<![CDATA[Discount is a type of online purchase promotion that is presented based on the total value of consumer purchases. In this paper, an online purchase optimization problem will be studied, where a buyer is interested in buying several items (x≥2) by considering the total value discounts from different retailers, so that result in significant cost savings. The comparison shopping websites can be an alternative for consumers to find and compare information on items they want to buy from many online retailers. An integer programming formulation is proposed to obtain a near-optimal model of the online purchase problem. Then this formulation was developed into a graph-based modeling which was presented to build an optimization model (OptiGraph). The OptiGraph model obtained consists of the OptiNode set (subgraph) SG_a,SG_b,SG_c (retailer a, b, and c which contains nodes m_1 and m_2 in each subgraph representing the item to be purchased) and the OptiEdge set which describes the relationship between nodes in the subgraph. All nodes and edges contain the constraint function properties of the integer programming formulation of the online purchase problem with discount.]]>
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