An interval-stochastic programming based approach for a fully uncertain multi-objective and multi-mode resource investment project scheduling problem with an application to ERP project implementation

Abstract Most of the real-life project scheduling cases may involve different types of uncertainties simultaneously such as randomness, fuzziness and dynamism. Based on this motivation, the present paper proposes a novel interval programming and chance constrained optimization based hybrid solution approach for a fully uncertain, multi-objective and multi-mode resource investment project scheduling problem (MRIPSP). The classical discrete-time binary integer programming formulation of the problem is extended by incorporating both the interval-valued and interval-stochastic project parameters as well as variables. In addition to the uncertain project parameters/inputs, the completion times of the activities which represent the project schedule and the availabilities of the renewable project resources are also stated as uncertain project variables and represented by interval numbers. Then, the proposed interval-stochastic multi-mode resource investment project scheduling (IS-MRIPSP) model is converted into its crisp equivalent form by using the proposed approach. The proposed approach is also able to consider different types of project scheduling risks and produces more reliable and risk-free solutions according to the project manager's attitude toward risks. Furthermore, in addition to the classical makespan objective, effective and efficient utilization of the renewable project resources, i.e., human resources, is also targeted. The efficiency and reliability factors of the human resources are also taken into consideration. In order to generate balanced project schedules which tradeoff between the project time and total human resource costs, compromise programming approach is adapted. Finally, in order to test the validity and practicality of the proposed approach, a real-life application is presented for an enterprise resource planning (ERP) implementation project scheduling problem of an international industrial software company.