A multi-skilled resource-constrained project scheduling with reliability constraints

This paper introduces a novel mixed-integer nonlinear programming model for an extended multi-skilled project scheduling problem with reliability constraints, where disruptions lead to delays in machine service times. Stochastic disruptions are modeled using an M/M/1 queue system and are incorporated in a bi-objective optimization model to minimize project makespan and cost simultaneously. The exact algorithm encompassed epsilon-constraint augmented (AUGMECON2) and VIKOR is employed to solve this complex problem under disruption, demonstrating its efficacy on small-scale instances from the project scheduling problem library (PSPLIB) dataset. Due to the computational complexity and high computation time, a hybrid non-dominated sorting genetic algorithm (HNSGA-II) is developed to solve larger problem instances, and its performance is compared with the multi-objective particle swarm optimization algorithm using several performance metrics. The findings demonstrate the superiority of HNSGA-II in terms of spacing metric, mean ideal distance, and diversification metric. Furthermore, sensitivity analyses are conducted to evaluate the impacts of retrieval and disruption rates on the objective function values. The analysis of key disruption parameters, namely retrieval and disruption rates, indicates that higher disruption rates increase both makespan and project costs, whereas higher retrieval rates reduce both objective functions.​