Nonlinear Integer Programming Transportation Models: An Alternative Solution

The combinatorial nature of integer programming is inevitable even after taking specific model structure into consideration. This is the root problem in implementing large-scale nonlinear integer programming models regardless of which algorithm one chooses to use. Consequently, we suggest that the size of origin-destination be moderate. In the case of large origin-destination problems, more information on the size of Xij is needed to drastically reduce the dimensionality problem. For instance, if Xij is to be greater than the threshold value to be eligible for the rate break, computation time can be noticeably reduced. In the case of large right-hand-side constraints, we suggest scaling these values to the nearest thousands or millions. The approach from Excel proposed in this paper is particularly appropriate if one can balance the sizes of origindestination and right-hand-side constraints in such a way that computation time is not excessive. For a large-scale problem, one must exploit the structure of the model and acquire more information on the bounds of discrete variables. Our approach certainly provides an alternative way to solve nonlinear integer programming models with virtually all kinds of algebraic functions even for laymen who do not feel comfortable with mathematic programming jargons.