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

in International Journal of Applied Mathematics and Computer Science (2016), 26

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 ... [more ▼]

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. [less ▲]

Erratum to: Internet shopping with price-sensitive discounts

in 4OR: a quarterly journal of operations research (2014), 12(4), 403-406

In Blazewich et al. (4OR-Q J Oper Res 12(1):35–48, 2014), an Internet shopping problem with price-sensitive discounts was introduced, in which a customer wants to buy a given set of products in a given ... [more ▼]

In Blazewich et al. (4OR-Q J Oper Res 12(1):35–48, 2014), an Internet shopping problem with price-sensitive discounts was introduced, in which a customer wants to buy a given set of products in a given set of Internet shops. This problem is an extension of the original Internet shopping optimization problem (ISOP) presented in Blazewich et al. (Int J Appl Math Comput Sci 20(2):385–390, 2010). For each Internet shop, standard prices for the products are given as well as a concave increasing discounting function of the total standard and delivery price. The problem is to buy all the required products at the minimum total discounted price. Among other results, approximability issues were shortly discussed. This note extends this discussion and corrects a flaw in Blazewich et al. (4OR-Q J Oper Res 12(1):35–48, 2014). [less ▲]

Ties between graph theory and biology

in Gross, Jonathan L.; Yellen, Jay; Zhang, Ping (Eds.) Handbook of Graph Theory (2013)

Last decades brought us a new scientific area of computational biology, placed at the junction of biology (especially molecular biology), computer science and mathematics. Its aim is to solve real-world ... [more ▼]

Last decades brought us a new scientific area of computational biology, placed at the junction of biology (especially molecular biology), computer science and mathematics. Its aim is to solve real-world problems arising in biology with the use of mathematical models and methods, and tools from computer science. Molecular biology, due to its rapid progress, yields more and more experimental data, possible to be processed on computers only. Efficient processing and advisable analysis must be accompanied by well suited models and methods, the ones coming from graph theory frequently appeared to be most useful. Here, the most interesting and breakthrough approaches of computational biology tied with graph theory are characterized. [less ▲]