Constraint programming-based transformation approach for a mixed fuzzy-stochastic resource investment project scheduling problem

In fuzzy mathematical programming literature, most of the transformation approaches were mainly focused on integer linear programs (ILPs) with fuzzy parameters/variables. However, ILP-based solution approaches may be inadequate for solving large-scaled combinatorial fuzzy optimization problems, like project scheduling under mixed fuzzy-stochastic environments. Moreover, many real-life project scheduling applications may contain different types of uncertainties such as fuzziness, stochasticity, and dynamism simultaneously. Based on these motivations, this paper presents a novel constraint programming (CP)-based transformation approach for solving a multi-objective and multi-mode, fuzzy-stochastic resource investment project scheduling problem (FS-MRIPSP) which is a well-known NP-complete problem. In fact, the proposed approach mainly depends on a bound and decomposition principle which divides fuzzy components of the problem into the crisp middle, lower, and upper level problems. Thus, it reduces the problem dimension and does not need to use any standard fuzzy arithmetic and ranking operations directly. Furthermore, the stochastic nature of the problem is also taken into account by using a multi-scenario-based stochastic programming technique. Finally, a weighted additive fuzzy goal program is embedded into the proposed CP-based transformation approach to produce compromise fuzzy project schedules that trade-off between expected values of project makespan and total resource usage costs. To show the validity and practicality of the proposed approach, a real-life application is presented for the production-and-operations management module implementation process of an international Enterprise Resource Planning software company. The fuzzy-stochastic project schedules generated by the proposed CP-based approach are also compared to the results of a similar ILP-based method. Computational results have shown that the CP-based approach outperforms the ILP-based method in terms of both solution quality and computational time.