USE OF OBJECT ORIENTED PROGRAMMING
More informationTransportation problem
Transportation problem It is a special kind of LPP in which goods are transported from a set of sources to a set of destinations subjects to the supply and demand of the source and destination, respectively,
More informationFundamentals of Operations Research. Prof. G. Srinivasan. Department of Management Studies. Indian Institute of Technology, Madras. Lecture No.
Fundamentals of Operations Research Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture No. # 13 Transportation Problem, Methods for Initial Basic Feasible
More informationAUTONOMOUS ROBOT NAVIGATION BASED ON FUZZY LOGIC AND REINFORCEMENT LEARNING
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi, Tomul LVI (LX), Fasc. 4, 2010 Secţia CONSTRUCŢII DE MAŞINI AUTONOMOUS ROBOT NAVIGATION BASED ON FUZZY
More informationA Computer Oriented Method for Solving Transportation Problem
Dhaka Univ. J. Sci. 63(1): 17, 015 (January) A Computer Oriented Method for Solving Transportation Problem Sharmin Afroz and M. Babul Hasan* Department of Mathematics, Dhaka University, Dhaka1000, Bangladesh
More informationBOOLEAN FUNCTION DECOMPOSITION BASED ON FPGA BASIC CELL STRUCTURE
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LXI (LXV), Fasc. 1, 2015 SecŃia AUTOMATICĂ şi CALCULATOARE BOOLEAN FUNCTION DECOMPOSITION BASED
More informationA New Approach for Solving Unbalanced. Fuzzy Transportation Problems
International Journal of Computing and Optimization Vol. 3, 2016, no. 1, 131140 HIKARI Ltd, www.mhikari.com https://doi.org/10.12988/ijco.2016.6819 A New Approach for Solving Unbalanced Fuzzy Transportation
More informationsuccess of Business enterprise especially in manufacturing organization. Goods manufactured by firm need to be distributed to dealers, distributers
INTRODUCTION ASSIGNMENT V/S TRANSPORTATION ASSUMPTIONS INITIAL BASIC FEASIBLE SOLUTION [IBFS] 5 METHODS. DEGENERACY IN TRANSPORTATION OPTIMAL SOLUTION [MODI METHOD] HOW TO PREPARE LOOP PROHIBITED PROBLEM
More informationALGORITHMIC APPROACH TO UNBALANCED FUZZY TRANSPORTATION PROBLEM. A. Samuel 1, P. Raja 2
International Journal of Pure and Applied Mathematics Volume 113 No. 5 2017, 553561 ISSN: 13118080 (printed version); ISSN: 13143395 (online version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v113i5.3
More informationAPPLICATIONS OF MICROSOFT EXCEL  SOLVER FOR HORIZONTAL AND LEVELLING NETWORKS ADJUSTMENT
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Volumul 63 (67), Numărul 12, 2017 Secţia HIDROTEHNICĂ APPLICATIONS OF MICROSOFT EXCEL  SOLVER FOR
More informationA method for unbalanced transportation problems in fuzzy environment
Sādhanā Vol. 39, Part 3, June 2014, pp. 573 581. c Indian Academy of Sciences A method for unbalanced transportation problems in fuzzy environment 1. Introduction DEEPIKA RANI 1,, T R GULATI 1 and AMIT
More informationOPERATIONS RESEARCH. Transportation and Assignment Problems
OPERATIONS RESEARCH Chapter 2 Transportation and Assignment Problems Prof Bibhas C Giri Professor of Mathematics Jadavpur University West Bengal, India Email : bcgirijumath@gmailcom MODULE3: Assignment
More informationCHECKING THE HOMOGENEITY OF CONCRETE USING ARTIFICIAL NEURAL NETWORK
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LXI (LXV), Fasc., 05 Secţia CONSTRUCŢII. ARHITECTURĂ CHECKING THE HOMOGENEITY OF CONCRETE USING
More informationA NEW APPROACH FOR FINDING AN OPTIMAL SOLUTION OF UNBALANCED INTUTIONISTIC FUZZY TRANSPORTATION PROBLEMS A. EDWARD SAMUEL 1 & P.
