Optimizing temporary work and overtime in the Time Cost Quality Trade-off Problem

Abstract In spite of its significant contribution to project success, quality has been scarcely addressed in the literature on deterministic project scheduling problems. Although it is recognized that higher qualities are associated with longer processing times, no relationship between quality and resource consumption has been analytically derived to support this statement. As manufacturing projects can be accelerated using additional manpower such as overtime and temporary workers, we derive an analytical relationship between quality and manpower since overtime and overmanning negate quality. We also take into account productivity losses due to overmanning. Contrary to most previous contributions that focus on the project overall quality as an aggregation of quality levels attained at the individual activities, we impose each activity to reach a minimum quality threshold, which is consistent with project management practices. Consequently, we develop a mixed integer linear programming (MILP) to optimize temporary work and overtime so as to accelerate a project with quality and productivity considerations. The objective is to simultaneously determine for each activity the number of permanent, temporary and overtime workers over the processing periods in order to minimize the makespan, the total cost and the overall quality losses subject to individual quality constraints, precedence relationships, nonpreemption and availability of resources. Our approach is successfully applied on numerous instances based on a real project of a high speed locomotive as well as on other projects taken from the literature.