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Novel dual discounting functions for the Internet shopping optimization problem: new algorithms. (English) Zbl 1347.90033

Summary: 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.

MSC:

90B35 Deterministic scheduling theory in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B80 Discrete location and assignment
65K05 Numerical mathematical programming methods
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