In Pinch Analysis, flows (e.g., water, hydrogen) from the sources are allocated to different sinks subject to quality constraints (e.g. contaminant concentration) while minimising the requirement of the valuable external resources (e.g. fresh water, external hydrogen). However, in many applications quality parameters associated with the sources are not deterministic due to varying operating and environmental conditions. Consequently, incorporation of these uncertainties is essential for reliable operation of the overall system. In this paper, uncertainties associated with each source quality are modelled as independent normal distributions with known mean and standard deviation. The overall objective of this paper is to optimise the operating cost of a source-sink allocation problem with multiple resources and uncertain qualities through the concept of prioritised cost. Chance constraint programming approach is applied to convert quality constraints associated with sources to a deterministic form. The resultant problem is approximated to a linear programming formulation and solved using Pinch Analysis approach. The proposed method is demonstrated with an illustrative example and results are verified through Monte-Carlo simulation.