multi-objective optimization of multi-mode resource-constrained project selection and scheduling problem considering resource leveling and time-varying resource usage

In this paper, a multi-objective mixed-integer programming model is developed to cope with the multi-mode resource-constrained project selection and scheduling problem, aiming to minimize the makespan, maximize the net present value of project cash flows, and minimize the fluctuation of renewable resource consumption between consecutive time periods. moreover, activities are considered to be subject to generalized finish-to-start precedence relations, and time-varying resource usage between consecutive time periods. to assess the performance of the proposed model, 30 different-sized numerical examples are solved using goal programming, epsilon constraint, and augmented epsilon constraint methods. afterward, tukey test is used to statistically compare the solution methods. moreover, vikor method is used to make an overall assessment of the solution methods. statistical comparisons show that there is a significant difference between the mean of the resource leveling objective functions for all the solution methods. in other words, goal programming statistically outperforms other solution methods in terms of the resource leveling objective function. this is not the case for the other objective functions and cpu times. in addition, results of the vikor method indicate that the goal programming method outperforms the other solution methods. hence, goal programming method is used to perform some sensitivity analyses with respect to the main parameters of the problem. results show that by improving any of the parameters at least one objective function improves. however, due to the conflicting nature and the impact of weights of objective functions, in most cases, the trend are not constant to describe a general pattern.