Abstract. 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.
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.
Abstract. Internet shopping is one of the main pillars of electronic commerce. According to the literature, the Internet Shopping Optimization Problem (ISOP) has been defined in order to optimize the global cost of online purchase, taking into account both the cost of products and shipping. In this study, it was decided to propose and analyze a very interesting, and really substantial, extension of the ISOP. Namely, trust factors were subjected to careful analysis from the customer point of view. The analysis is based on a specially prepared questionnaire, supplemented by the information from the literature and our own observations. Thus, it was possible to propose a definition of a new mathematical model of the problem, and to prove its affiliation to the class of strongly NP-hard problems. In addition, the heuristic algorithm is proposed, which can be used to solve the problem.
This paper addresses a forest harvesting problem with adjacency constraints, including additional environmental constraints to protect wildlife habitats and minimize infrastructure deployment costs. To this end, we propose an integer programming model to include those considerations during the optimization of the harvest regime of a Mexican forest. The model considered was based on the Unit Restriction Model, a benchmark approach that merges the management units before the optimization process. The resulting model, namely the Green Unit Restriction Model (GURM) and the benchmark model (URM) from the literature were tested with the forest Las Bayas, using information obtained from the SiPlaFor project from Universidad Juárez. The proposed model was solvable in all tested instances. Furthermore, a sensitivity analysis study over a core data set of test instances was carried out on the different parameters of the GURM model to determine optimal configurations for the specific case study. Several environmental measures were assessed in our experimental work. The parameters evaluated were the distance value between pairs of units harvested in the same period, the distance value between those considered natural reserve units, the timber volume to be harvested, the green-up period, and the minimum forest reserve area. An interesting observation from the experiments was that the maximum area inversely affected the URM and GURM models; larger regions resulted in a reduced number of management units in the URM model, thus reducing the computational time to solve the instance of the problem, but in this case, at the expense of a reduced profit. One of the interesting findings was that, in all experiments under all different factors, harvesting every 5 or 6 years yields better profits than harvesting every 10 or 12 years. The current standard in the Mexican system is to harvest every 10 years.
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