In this paper, linear programming formulations, complemented by concept based pinch analysis results, are developed to target the minimum energy requirements in a heat integrated fixed flow rate water allocation networks. These formulations can be applied for the cases of heat integration through isothermal and non-isothermal mixing in water allocation networks involving single as well as multiple contaminants. The earlier reported approaches are based on linear programming formulation for the case of isothermal mixing and either mixed integer non-linear programming or discontinuous non-linear programming formulations for the case of non-isothermal mixing. It has been observed that the earlier reported methodologies produce sub-optimal results for the case of non-isothermal mixing. However, the proposed methodologies produce the optimum results because of the rigorously proved linear formulation. Utility requirements for isothermal as well as for non-isothermal mixing cases are compared over a range of minimum approach temperatures, to evaluate the energy performance using illustrative examples. (C) 2011 Elsevier Ltd. All rights reserved.