This thesis handles a fundamental problem in retail: given an enormous variety of products which does the retailer display to its customers? This is the assortment planning problem. We solve this problem by developing algorithms that, given input parameters for products, can efficiently return the set of products that should be displayed. To develop these algorithms we use a mathematical model of how customers react to displayed items, a customer choice model. Below we consider two classic customer choice models, the Multinomial Logit model and Nested Logit model. Under each of these customer choice models we develop algorithms that solve the assortment planning problem. Additionally, we consider the constrained assortment planning problem where the retailer must display products to customers but must also satisfy operational constraints.