Internet Shopping Optimization Problem Research Articles

Novel Particle Swarm Optimization Algorithm to Solve the Internet Shopping Optimization Problem with Shipping Costs

In this paper, we approach the Internet Shopping Optimization Problem with Shipping Costs (IShOP), an NP-hard-relevant problem in the current e-commerce environment. To our knowledge, several solution metaheuristic algorithms have been reported in the literature. In this paper, we propose a novel Particle Swarm Optimization algorithm (PSO) to solve the problem. PSO incorporates a neighborhood diversification technique (NDT), a local search (LS) technique, and an adaptive parameter tuning (APT) method. The proposed algorithm (NDTLSAA-PSO) includes two techniques at the end of each iteration to avoid premature convergence in the search process, balancing exploration and exploitation in selecting candidate solutions. A comparison of the performance of the proposed algorithm has been made against the performance of the best state-of-the-art memetic algorithm solution of the IShOP. A total of 90 instances classified into three groups of small, medium, and large sizes were resolved. The Wilcoxon and Holm non-parametric tests were applied to validate the significance of the differences observed between these two algorithms. The results show that the proposed NDTLSAA-PSO algorithm is superior to the memetic algorithm. In addition, the proposed algorithm obtains the best results in all the in-stances evaluated in terms of quality.

A Linear Genetic Programming Approach for the Internet Shopping Optimization Problem with Multiple Item Units (ISHOP-U)

A Linear Genetic Programming Approach for the Internet Shopping Optimization Problem with Multiple Item Units (ISHOP-U)

Multi-objective Evolutionary Algorithm based on Decomposition with Adaptive Adjustment of Control Parameters to Solve the Bi-objective Internet Shopping Optimization Problem (MOEA/D-AACPBIShOP)

Multi-objective Evolutionary Algorithm based on Decomposition with Adaptive Adjustment of Control Parameters to Solve the Bi-objective Internet Shopping Optimization Problem (MOEA/D-AACPBIShOP)

The Internet Shopping Optimization Problem with Multiple Item Units (ISHOP-U): Formulation, Instances, NP-Completeness, and Evolutionary Optimization

In this work, we investigate the variant of the Internet Shopping Optimization Problem (ISHOP) that considers different item units. This variant is more challenging than the original problem. The original ISHOP is already known as a combinatorial NP-hard problem. In this work, we present a formal proof that the ISHOP variant considering different item units belongs to the NP-Hard complexity class. The abovementioned variant is familiar to companies and consumers who need to purchase more than one unit of a specific product to satisfy their requirements. For example, companies buy different quantities of construction materials, medical equipment, office supplies, or chemical components. We propose two new evolutionary operators (crossover and mutation) and an unfeasible solution repair method for the studied ISHOP variant. Furthermore, we produce a new benchmark of 15 synthetic instances where item prices follow a random uniform distribution. Finally, to assess our evolutionary operators, we implemented two Evolutionary Algorithms, a Genetic Algorithm (GA) and a Cellular Genetic Algorithm (CGA), and an experimental evaluation against a Water Cycle Algorithm (WCA) from the state-of-the-art. Experimental results show that our proposed GA performs well with statistical significance.

Systematic literature review on adjustable robust counterpart for internet shopping optimization problem

Internet Shopping Optimization Problem (ISOP) is the application of optimization to online shopping activities of all complexity. The ISOP is useful for consumers in minimizing the cost of purchasing goods. This paper presents a bibliometric analysis of peer-reviewed papers based on ISOP topics by utilizing the R application program in the mapping. Overall, 101 papers (233 authors) in the Scopus database have used ISOP topics with research growth of 11.61% annually. The researcher presents a network of citations from productive authors, the impact of research, trends in terms that have been used, and shows a collaborative network of citations. Finally, the researcher presents the thematic analysis of the papers that apply the ISOP as a research topic and shows how the research forms clusters based on analytical solutions and numerical simulations that generate suggestions in finding the latest topics in the ISOP study. Another target for this paper is to produce review analysis results through Preferred Reporting Items for Systematic reviews and Meta Analyses (PRISMA). Through bibliometric and PRISMA analysis, it was found that the latest method in completing ISOP optimization is the ARC method. The ARC method in the ISOP is still little published among researchers in the world.

Heuristic algorithms for the Internet shopping optimization problem with price sensitivity discounts

PurposeRapid advancements in internet technology have made it possible to develop electronic commerce in general and internet shopping in particular. Easy access to a vast number of existing internet stores enables buyers to customize their shopping processes to minimize the total purchase cost. This paper aims to investigate a novel internet shopping problem, which consists of the diversification of a given list of products to buy among many stores and to use discounts offered by the stores.Design/methodology/approachThe adequate discrete optimization problem referred to as internet shopping optimization problem with price sensitivity discounts (ISOPwD) is investigated, which turned out to be strongly nondeterministic polynomial (NS)-hard. Two heuristic solution algorithms have been derived using the tabu search (TS) and the simulated annealing (SA) metaheuristics for having a solution in a reasonable time. The algorithms have been assessed via computational experiments, and they have been compared with another algorithm known from the literature that has been elaborated for a simpler version of ISOPwD.FindingsThe conducted evaluation has shown the advantage of both heuristic algorithms on the algorithm known from the literature. Moreover, the TS-based algorithm outperformed the other one in terms of the total cost incurred by customers and the computational time.Research limitations/implicationsThe special primary piecewise linear discounting function is only taken into account. Other possible discounts connected, for example, with bundles of products and (or) coupons are not considered.Practical implicationsThe elaborated algorithms can be recommended for internet shopping providers who want to introduce the ability to search a cost-optimized set of products in their databases or for applications that combine offers from various online retailers, e.g. internet price comparison services and auction sites.Originality/valueThe novelty of considered ISOPwD, in comparison with similar problems discussed in the literature, deals with an arbitrary number of purchased products, the possibility to buy an identical product in different stores and the consideration of the weight, the amount and the availability of goods as parameters of ISOPwD.

Trustworthy Online Shopping with Price Impact

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.

Internet Shopping Optimization Problem With Delivery Constraints

Internet Shopping Optimization Problem With Delivery Constraints

Algorithms solving the Internet shopping optimization problem with price discounts

AbstractThe 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.

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

Abstract 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.

Erratum to: Internet shopping with price-sensitive discounts

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).

Novel dual discounting functions for the Internet shopping optimization problem: new algorithms

One of the very important topics in discrete optimization, motivated by practical applications, is Internet shopping, which is becoming increasingly popular each year. More classical versions of the Internet shopping optimization problem (ISOP) are closely related to the facility location problem and some scheduling problems and have been intensively studied in the literature. In this paper, extensions of the problem are defined and studied. The issue is to buy all the necessary products for a minimum total possible price. This includes all prices of products as well as shipping costs. Studies in this paper include the ISOP with price sensitive discounts and a newly defined optimization problem: the ISOP including two different discounting functions, namely a shipping cost function as well as a price discounting function. First, these are formulated as mathematical programming problems. Then, some algorithms are constructed and extensively tested in a computational experiment.

Internet shopping optimization problem

Internet shopping optimization problemA high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.