An Optimization Model For The Resource-Constrained Project Scheduling Problem With Stochastic Activity Durations

Project scheduling is a central field within operations research and management science. It essentially deals with the allocation of scarce resources to individual activities over time. These activities form a project network and have precedence relations between them. The basic problem type in project scheduling is the well-known resource-constrained project scheduling problem (RCPSP). However, in practice, many uncontrollable factors may result in many types of disruptions such as extended activity duration, activity rework, delayed supply, increased cost, or resource unavailability. Therefore, it is rational for project managers to request schedule stability or robustness besides project makespan minimization.A robust optimization model for project scheduling with stochastic activity durations is established in this paper. Two measures of schedule infeasibility are developed. One measures the infeasibility on precedence relations, and another measures the infeasibility on resource constraints. The sum of schedule infeasibility values is used to measure the schedule model-robustness, and the variance of project makespan is used to measure the schedule solution-robustness.A genetic algorithm is proposed to solve the robust optimization model. The direct representation is adopted for solution encoding. Various genetic operators are developed for the robust optimization genetic algorithm. As demonstrated in the illustrative example, the robustness coefficients can control the degree of robustness, which gives decision-makers the flexibility in adjusting schedules according to the environment uncertainty and risk preference. The computational test verified that the genetic operators are effective to improve the schedule robustness and the parameter values also influence the algorithm performance significantly.