Using geometric programming to profit maximization with interval coefficients and quantity discount

Profit maximization is an important issue to the firms that pursue the largest economic profit possible. Different from previous studies, this paper considers the profit-maximization problem with interval coefficients and input quantity discount. Intuitively, when the problem has interval coefficients, the derived profit value should lie in an interval as well. We utilize signomial geometric programming to derive the interval profit value. The idea is to find the upper bound and lower bound of the range by employing the two-level mathematical programming. Following the duality theorem and a variable separation technique, the two-level geometric programs are transformed into a class of one-level geometric programs. Solving the pair of geometric programs produces the interval of the profit value. An example is given to illustrate the idea proposed in this paper.