Conservation of resources is one of the critical solutions for sustainable development. Segregated targeting problems, a special kind of topologically constrained source-sink problem for achieving sustainability through conservations of various resources, comprise of internal sources and multiple zones of demands with a dedicated external resource for each zone. The dedicated resource supplies flow to the demands present in that zone only. In contrast, internal sources supply flow to the demands of every zone. The overall operating cost of these topologically constrained source-sink problems can be reduced significantly by utilizing additional resources that are shared by all the zones. This research gap is addressed in this paper through the introduction of common resources. A mathematically rigorous approach based on Pinch Analysis principles is developed. A novel concept of the extended prioritized cost is introduced in this paper to determine the overall cost optimality for such problems, and the applicability of Pinch Analysis is extended for such topologically constrained networks. Extended prioritized cost governs the allocation of flow from common resources to different zones. Two examples and a case study of an integrated iron and steel industry illustrate the proposed approach’s applicability. It is concluded from these examples that the introduction of common resources leads to 20–45% cost reduction for the overall problem. Sensitivity analysis is also performed for these examples and pictorially depicted through a novel sensitivity diagram. The proposed sensitivity diagram identifies different optimality regions for the economical addition of common resources.