![]() ; Bouvry, Pascal ![]() 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 ▲] Detailed reference viewed: 132 (4 UL)![]() ; Bouvry, Pascal ![]() in 4OR: a quarterly journal of operations research (2014), 12(1), 35-48 A customer would like to buy a given set of products in a given set of Internet shops. For each Internet shop, standard prices for the products are known as well as a concave increasing discounting ... [more ▼] A customer would like to buy a given set of products in a given set of Internet shops. For each Internet shop, standard prices for the products are known as well as a concave increasing discounting function of total standard and delivery price. The problem is to buy all the required products at the minimum total discounted price. Computational complexity of various special cases is established. Properties of optimal solutions are proved and polynomial time and exponential time solution algorithms based on these properties are designed. Two heuristic algorithms are suggested and computationally tested. [less ▲] Detailed reference viewed: 144 (2 UL)![]() Bisdorff, Raymond ![]() in 4OR: a quarterly journal of operations research (2008), 6(2), 143-165 Detailed reference viewed: 132 (7 UL)![]() Bisdorff, Raymond ![]() in 4OR: a quarterly journal of operations research (2004), 2(4), 293-308 Detailed reference viewed: 62 (6 UL) |
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