Incorporating Variable Demand Assignment Into Discrete Network Design Problem

Abstract

The network design problem (NDP) is a bi-level problem with integer and decimal variables that aims to minimize the users' total cost under the budget constraints. Although utilizing variable demand models will theoretically change the NDP’s result, the demand was assumed to be fixed and known in the literature. In this paper, a mathematical analysis will be presented to justify the importance of using variable demand in the discrete network design problem (DNDP). The DNDP for Sioux-falls network will be solved in both variable and fixed demand conditions by using total enumeration (in the upper-level) and Frank-Wolf (in the lower-level) method. The result shows that DNDP findings for variable and fix demand conditions have significant differences, especially in the mid-budget level.