An Application of Symbolic Logic to a Selection Problem

Given a set of jobs that must be performed, although not necessarily concurrently, a set of resources to perform the jobs, a set of cost measures for the resources, and a set of restrictions on the resources that may be used, the selection problem is to find a least-cost subset of resources that satisfies the restrictions and is capable of performing all the jobs. This selection problem is generalized into minimizing a linear function of Boolean variables subject to Boolean restriction equations. A “smallest” complete set of solutions is found that contains all optimal solutions.