Using Probabilistic Information in Solving Resource Allocation Problems for a Decentralized Firm

This paper formulates a general linear programming problem for a multidivision firm where headquarters possesses probabilistic information regarding each division’s opportunities. It is assumed that headquarters is willing to risk implementing a plan which may not be optimal in order to avoid collecting detailed information from the divisions. Headquarters willingness to take a risk is modelled via the use of chance constraints. An iterative procedure which is derived from the Dantzig-Wolfe decomposition principle is presented which allows headquarters to combine deterministic information from the divisions with its stochastic information to arrive at a resource allocation plan. Characteristics of the resulting plan are discussed relative to headquarter’s risk attitude and its probabilistic information. The procedure is adapted to situations where the size of headquarters programming problem has to be reduced.