Optimizing temporary work and overtime in the Time Cost Quality Tradeoff 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.

A LazyConstraints Approach to ResourceConstrained Project Scheduling We study the complex combinatorial optimization problem to schedule the activities of a single project with the objective to complete the project within the shortestpossible amount of time such that the limited resource capacities as well as the prescribed precedence relations between pairs of the activities are taken into account. In addition to various specific solution algorithms, the related literature proposes several MixedInteger Linear Programming (MILP) models, but these models remain complex to solve even for smallsized instances. We present a novel approach based on an MILP model in which the resourcecapacity constraints are formulated for all inclusionminimal sets of activities which, due to the limited capacities of the resources, cannot be processed simultaneously. We propose to remove these constraints from the model and iteratively add those constraints back which are violated in the solutions obtained. For a set of test instances from the literature, our computational results indicate that with respect to both, the deviation of the project duration obtained from the lower bound devised from the criticalpath length and the number of instances solved to optimality, the novel lazyconstraints approach outperforms ten stateoftheart MILP models.