Abstract
In this dissertation, we focus on three different problems. We first study assortment problems under the classical marginal distribution model (MDM) where the optimal order quantities of products are determined using a newsvendor model. We provide a reformulation to such problems in terms of a max-max optimization problem where the inner part is a knapsack problem and propose a pseudo-polynomial approximation algorithm to tackle the problem. Then, without considering the optimal order quantities for products, we concentrate on a special case and study assortment problems under the marginal exponential model (MEM): we show that optimal solutions to such assortment problems can be efficiently determined under some mild conditions and provide a simple approach that finds near optimal solutions when these conditions fail. Finally, we consider a special structured assortment problem where each product may have its predecessor and successors and a product can only be bought if its predecessor has already been purchased. We show that problems with only chain structures where choice behavior of bundled options are modelled by nested logit (NL) model are polynomially solvable even when dissimilarity parameters are free. For more general cases, i.e., problems with tree structures under other choice models, we provide an efficient algorithm to approximate the solution with the approximation guarantee, 1 jKj , where jKj is the number of leaf nodes given the structure of the problem.