Volume 9, No. 1, Jan.  2018 (Special ssue) nternational Journal of Mathematical Archive9(1), 2018, 4046 Available online through www.ijma.info SSN 2229 5046 A NEW APPROACH FOR FNDNG AN OPTMAL SOLUTON
More informationAntti Salonen KPP227 KPP227 1
KPP KPP Transportation method A quantitative approach for cost effective allocation of resources from multiple sources to multiple destinations. In this course we deal with three different methods:  Least
More informationModified Procedure to Solve Fuzzy Transshipment Problem by using Trapezoidal Fuzzy number.
International Journal of Mathematics and Statistics Invention (IJMSI) EISSN: 2321 4767 PISSN: 23214759 Volume 4 Issue 6 August. 216 PP334 Modified Procedure to Solve Fuzzy Transshipment Problem by
More informationApplication of Bounded Variable Simplex Algorithm in Solving Maximal Flow Model
Dhaka Univ. J. Sci. (): 9, 3 (January) Application of Bounded Variable Simplex Algorithm in Solving Maximal Flow Model Sohana Jahan, Marzia Yesmin and Fatima Tuj Jahra Department of Mathematics,University
More informationقالىا سبحانك ال علم لنا إال ما علمتنا صدق هللا العظيم. Lecture 5 Professor Sayed Fadel Bahgat Operation Research
قالىا سبحانك ال علم لنا إال ما علمتنا إنك أنت العليم الحكيم صدق هللا العظيم 1 والصالة والسالم علي اشرف خلق هللا نبينا سيدنا هحود صلي هللا عليه وسلن سبحانك اللهم وبحمدك اشهد أن ال هللا إال أنت استغفرك وأتىب
More informationTransportation Problems
Transportation Problems Transportation is considered as a special case of LP Reasons? it can be formulated using LP technique so is its solution 1 (to p2) Here, we attempt to firstly define what are them
More informationMODELING THE FORCEELONGATION CURVE OF SINGLE YARNS
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVI (LX), Fasc. 1, 2010 SecŃia TEXTILE. PIELĂRIE MODELING THE FORCEELONGATION CURVE OF SINGLE
More informationVARIATION OF INTERNAL FORCES USING ARTIFICIAL NEURONAL NETWORK
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Volumul 63 (67), Numărul 1, 2017 Secţia CONSTRUCŢII. ARHITECTURĂ VARIATION OF INTERNAL FORCES USING
More informationTwostage Interval Time Minimization Transportation Problem with Capacity Constraints
Twostage Interval Time Minimization Transportation Problem with Capacity Constraints Abstract Prabhjot Kaur, Kalpana Dahiya * University Institute of Engineering and Technology, Panjab University, Chandigarh.
