Some Properties of a Class of Continuous Linear Programs

This paper discusses a class of linear programs posed in a function space; a member of this class is called a separated continuous linear program (SCLP). Such problems occur, for example, in the planning of production and inventory. We characterize the $L_\infty $ extreme point solutions of SCLP in a manner analogous to the basic solutions of finite dimensional linear programming and give a sufficient condition for there to exist optimal extreme point solutions with finitely many constant-basis intervals. SCLP is to date the most general continuous linear program for which such strong characterizations have been found.