On inequality constraints in well-known optimisation problems: properties and applications

Abstract

This work studies transportation, assignment, transshipment, shortest path, and dynamic lot sizing problems. Particularly, it shows how to modify their formulations to handle excess supply and node elimination. The paper proceeds by using the conservation of flow to derive the original constraints of these problems. Thereafter, a general form of the conservation of flow is used to reformulate these problems. The results are problems with inequality constraints. This paper shows that solving each of these new formulations returns the same optimal solution as its original form. It also shows how problems with inequality constraints can handle excess supply and node elimination. Along the way, some additional properties of these alternative formulations are explored.