This paper gives optimality conditions to obtain a priori precedence relationships among some of the jobs in a single machine scheduling problem so as to curtail the enumeration while using branch-and-bound technique. The objective is to minimize a quadratic (or generalized quadratic) penalty...

This note considers a problem of simultaneous selection of a subset of N projects and determination of an optimal sequence to implement these projects so as to maximize the net present value of the total return. We first establish an optimal sequence of all projects which does not depend on the...