Deterministic bundle pricing of two products with limited stock

In this study, we consider a firm in a monopoly environment which sells two types of perishable products using a commodity bundling practice. Our goal is to find the optimal strategy of selling these two products. We determine whether they should be offered separately or in a bundle, define their optimal prices and determine the initial amount of the bundle which should be made from components with limited stocks. We consider a benefit lost cost in a case that the customer segment does not find his desirable product. We also consider a shortage cost in a case that the customer segment selects a product or the bundle but there is not enough of it to satisfy all of the customer segment demands. We assume there are several different customer segments which have different behaviors with different reservation prices. Customer reservation prices are known for each product. Reservation prices for the bundle are determined by degree of contingency. We first solve this problem using integer nonlinear programming by LINGO software but this method gives hand local optimum results so we decide to solve it with a genetic algorithm to be able to find better results. We have 2 different approaches in using GA. First we suppose that the inventory levels are fixed and second we suppose that the prices are fixed and then we find the optimum result.