Manufacturers can increase the advertising expenditures of their retailers by bearing a fraction of the occurring costs within the framework of a vertical cooperative advertising program. We expand the existing research which deals with advertising and pricing decisions in a...

This paper proposes a bi-level transit network design problem where the transit routes and frequency settings are determined simultaneously. The upper-level problem is formulated as a mixed integer non-linear program with the objective of minimizing the number of passenger transfers, and the...

In this paper, we have developed a new method to solve bi-level quadratic linear fractional programming (BLQLFP) problems in which the upper-level objective function is quadratic and the lower-level objective function is linear fractional. In this method a BLQLFP problem is transformed into an...

Planning to mitigate the impacts of a disaster can be an important activity for both private companies and public agencies. In this article, the authors consider a supply system that provides needed goods or services to a region that may be the subject of some type of disaster, such as an attack...

This study constructs a royalty negotiation model for the bi-level programming (BLP) problem and develops a heuristic algorithm for solving the BLP problem. Concession rate, learning effect, and the time value discount rate are integrated into the proposed algorithm to reflect an authentic...

Discrete network design problem (DNDP) is generally formulated as a bi-level programming. Because of non-convexity of bi-level formulation of DNDP which stems from the equilibrium conditions, finding global optimal solutions are very demanding. In this paper, a new branch and bound algorithm...