The online movie rental industry in the United States has grown at a rapid pace during the past decade. Netflix and Blockbuster are two prime examples of companies that operate in this arena, each with a large subscriber base. These two companies employ two standard methods for movie delivery: streaming and DVD-by-mail services. Although the industry is clearly undergoing a transition into streaming service, a substantial fraction of subscribers continue to prefer the more traditional DVD-by-mail service. We will study the problem of how to efficiently manage DVD-by-mail service.
An essential task in solving our problem is a proper modeling of subscriber demand. We will therefore first develop a demand formulation based on data from Blockbuster. This formulation is then used to construct a nonlinear mathematical program for making the following decisions: (i) the initial order quantity of a new movie (DVD) title and (ii) the shipment size of the title for every period (i.e., day) after its release. By exploiting the structure of this mathematical program, we develop a heuristic algorithm based on a simple shipment policy. Through extensive computational experiments, we demonstrate that our algorithm provides optimal or close to optimal solutions for practically relevant problem instances. The proposed policy and solution are simple, easy to understand, and easily implementable in practice.