Vendor selection with bundling: A comment

In a recent article by Rosenthal, Zydiak, and Chaudhry, a mixed integer linear programming model was introduced to solve the vendor selection problem for the case in which the vendor can sell items individually or as part of a bundle. Each vendor offered ony one type of bundle, and the buyer could purchase at most one bundle per vendor. The model employed n(m + 1) binary variables, where n is the number of vendors and m is the number of products they sell. The existing model can lead to a purchasing paradox: it may force the buyer to pay more to receive less. We suggest a reformulation of the same problem that (i) eliminates this paradox and reveals a more cost-effective purchasing strategy; (ii) uses only n integer variables and significantly reduces the computational workload; and (iii) permits the buyer to purchase more than one bundle per vendor.