This paper optimizes joint mixed bundling, assortment planning and pricing problems for complementary retail categories that comprise substitutable items. These categories are divided into one primary category and multiple secondary categories and based on cross-selling effect, customers of primary category can opt to buy from other categories. It is assumed that the bundle can comprise one product of each offered complementary categories. A mixed-integer nonlinear programming is proposed that maximizes total profit by optimizing strategy of bundling, assortment selection and prices of single products and the bundle under a maximum-surplus customer choice model. Then because of computational considerations, this model is linearized and converted to a mixed-integer linear programming; whereby exact solution for even large-scale problems can be obtained. The results show that if cross-selling effect between product categories is overlooked or bundling of products is not allowed, then significant profit losses, will be resulted. To the best of our knowledge, this is the first study on bundling strategies in assortment selection decisions.

Today, distributing high quality perishable foods is one of the challenging issues in food industry. This paper introduces a deterministic vehicle routing problem model with multiple middle depots and proposes the freshness of perishable foods as a new concept to obtain optimal delivery routes. For the proposed mathematical model, profit maximization of delivering the product, minimization of the transportation costs and vehicle traveling time, and maximum level of delivered product perishability (loss of freshness) are considered. GAMS software is implemented to show the authority of the model. Furthermore, genetic algorithm (GA) has been developed to solve the model for large size instances. Several problems are tested in order to compare the exact and the GA solutions.