Paper Title
A Novel Multi-Objective Multi-Mode Multi-Skill Mathematical Model for Time Cost and Quality Trade-off in Project Scheduling

Abstract
In this paper, a novel multi-objective multi-mode multi-skilled project scheduling problem (MOMMMSPSP) with a time cost quality trade-off approach is proposed. In this problem, Each Activity can be performed in different executing modes, and each mode needs different requirements; requirements in this problem are different skills, which should be done by staff. Furthermore, staff members have various skills and specialties and can perform different skills in different activities. To model this problem, an integer linear programming formulation is proposed to optimize the objectives concurrently, including (1) minimizing total project completion time, (2) minimizing the total salary of the workforce involved in performing activities, and (3) maximizing the quality of workforce on performing skills of activities. Then Lp metric technique is utilized to transform the multi-objective problem to a single objective problem and find the optimal solution; thus, the proposed Lp metric model has been solved optimally by GAMS in small-sized. Analyzing the results showed that the optimal solution obtained from an Lp metric method in small-sized is optimal and reliable. Solving the model has created reasonable and feasible solutions for small-sized problems. The proposed model is firmly NP-hard, and bringing exact solutions is time-consuming. Keywords - Lp metric, Multi-Skilled Project Scheduling Problem, Multi-mode Resource Constraint Project-Scheduling Problem, Time Cost Quality Trade-off Problem.