Modeling DMU’s Internal Structures: Cooperative and Noncooperative Approaches

An important area of development in recent years in data envelopment analysis has been the applications wherein internal structures of DMUs are considered. For example, DMUs may consist of subunits or represent two-stage processes. One particular subset of such processes is those in which all the outputs from the first stage are the only inputs to the second stage. This chapter first reviews these models and discusses relations among various approaches. Our focus here is the approaches based upon either Stackelberg (leader–follower) or cooperative game concepts. We then examine the more general problem of an open multistage process where some outputs from a given stage may leave the system while others become inputs to the next stage. As well, new inputs can enter at any stage. We then discuss the modeling of this more general network structure.