Assortment planning deserves much attention from practitioners and academics due to its direct impact on retailers' commercial success. In this paper we focus on the increasingly popular retail practice to use combined product assortments with both "standard" and more fashionable and short-lived "variable" products for building up store traffic of "loyal" and "non-loyal" heterogeneous customers and enlarging the sales due to the potential cross-selling effect. Addressing the assortment planning as a bilevel optimization problem, we focus on decision-dependent uncertainties: the retailer's binary decision about product inclusion influences the distribution of the product's demand. Furthermore, our model accounts for customers' optimal purchase quantities, which depend on budget constraints limiting the basket that a customer is able to purchase. We propose iterative heuristics using optimal quantization of demand and customers budget distributions to define the total assortment and the inventory level per product. These heuristics provide lower bounds on the optimal value. We conduct a comparison to other existing lower bounds and we formulate upper bounds via linear (LP) and semidefinite (SDP) relaxations for the performance evaluation of the heuristics and for an efficient numerical solution in high-dimensional cases. For managerial insights, we compare the proposed approach with three assortment planning strategies: (1) the retailer does not carry variable products; (2) the retailer ignores the cross-selling effect; and (3) the maximum space allocated to each product is fixed. Our results suggest that variable assortment boosts the retailers profits if the cross-selling effect is not neglected in the decision about products quantities. (C) 2020 The Authors. Published by Elsevier B.V.