A Benders decomposition algorithm for the mixed bundle pricing problem with limited stocks

In this paper a mixed bundling problem for a retailer of two products with monopoly power in the market is studied. The retailer needs to make joint pricing and inventory decisions with the aim of maximizing profit. Ordering decisions have to be made before selling season starts. At the start of selling season, the price of each product and a bundle consisting one unit of each product have to be determined. Moreover, the optimal number of bundles to be offered in the market has to be decided. In this regard, this study proposes a mixed-integer linear programming model based on the concept of reservation price model. What is more, a Benders decomposition algorithm (BDA) is developed to solve the problem optimally. In order to accelerate the convergence of the algorithm, a number of valid inequalities are incorporated in it. Finally, a numerical example is proposed to illustrate the applicability of the proposed model and the algorithm