Cloud computing refers to a paradigm where users request necessary computing resources through the Internet, and now there are numerous cloud service providers offering various resources and services at affordable costs. However, finding a provider that adequately caters to both commercial and operational needs is becoming increasingly challenging. This research proposes a bi-objective virtual machine resource allocation problem, which includes payment cost and execution time as the primary objective criteria. The proposed solution approach involves presenting a bi-objective mixed integer problem formulation followed by a two-phase method based on combinatorial optimization techniques to discover all Pareto optimal solutions. In phase 1, the utilized two-phase combinatorial technique locates all supported Pareto optimal solutions, while in phase 2, it obtains the inner non-supported Pareto optimal solutions. Additionally, suitable weights for payment cost and execution time objectives are determined corresponding to all existing Pareto optimal solutions.

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