Abstract
In fuzzy mathematical programming literature, most of the transformation approaches were mainly focused on integer linear programs (ILPs) with fuzzy parameters/variables. However, these ILP-based solution approaches may be inadequate for solving large-scaled combinatorial fuzzy optimization problems, like project scheduling under fuzzy-stochastic environments. Moreover, many project scheduling applications may contain different types of uncertainties such as fuzziness, stochasticity, dynamism etc. simultaneously in real-life settings. 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 solution approach mainly depends on a bound & decomposition principle which divides fuzzy components of the problem into 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, 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 (WAFGP) is embedded into the proposed CP-based transformation approach in order to produce compromise fuzzy project schedules which trade-off between the expected values of project makespan and total resource usage costs. To show validity and practicality of the proposed approach, a real-life application is also presented for a production-and-operations management (POM) module implementation process of an international Enterprise Resource Planning (ERP) software. The generated fuzzy project schedules under different scenarios by the proposed CP-based approach are also compared to the results of a similar ILP-based transformation approach. Computational results have shown that the proposed CP-based approach outperforms than the ILP-based approach in terms of both solution quality and computational time.
Constraint Programming-Based Transformation Approach for a Multi-Objective & Multi-Mode Resource Investment Project Scheduling Problem Under Mixed Fuzzy-Stochastic Uncertainties
