Chlorofluorocarbon (CFC)-based refrigerants (such as CFC12) have found widespread uses in home refrigerators and automotive air conditioners primarily due to their non-toxic, non-flammable nature and their high overall thermodynamic efficiency. However, CFC and hydrochlorofluorocarbon (HCFC) refrigerants with intermediate to high ozone depletion potentials (ODPs) will be banned during the next two decades. The outcome of replacing CFCs in the vapor recompression cycle and various other processes is vital to several industries. Feasible solutions appear to include mixtures of hydrofluorocarbons (HFCs) which have the potential for matching thermodynamic properties of current working fluids while meeting several criteria for ozone depletion potential, flammability, toxicity, materials compatibility and cost. In this paper, a proof-of-concept study is made to show that mathematical programming carl be used effectively to identify a small set of alternative refrigerant mixtures which then can be evaluated experimentally. In the mathematical programming model, binary variables specify the type and number of single component refrigerants that exist in a mixture and continuous variables specify the mixture properties, in addition to the proportion in which the single component refrigerants are blended to form the mixture. The environmental issue has been addressed partially by incorporating the ODP, a quantitative measure of the ozone depleting capability of it compound, into the mathematical programming framework. The results indicate the viability of the approach.