This study aims at formulating an optimization problem for multi-category assortment planning that considers cross-category effects. Cross-category effects are mainly due to complementary or substitute categories, display proximity, and consumer characteristics. Therefore, this study derives a nested multivariate logit model, namely shopping basket model, for any number of categories and brands. Furthermore, this shopping basket model accounts for all main factors that cause cross-category effects. The resulting constrained, integer, global optimization problem maximizes a combined utility function of heterogeneous consumers. This problem has a quadratic and non-concave objective function with several knapsack-like constraints and other constraints; different from the literature, these knapsack constraints consider widths of products. Shopping basket analysis and optimization are applied to real basket data of consumers obtained from one of the biggest supermarket chain in Turkey. In particular, optimization problem is resolved ignoring cross-category effects. The maximum utility of the problem without cross-category effects is only 5.72% of the one with cross-category effects. This result is similar to the current results in the literature with only two categories.