A quantitative approach for estimating the opportunity cost with cross-selling

Most inventory models suppose that opportunity cost of lost sales includes lost revenue and penalty cost (goodwill loss), where the lost revenue is equal to the item's price or marginal profit. However, efficient method for evaluating the penalty cost has not been proposed. In this paper, considering cross-selling effect that the lost sales of one item may influence the sales of other items, we propose a quantitative approach to estimate the opportunity cost based on association rules, in which the penalty cost of lost sales is regarded as the sum of partial dollar usage of all the other related items. Therefore, the opportunity cost of an item is defined as the sum of its own dollar usage and all associated dollar usage. We prove that the unit opportunity cost (UOC) of an item is equal to its own unit dollar usage added the sum of the product that multiplies the unit dollar usage of the associated item by the corresponding confidence. A numerical example and an empirical study with two datasets are used to evaluate the proposed approach. The utility of the opportunity cost is also remarked by analysing the influences of the opportunity cost on inventory policy.