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 so as to maximize the expected revenue 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 show how the optimal set of products to offer changes with the remaining resource inventory and establish that the optimal policy can be implemented through protection levels. 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.
For example, REF study the network revenue management problem under the Markov chain choice model and present an algorithm based on linear optimization.
Revenue Management Under the Markov Chain Choice Model
Oper. Res.
Oper. Res.
Mathematics Computer Science