In the existing literature, in all the plant location problems the per unit transportation costs and quantities have been considered to be fixed numbers at known positive levels. But, in reality, those costs and quantities can fluctuate due to several reasons and are hence not precise. Here, the impreciseness has been represented with numbers that are in intervals. Subsequently, the plant location problem has been expressed as a cost minimization problem with interval-valued coefficients. In order to solve the said interval-valued optimization problem a GA has been developed. To demonstrate the model, several examples have been considered and presented. In some examples, fixed valued costs and quantities have been considered and their results have been tested with the technique prescribed by ‘least cost centre analysis’ available in the literature. Finally, sensitivity analyses with respect to GA parameters have been done and exhibited graphically. The analysis displays that the GA developed by us is fairly stable. For the first time in plant location optimization, transportation costs and quantities have been considered as interval numbers. Apart from the GA developed in this paper, the formulated problem cannot be probably solved by any other existing methods. ‘Least Cost Centre Analysis’ provides a solution for only fixed coefficients, but our method can solve for intervals as well.