When formulating linear programming problem, variables should have been regarded as taking integer
values but for the sake of convenience, let them take fractional values and at the end any fractional part could be
neglected. Whilst this is acceptable in some situations, in many cases it is not, and in such cases one must find a
numeric solution in which the variables take integer values. Problems in which this is the case are called integer
program and the subject of solving such programs is called integer programming. For solving integer programming
problem no similar general purpose and computationally effective algorithms exist. Indeed theory suggests that not
general-purpose computational complexity and concerns NP-completeness. It was developed from the early 1970’s
onward and basically is a theory concerning “how long it takes algorithms to run”. This means that integer
programmings are a lot harder to solve than linear programming. In this paper a new algorithm to solve zero-one
integer linear programming problem if all the variables are restricted to take the values zero or one is given. This
algorithm consists of two steps. In step 1 the intercepts of a promising variable based on the different constraints are
found out. Using the intercept matrix obtained for all the promising variables, a maximum of m variables are
selected and arranged where m is the number of constraints. Also the maximum value that each of the arranged
variables can assume is found out. In step 2, the arranged all variables are allowed to enter into the basis
simultaneously. A method has been suggested to find out the integer value restricted to zero or one with which a
variable has to enter the basis. The simplex method while finding the improved basic feasible solution if moves along
the edges of the feasible region. In the proposed zero-one integer linear programming algorithm the improved
solution moves in the interior of the feasible region.