More informationOptimal Solution of a Mixed type Fuzzy Transportation Problem
Intern. J. Fuzzy Mathematical Archive Vol. 15, No. 1, 2018, 8389 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 20 March 2018 www.researchmathsci.org DOI: http://dx.doi.org/10.22457/ijfma.v15n1a8
More informationFull Length Research Article. Comparison of Transportation Algorithms Using Data from Katsina State Transport Authority, Katsina State, Nigeria
vailable online at http://www.ajol.info/index.php/njbas/index Nigerian Journal of asic and pplied Science (September, 2013), 21(3): 207214 OI: http://dx.doi.org/10.4314/njbas.v21i3.6 ISSN 07945698 omparison
More informationIV. Special Linear Programming Models
IV. Special Linear Programming Models Some types of LP problems have a special structure and occur so frequently that we consider them separately. A. The Transportation Problem  Transportation Model 
More informationSolutions for Operations Research Final Exam
Solutions for Operations Research Final Exam. (a) The buffer stock is B = i a i = a + a + a + a + a + a 6 + a 7 = + + + + + + =. And the transportation tableau corresponding to the transshipment problem
More informationSimulation. Lecture O1 Optimization: Linear Programming. Saeed Bastani April 2016
Simulation Lecture O Optimization: Linear Programming Saeed Bastani April 06 Outline of the course Linear Programming ( lecture) Integer Programming ( lecture) Heuristics and Metaheursitics (3 lectures)
More informationOptimization Methods: Linear Programming Applications Transportation Problem 1. Module 4 Lecture Notes 2. Transportation Problem
Optimization ethods: Linear Programming Applications Transportation Problem odule 4 Lecture Notes Transportation Problem Introduction In the previous lectures, we discussed about the standard form of a
More informationANALYSIS OF DATA TRANSMITTED BETWEEN THE SERVER AND THE CLIENT THROUGH DIFFERENT TYPES OF COMMUNICATION
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 1, 2013 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ ANALYSIS OF DATA TRANSMITTED
More informationMATLABBASED TEST BENCH FOR GENETIC ALGORITHM PARAMETER TUNING
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Volumul 62 (66), Numărul 4, 2016 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ MATLABBASED TEST BENCH
More informationMAC LEVEL BASED QUALITY OF SERVICE MANAGEMENT IN IEEE NETWORKS
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVII (LXI), Fasc. 4, 2011 SecŃia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ MAC LEVEL BASED QUALITY
More informationA STUDY ON CLASSIFIERS ACCURACY FOR HAND POSE RECOGNITION
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 2, 2013 SecŃia AUTOMATICĂ şi CALCULATOARE A STUDY ON CLASSIFIERS ACCURACY
More informationSolving ONE S interval linear assignment problem
RESEARCH ARTICLE OPEN ACCESS Solving ONE S interval linear assignment problem Dr.A.Ramesh Kumar 1,S. Deepa 2, 1 Head, Department of Mathematics, Srimad Andavan Arts and Science College (Autonomous), T.V.Kovil,
More informationKEYWORDS Fuzzy numbers, trapezoidal fuzzy numbers, fuzzy Vogel s approximation method, fuzzy UV distribution method, ranking function.
Applications (IJERA ISSN: 22489622 www.ijera.com Method For Solving The Transportation Problems Using Trapezoridal Numbers Kadhirvel.K, Balamurugan.K Assistant Professor in Mathematics,T.K.Govt.Arts College,
More informationAN EVALUATION SYSTEM FOR CONTESTS AND CLASSROOMS
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Volumul 64 (68), Numărul 1, 2018 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ AN EVALUATION SYSTEM
