The Selection Allocation Problem

The Selection Allocation Problem (SAP) is a single period decision problem which involves selecting profit-maximizing (or cost-minimizing) activities from various distinct groups, and determining the volume of those activities. The activities in each group are selected subject to the availability of that group's resource, which is provided by either pooling or blending raw inputs from several potential sources. Imbedded in the decision process is the additonal task of determining how much raw input is to be allocated to each group to form the resource for that group. Instances of this problem can be found in many different areas, such as in tool selection for flexible manufacturing systems, facility location, and funding for social services. Our goal in this paper is to identify and exploit special structures in the SAP and use those structures to develop an efficient solution procedure.