| Assortment optimization is a classic problem in revenue management.The traditional assortment optimization only considers the objective of maximizing expected revenue.But more and more firms care about how to achieve the different targets of revenue or sales or service level nowadays.Hence,this work is motivated by the new context.In this thesis,there are three main parts of the assortment optimization problems with target constraints.The first part is an offline assortment optimization with a single target chance constraint of revenue.It is a static problem that an optimal assortment should be offered in the long run.Meanwhile,the preference of customers is not fully known,which is characterized by a distribution with partial information.We apply the methodology of robust optimization to deal with the uncertainty of preference,introduce the concept of Conditional Valueat-Risk to approximate the chance constraint,and reformulate the problems under the multinomial logit choice model in two different cases,single class and multiple classes of customers,as convex optimization counterparts.The optimal solutions have the property of revenue-ordered under some conditions.The second part is an online assortment optimization with multiple target constraints of sales.It is a multi-period problem that a different assortment can be offered in each period.The preference of customers is known,which is characterized by a distribution of different types.Each customer’s type can be observed before that an assortment is offered in each period.We find the necessary and sufficient condition of the multiple target constraints,propose an online policy to offer assortment in each period,and prove that the targets can be accomplished under this policy in the long run.Moreover,we find the feasibility set of targets,which is a polyhedron under the multinomial logit choice model.Hence,feasible targets can be decided efficiently to optimize the objective at the first stage in different problems,then the online assortment problem could be resolved by our online policy.Finally,we consider two applications of online assortment optimization with joint target and inventory constraints in the third part,which have state transiting over periods: personalized assortment optimization problem with inventory constraints and online rebalancing problem.The similar online assortment policy is adopted.The numerical studies show that our online policy still works well in both of the cases.We also introduce the formulations of optimization problems to decide the targets for the two applications,especially,in which a joint repositioning and rebalancing framework is to find the best targets for the rebalancing problem. |
