Revenue management under the markov chain choice model

We consider revenue management problems when customers choose among the offered products according to the Markov chain choice model. In this choice model, a customer arrives into the system to purchase a particular product. If this product is available for purchase, then the customer purchases it. Otherwise, the customer transitions to another product or to the no purchase option, until she reaches an available product or the no purchase option.We consider three classes of problems. First, we study assortment problems, where the goal is to find a set of products to offer to maximize the expected revenue obtained from each customer. We give a linear program to obtain the optimal solution. Second,we study single resource revenue management problems, where the goal is to adjust the set of offered products over a selling horizon when the sale of each product consumes the resource.We showhowthe optimal set of products to offer changes with the remaining resource inventory. Third, we study network revenue management problems, where the goal is to adjust the set of offered products over a selling horizon when the sale of each product consumes a combination of resources. A standard linear programming approximation of this problem includes one decision variable for each subset of products. We show that this linear program can be reduced to an equivalent one with a substantially smaller size. We give an algorithm to recover the optimal solution to the original linear program from the reduced linear program. The reduced linear program can dramatically improve the solution times for the original linear program.