More informationCOMPARATIVE STUDY OF NEW PROPOSED METHOD FOR SOLVING ASSIGNMENT PROBLEM WITH THE EXISTING METHODS
COMPARATIVE STUDY OF NEW PROPOSED METHOD FOR SOLVING ASSIGNMENT PROBLEM WITH THE EXISTING METHODS MANVIR KAUR ASSISTANT PROFESSOR SACHDEVA GIRLS COLLEGE, GHARUAN (MOHALI) ABSTRACT Assignment Problem is
More informationA NEW SYSTOLIC ALGORITHM OF 2D DCT TRANSFORM BASED ON PSEUDOCORRELATION STRUCTURES FOR A UNIFIED VLSI ARCHITECTURE
BULETIUL ISTITUTULUI POLITEHIC DI IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LXI (LXV), Fasc. 2, 25 Secţia ELECTROTEHICĂ. EERGETICĂ. ELECTROICĂ A EW SYSTOLIC ALGORITHM OF 2D
More informationModified Distribution Method
istributors C 8 Step : Make an initial allocation with the NorthWest corner rule. KPP istributors C 8 V j Step : Make an initial allocation with the NorthWest corner rule. Step : Introduce the variables,
More informationDISTRIBUTED DIFFERENTIAL CRIPTANALYSIS OF FEAL  8
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LV (LIX), Fasc. 1, 2009 SecŃia AUTOMATICĂ şi CALCULATOARE DISTRIBUTED DIFFERENTIAL CRIPTANALYSIS
More informationTRANSPORTATION AND ASSIGNMENT PROBLEMS
TRANSPORTATION AND ASSIGNMENT PROBLEMS Transportation problem Example P&T Company produces canned peas. Peas are prepared at three canneries (Bellingham, Eugene and Albert Lea). Shipped by truck to four
More informationOPERATIONS RESEARCH. Dr. Mohd Vaseem Ismail. Assistant Professor. Faculty of Pharmacy Jamia Hamdard New Delhi
OPERATIONS RESEARCH OPERATIONS RESEARCH By Dr. Qazi Shoeb Ahmad Professor Department of Mathematics Integral University Lucknow Dr. Shakeel Javed Assistant Professor Department of Statistics & O.R. AMU,
More informationA Strategy to Solve Mixed Intuitionistic Fuzzy Transportation Problems by BCM
MiddleEast Journal of Scientific Research 25 (2): 374379, 207 SSN 9909233 DOS Publications, 207 DO: 0.5829/idosi.mesr.207.374.379 A Strategy to Solve Mixed ntuitionistic Fuzzy Transportation Problems
More informationMLR Institute of Technology
Course Name : Engineering Optimization Course Code : 56021 Class : III Year Branch : Aeronautical Engineering Year : 201415 Course Faculty : Mr Vamsi Krishna Chowduru, Assistant Professor Course Objective
More informationH. W. Kuhn. Bryn Mawr College
VARIANTS OF THE HUNGARIAN METHOD FOR ASSIGNMENT PROBLEMS' H. W. Kuhn Bryn Mawr College The author presents a geometrical modelwhich illuminates variants of the Hungarian method for the solution of the
More informationOperations Research. UnitI. Course Description:
Operations Research Course Description: Operations Research is a very important area of study, which tracks its roots to business applications. It combines the three broad disciplines of Mathematics, Computer
More information4. Linear Programming
/9/08 Systems Analysis in Construction CB Construction & Building Engineering Department AASTMT by A h m e d E l h a k e e m & M o h a m e d S a i e d. Linear Programming Optimization Network Models 
More informationPLC APPLICATION FOR BRUSHLESS MOTOR POSITIONING
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Volumul 64 (68), Numărul 2, 2018 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ PLC APPLICATION FOR
More informationNEW GEOMETRIES FOR 3D LASER SENSORS WITH PROJECTION DISCRIMINATION
BULETINUL INSTITUTULUI OLITEHNIC DIN IAŞI ublicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVI (LX), Fasc. 1, 2010 Secţia AUTOMATICĂ şi CALCULATOARE NEW GEOMETRIES FOR 3D LASER SENSORS WITH
