Metric estimation approach for managing uncertainty in resource leveling problem

Real-life applications in project planning often involve grappling with inaccurate data or unexpected events, which can impact the project duration and cost. The delay in the project execution can be overcome by investing in additional resources to avoid compromising the project duration. The goal of the resource leveling problems (RLP) is to determine the optimal amount of resources to invest in, aiming to minimize the associated complementary costs and adhere to the fixed deadline. To tackle data uncertainty in the RLP, the literature has predominantly focused on developing robust and stochastic approaches. In contrast, sensitivity analysis and reactive approaches have received comparatively less attention, especially concerning the generalized RLP with flexible job durations. In this problem, the duration of each job depends on the amount of resources available for its execution. Therefore, utilizing more resources may help reduce the project duration but at an additional cost. This paper introduces a novel approach that addresses the generalized RLP with uncertain job and resource parameters, incorporating reactive and sensitivity-based methodologies. The proposed approach extends the concept of evaluation metrics from machine scheduling to the domain of the RLP with flexible job durations. It is based on a metric-based function that estimates the impact of changes in input data on the solution quality, considering both optimality and feasibility for the new problem instance. The approach is tested through numerical experiments conducted on benchmark instance sets to investigate the impact of variations in different problem parameters. The obtained results demonstrated a meaningful accuracy in estimating the impact on the value of the objective function. Additionally, they underscored the importance of utilizing optimality/feasibility preservation conditions, as for a significant portion of the tested instances, the use of these conditions gave a satisfactory outcome.