Coordination of a multidivisional organization through two levels of management

This paper develops the bilevel multidivisional programming problem (BMPP) as a model for a decentralized organization. In particular, a hierarchical arrangement comprising one superior unit and M subordinate units is proposed where each unit is assumed to control a unique set of decision variables defined over jointly dependent strategy sets. Individual but interdependent objective functions are also assumed so that each unit may influence but not control another. In the formulation, decisions are made in two stages with top management given the first choice followed by the concurrent responses of the divisions. In this way it is possible to account for production externalities at the lower level and coordination activities at the higher level. As such, after outlining the major geometry of the linear case, the usefulness of the general model is discussed from a management perspective. Ramifications relating to opportunity costs, capacity utilization and computational requirements are presented and highlighted through a variety of examples.