  Many research has been conducted about quadratic programming and inverse
optimization. In this paper we present the combination aspect of these
subjects, applying on transportation problem. First, we obtain the inverse form
of quadratic tranportation problem under $L_1$ norm by using duality as well as
introducing the optimal value. Then, we do the same process for inverse
quadratic transportation problem (IQTP) under $L_\infty$ norm.
