Optimal buying from online retailers offering total value discounts

Discounts based on the total value of purchase is a common business practice among the online retailers. The discounts offered could be in the form of rebates, cash backs, gift vouchers, or reward points. The comparison shopping bots provide only price information for individual products but do not consider the total value discounts that could be accrued by buying more products from the same retailer. In this paper, we consider a buyer interested in buying M different items from N retailers who offer total value discounts. The buyer is faced with an optimization problem of choosing the retailers and the items to buy from them to minimize the total buying cost taking into account the total value discounts offered by the retailers. We propose an integer programming formulation for the problem, which can be integrated with the current comparison shopping search engines. As this problem needs to be solved online, we propose a linear programming based heuristic to obtain a nearoptimal solution that could be used with the commercial solvers to accelerate the solution time. Copyright 2008 ACM.