More informationFinding the Optimal Solution of Fuzzy Transportation Problems
Finding the Optimal Solution of Fuzzy Transportation Problems Aseel Hammed Abed Sadda College of Basic Education, Universty of AlMustansiriya/Baghdad Email: uot _magaz@yahoo.com Received on: 29/6/2011&
More informationA new approach for solving cost minimization balanced transportation problem under uncertainty
J Transp Secur (214) 7:339 345 DOI 1.17/s12198141471 A new approach for solving cost minimization balanced transportation problem under uncertainty Sandeep Singh & Gourav Gupta Received: 21 July 214
More informationThe Islamic University of Gaza Faculty of Commerce Quantitative Analysis  Dr. Samir Safi Midterm #228/4/2014
The Islamic University of Gaza Faculty of Commerce Quantitative Analysis  Dr. Samir Safi Midterm #228/4/2014 Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1)
More informationSUGGESTED SOLUTION CA FINAL MAY 2017 EXAM
SUGGESTED SOLUTION CA FINAL MAY 2017 EXAM ADVANCED MANAGEMENT ACCOUNTING Test Code  F M J 4 0 1 6 BRANCH  (MULTIPLE) (Date : 11.02.2017) Head Office : Shraddha, 3 rd Floor, Near Chinai College, Andheri
More informationPOSTRENDERING ENHANCEMENT OF VOLUMES
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LV (LIX), Fasc. 3, 2009 SecŃia AUTOMATICĂ şi CALCULATOARE POSTRENDERING ENHANCEMENT OF VOLUMES
More informationSELFADAPTABLE SECURITY ARCHITECTURE FOR POWERAWARE EMBEDDED SYSTEMS
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVI (LX), Fasc. 3, 2010 SecŃia AUTOMATICĂ şi CALCULATOARE SELFADAPTABLE SECURITY ARCHITECTURE
More informationA FAULT PRIMITIVE BASED MODEL OF ALL STATIC FOUR CELL COUPLING FAULTS IN RANDOMACCESS MEMORIES
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIV (LVIII), Fasc. 1, 2008 Secţia AUTOMATICĂ şi CALCULATOARE A FAULT PRIMITIVE BASED MODEL OF
More informationCDG2A/CDZ4A/CDC4A/ MBT4A ELEMENTS OF OPERATIONS RESEARCH. Unit : I  V
CDG2A/CDZ4A/CDC4A/ MBT4A ELEMENTS OF OPERATIONS RESEARCH Unit : I  V UNIT I Introduction Operations Research Meaning and definition. Origin and History Characteristics and Scope Techniques in Operations
More informationApplication of Twodimensional Periodic Cellular Automata in Image Processing
International Journal of Computer, Mathematical Sciences and Applications Serials Publications Vol. 5, No. 12, JanuaryJune 2011, pp. 49 55 ISSN: 09736786 Application of Twodimensional Periodic Cellular
More informationAn Improved Decomposition Algorithm and Computer Technique for Solving LPs
International Journal of Basic & Applied Sciences IJBASIJENS Vol: 11 No: 0 12 An Improved Decomposition Algorithm and Computer Technique for Solving LPs Md. Istiaq Hossain and M Babul Hasan Abstract 
More informationFuzzy multi objective transportation problem evolutionary algorithm approach
Journal of Physics: Conference Series PPER OPEN CCESS Fuzzy multi objective transportation problem evolutionary algorithm approach To cite this article: T Karthy and K Ganesan 08 J. Phys.: Conf. Ser. 000
More informationMATA GUJRI MAHILA MAHAVIDYALAYA (AUTO), JABALPUR DEPARTMENT OF MATHEMATICS M.Sc. (MATHEMATICS) THIRD SEMESTER
MATA GUJRI MAHILA MAHAVIDYALAYA (AUTO), JABALPUR DEPARTMENT OF MATHEMATICS 201718 M.Sc. (MATHEMATICS) THIRD SEMESTER Name of the Papers Theory Min. C.C.E. Min. Practical Min. Total (MM) Pass. Pass. Pass
More informationBARCODE READER MANAGEMENT WITH THE ATMEL MICROCONTROLLER (I)
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Volumul 63 (67), Numărul 1, 2017 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ BARCODE READER MANAGEMENT
