How to efficiently solve Internet Shopping Optimization Problem with price sensitive discounts?

In this paper we deal with the Internet Shopping Optimization Problem. An extended model that includes price sensitive discounts is considered. A set of algorithms to solve the Internet Shopping Optimization Problem with Price Sensitivity Discounts (ISOPwD) is introduced. The algorithms are designed to consider a different solution quality regarding computational time and results close to the optimum solution. Simulations based on real world data assess the new set of heuristics. The results of the proposed algorithms were compared with the optimal solutions, computed by a branch and bound algorithm. The scalability is evaluated by increasing the problem sizes. Computational experiments are performed and their results are carefully analyzed and discussed. The paper should be perceived as a work in progress - position paper.