Opsearch, Vol. 34, No. 1, 1997 0030-3887/95 $ 2.00 + 0.00 © Operational Research Society of India New Technique for Solving Primal All-integer Linear Programming Shambhu Sharma Department of Mathematics, L.P. Shahi College, Patna, India and Dr Bishram Sharma Department of Mathematics Science College, Patna, India Abstract This paper provides a new technique of selecting the pivot column and the source row in primal all-integer linear programming. by which the number of iterations has been reduced in going through the initial simplex table to the optimal simplex table. 1. INTRODUCTION All the existing methods to solve the integer linear programming problem [2, 3, 4] are based on the concepts of selecting the pivot column and the source row as given in the linear programming. None of these methods exploit the simple and well known fact that the method of selecting the pivot column and the source row, given in the linear programming does not give the better improvement of the objective function. We have searched the pivot column by minimum of the product of the negative coefficient of the objective function and the minimum of the ratios used in [4] for the source row. The source row automatically comes out by this technique. However the formulation of cut and the iteration process of our technique are the same as the other well known methods. 2. THEORETICAL FOUNDATIONS Consider the problem Max Xo cx Such that Ax = b (1 ) x 0, integers