More informationA New Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment
A ew Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment ABSTRACT idhi Joshi 1, Surjeet Singh Chauhan (Gonder) 2, Raghu Raja 3 Research Scholar, PTU, Jalandhar nids_22@yahoo.co.in
More informationEvaluation of Heuristic Algorithms for Solving a Transportation Problem
Evaluation of Heuristic Algorithms for Solving a Transportation Problem Kacper Rychard, Iwona PozniakKoszalka, Leszek Koszalka, and Andrzej Kasprzak Dept. of Systems and Computer Networks Wroclaw University
More informationComparative Analysis of Vertical Fragmentation Techniques in Distributed Environment
Comparative Analysis of Vertical Fragmentation Techniques in Distributed Environment Mukta Goel 1, Shalini Bhaskar Bajaj 2 1 Assistant Professor, IT, TIT&S, Bhiwani, Haryana, India, 2 Professor, CSE, AUH,
More informationJournal of Business & Economics Research November, 2009 Volume 7, Number 11
Alternate Solutions Analysis For Transportation Problems Veena Adlakha, University of Baltimore, USA Krzysztof Kowalski, Connecticut Department of Transportation, USA ABSTRACT The constraint structure
More informationA New Technique for Segmentation of Handwritten Numerical Strings of Bangla Language
I.J. Information Technology and Computer Science, 2013, 05, 3843 Published Online April 2013 in MECS (http://www.mecspress.org/) DOI: 10.5815/ijitcs.2013.05.05 A New Technique for Segmentation of Handwritten
More informationWhat is the Optimal Bin Size of a Histogram: An Informal Description
International Mathematical Forum, Vol 12, 2017, no 15, 731736 HIKARI Ltd, wwwmhikaricom https://doiorg/1012988/imf20177757 What is the Optimal Bin Size of a Histogram: An Informal Description Afshin
More informationFuzzy Transportation by Using Monte Carlo method
Advances in Fuzzy Mathematics. ISSN 0973533X Volume 12, Number 1 (2017), pp. 111127 Research India Publications http://www.ripublication.com Fuzzy Transportation by Using Monte Carlo method Ashok S.Mhaske
More informationA Deterministic Dynamic Programming Approach for Optimization Problem with Quadratic Objective Function and Linear Constraints
A Deterministic Dynamic Programming Approach for Optimization Problem with Quadratic Objective Function and Linear Constraints S. Kavitha, Nirmala P. Ratchagar International Science Index, Mathematical
More informationA Novel Approach for the Solution of Multi Objective Interval Transportation Problem
Journal of Physics: Conference Series PAPER OPEN ACCESS A Novel Approach for the Solution of Multi Objective Interval Transportation Problem To cite this article: G Ramesh et al 2018 J. Phys.: Conf. Ser.
More informationA method for solving unbalanced intuitionistic fuzzy transportation problems
Notes on Intuitionistic Fuzzy Sets ISSN 1310 4926 Vol 21, 2015, No 3, 54 65 A method for solving unbalanced intuitionistic fuzzy transportation problems P Senthil Kumar 1 and R Jahir Hussain 2 1 PG and
More informationDESIGN AND REAL TIME IMPLEMENTATION OF MULTIPLEMODEL CONTROL SOLUTION FOR SOME CLASSES OF NONLINEAR PROCESSES
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVII (LXI), Fasc. 1, 2011 SecŃia AUTOMATICĂ şi CALCULATOARE DESIGN AND REAL TIME IMPLEMENTATION
More informationThe simplex method and the diameter of a 01 polytope
The simplex method and the diameter of a 01 polytope Tomonari Kitahara and Shinji Mizuno May 2012 Abstract We will derive two main results related to the primal simplex method for an LP on a 01 polytope.
