Piecewise Linear Transportation

Piecewise Linear Transportation

The Piecewise Linear Transportation problem models a simple transportation model with one complication, namely the objective function representing the cost is a piecewise linear function. This piecewise linear cost function is used to model price discounts. The piecewise linear function is modelled using the integer linear programming trick of Chapter 7.6 of the AIMMS Optimization Modeling book.

Problem Type

MIP (small)


Piecewise linear, special ordered set, SOS2, SOS 2, network object.


The Piecewise Linear Transportation problem is described by Christensen and Labbé (2015) but the model formulation in this project differs from their formulation.


Christensen, T.R.L., M. Labbé, A branch-cut-and-price algorithm for the piecewise linear transportation problem, European Journal of Operational Research 245(3) (2015), pp. 645-655.


A zip file with this example can be downloaded here.