ONES METHOD FOR FINDING AN OPTIMAL SOLUTION FOR TRANSPORTATION PROBLEM Pushpa Latha Mamidi Assistant Professor of Mathematics, Vishnu Institute of Technology, Bhimavaram, A.P., India Email: pushpamamidi@gmail.com Abstract: In this paper, a new method named Ones Method is proposed for finding an optimum solution for a wide range of transportation problems, directly. The new method is based on allocating units to the cells in the transportation matrix initiating with maximum number of ones starting with minimum demand/supply to the cell and then try to find an optimum solution to the given transportation problem. The proposed method is a systematic procedure, easy to apply and can be utilized for all types of transportation problem. A numerical illustration is established and the optimality of the result yielded by this method is also checked. Keywords: Transportation Problem, Assignment Problem, Optimal solution, i.b.f.s, VAM I. INTRODUCTION Transportation problem is used to transport various amounts of single homogeneous commodity that are initially stored at various origins, to different destinations in such a way that the total transportation cost is a minimum. It is a special class of Linear Programming Problem. In 1941 Hitchcock[1] developed the basic transportation problem along with the constructive method of solution and after that in 1949 Koopams [4] discussed the problem in detail. Again in 1951 Dantzig[9] formulated the Transportation Problem as L.P.P. The simplex method is not suitable for the Transportation Problem especially for large scale transportation problem due to its special structure of the model in 1954 Charnes and Cooper[10] was developed Stepping Stone Method for the efficiency reason. For obtaining an optimum solution for Transportation Problem it was required to solve the problem in two stages. In the first stage the initial basic feasible solution (i.b.f.s) was obtained by using any one of the methods such as North West Corner Rule, Row Minima, Column Minima, Least Cost, Vogle’s Approximation methods. Then finally MODI method was used to get an optimum solution. In last few years P.Pandian et.al[13], Sudhakar et.al[6], N.M.Deshmukh[2], G.Reena Patel et.al[5], Aramerthakannan et.al[7], Abdul Quddoos[3], ezhil rannan[11] and many others proposed different methods for finding an optimum solution directly. This paper presents a new approach for finding an optimum solution directly with a systematic procedure. Mathematical Representation Let there are ‘m’ origins, O i having a i (i=1,2…….m) units of source which are to be transported to ‘n’ destinations D j ’s with b j (j=1,2….n) units of demand respectively. Let C ij be the cost of shipping one unit product from i th origin to j th destination and x ij be the amount to be shipped form i th origin to j th destination. It is also assumed that total availabilities satisfy the total requirements i.e., Mathematically the problem can be stated as Min Z = Proceedings International Conference On Advances In Engineering And Technology ISBN NO: 978 - 1503304048 www.iaetsd.in International Association of Engineering & Technology for Skill Development 41