More informationOperations Research. Lecture Notes By Prof A K Saxena Professor and Head Dept of CSIT G G Vishwavidyalaya, BilaspurIndia
Lecture Notes By Prof A K Saxena Professor and Head Dept of CSIT G G Vishwavidyalaya, BilaspurIndia Some important tips before start of course material to students Mostly we followed Book by S D Sharma,
More informationSolution of m 3 or 3 n Rectangular Interval Games using Graphical Method
Australian Journal of Basic and Applied Sciences, 5(): 110, 2011 ISSN 19918178 Solution of m or n Rectangular Interval Games using Graphical Method Pradeep, M. and Renukadevi, S. Research Scholar in
More informationApplication of a Dual Simplex method to Transportation Problem to minimize the cost
Application of a Dual Simplex method to Transportation Problem to minimize the cost Manisha.V. Sarode Assistant Professor, Dept. of Mathematics, Priyadarshini Indira Gandhi College of Engineering, Nagpur
More informationInvestigating the Effect of Different Kernel Functions on the Performance of SVM for Recognizing Arabic Characters
Investigating the Effect of Different Functions on the Performance of SVM for Recognizing Arabic Characters Sayed Fadel 1,2, Said Ghoniemy 1,2, Mohamed Abdallah 1,3, Hussein Abu Sorra 1, Amira Ashour 1,4,
More informationA Computational Study on the Number of. Iterations to Solve the Transportation Problem
Applied Mathematical Sciences, Vol. 8, 2014, no. 92, 45794583 HIKARI Ltd, www.mhikari.com http://dx.doi.org/10.12988/ams.2014.46435 A Computational Study on the Number of Iterations to Solve the Transportation
More informationSubset Cut Enumeration of Flow Networks with Imperfect Nodes
International Journal of Performability Engineering Vol. 11, No. 1, January 2015, pp. 8190. RAMS Consultants Printed in India Subset Cut Enumeration of Flow Networks with Imperfect Nodes SUPARNA CHAKRABORTY*,
More informationSYLLABUS. M.Sc. III rd SEMESTER Department of Mathematics Mata Gujri Mahila Mahavidyalaya,(Auto), Jabalpur
SYLLABUS M.Sc. III rd SEMESTER 201819 Department of Mathematics Mata Gujri Mahila Mahavidyalaya,(Auto), Jabalpur MATA GUJRI MAHILA MAHAVIDYALAYA (AUTO), JABALPUR M.Sc. (MATHEMATICS) THIRD SEMESTER Name
More informationA Supply Chain Game Theory Framework for Cybersecurity Investments Under Network Vulnerability
A Supply Chain Game Theory Framework for Cybersecurity Investments Under Network Vulnerability Professor Anna Nagurney Department of Operations and Information Management Isenberg School of Management
More informationOPERATIONS RESEARCH. Linear Programming Problem
OPERATIONS RESEARCH Chapter 1 Linear Programming Problem Prof. Bibhas C. Giri Department of Mathematics Jadavpur University Kolkata, India Email: bcgiri.jumath@gmail.com 1.0 Introduction Linear programming
More informationFuzzy Variable Linear Programming with Fuzzy Technical Coefficients
Sanwar Uddin Ahmad Department of Mathematics, University of Dhaka Dhaka1000, Bangladesh sanwar@univdhaka.edu Sadhan Kumar Sardar Department of Mathematics, University of Dhaka Dhaka1000, Bangladesh sadhanmath@yahoo.com
More informationIntroduction to Linear Programing Problems
Paper: Linear Programming and Theory of Games Lesson: Introduction to Linear Programing Problems Lesson Developers: DR. MANOJ KUMAR VARSHNEY, College/Department: Department of Statistics, Hindu College,
More informationAn Alternative Approach for Solving Extreme Point Linear and Linear Fractional Programming Problems
Dhaka Univ. J. Sci. 63(2): 7784, 2015 (July) An Alternative Approach for Solving Extreme Point Linear and Linear Fractional Programming Problems Touhid Hossain, Md. Rajib Arefin and Md. Ainul Islam Department
More informationNetwork Topology Control and Routing under Interface Constraints by Link Evaluation
Network Topology Control and Routing under Interface Constraints by Link Evaluation Mehdi Kalantari Phone: 301 405 8841, Email: mehkalan@eng.umd.edu Abhishek Kashyap Phone: 301 405 8843, Email: kashyap@eng.umd.edu
More informationProposed syllabus for
Proposed syllabus for Skill Enhancement Course Papers for B.Sc.(H) Mathematics/ B.Sc. (Prog)/B.A.(Prog) Department of Mathematics University of Delhi Delhi110007 1 Sl. No. CORE COURSE (12) I II III IV
More informationOn A Traffic Control Problem Using CutSet of Graph
1240 On A Traffic Control Problem Using CutSet of Graph Niky Baruah Department of Mathematics, Dibrugarh University, Dibrugarh : 786004, Assam, India Email : niky_baruah@yahoo.com Arun Kumar Baruah Department
More information