The next most common approximation is to simplify Equation 14 to become Equation 15a by adding a constant term Σtij.
A further approximation can then be applied using equation 15b to yield Equation 15c, and eventually 15d. A simple
substitution of tij to Tij finally yields Equation 15e, which can then be solved using simple weighted linear regression.
Unfortunately, while the solution is much easier to obtain, it has two main faults. The first of these is that the solutions
found using regression deviate considerably from those found using either the original objective function or its Stirling’s
approximation. Secondly, the approximation is such that at times it can yield negative values for the number of trips
between a given O-D pair, which is meaningless.