Box Stacking with no Rotation

You are given a set of n types of rectangular 3-D boxes, where the i^th box has height h(i), width w(i) and depth d(i) (all real numbers). The boxes cannot be rotated and can only be stacked on top of one another if each box in the stack is strictly larger than the box above it in width, height and depth. We have to build the tallest stack possible, where height of a stack is sum of heights of each box

Can we implement it using LIS where we first sort the stacks in descending order of volume and then apply LIS ??