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2 2016

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Exact and heuristic approaches to solve the Internet shopping optimization problem with delivery costs

Lopez-Loces M. C., Musial J., Pecero J. E., Fraire-Huacuja H. J., Blazewicz J., Bouvry P.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 2

391--406

Internet shopping has been one of the most common online activities, carried out by millions of users every day. As the number of available offers grows, the difficulty in getting the best one among all the shops increases as well. In this paper we propose an integer linear programming (ILP) model and two heuristic solutions, the MinMin algorithm and the cellular processing algorithm, to tackle the Internet shopping optimization problem with delivery costs. The obtained results improve those achieved by the state-of-the-art heuristics, and for small real case scenarios ILP delivers exact solutions in a reasonable amount of time.

Algorithms solving the Internet shopping optimization problem with price discounts

Musial J., Pecero J. E., Lopez-Loces M. C., Fraire-Huacuja H. J., Bouvry P., Blazewicz J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2016

Vol. 64, nr 3

505--516

The Internet shopping optimization problem arises when a customer aims to purchase a list of goods from a set of web-stores with a minimum total cost. This problem is NP-hard in the strong sense. We are interested in solving the Internet shopping optimization problem with additional delivery costs associated to the web-stores where the goods are bought. It is of interest to extend the model including price discounts of goods. The aim of this paper is to present a set of optimization algorithms to solve the problem. Our purpose is to find a compromise solution between computational time and results close to the optimum value. The performance of the set of algorithms is evaluated through simulations using real world data collected from 32 web-stores. The quality of the results provided by the set of algorithms is compared to the optimal solutions for small-size instances of the problem. The optimization algorithms are also evaluated regarding scalability when the size of the instances increases. The set of results revealed that the algorithms are able to compute good quality solutions close to the optimum in a reasonable time with very good scalability demonstrating their practicability.