A survey of variants and extensions of the resource-constrained project scheduling problem <s> Robustness-Based Objectives <s> This study constitutes an initial effort for modeling and solving resource constrained project scheduling problems with the objective of maximizing quality. Two mixed integer formulations of the problem are introduced. The first formulation assumes integral activity durations and completion times. These assumptions are relaxed in the second formulation. In both formulations the quality of a project is measured by the amount of rework required and the corresponding additional cost incurred. These quality measures are expressed in a common unit of measure and incorporated into the objective function. The second mixed integer formulation is found to be more efficient and thus computational results are reported based on that model. A set of resource constrained scheduling problems are solved using the quality objective and traditional objective functions from the literature. In general it is found that the schedules obtained when maximizing quality outperform the schedules obtained with minimizing makespan or maximizing the net present value of project cash flows objectives in terms of makespan, cost and computational times. <s> BIB001 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Robustness-Based Objectives <s> Abstract A common problem which arises in project management is the fact that the planned schedule is often disrupted by several uncontrollable factors like additional time that might be required for rework and correction of detected defects. As a result, project managers are often unable to meet the promised completion dates. It is therefore vital to take into account such possible disruptions and their potential negative consequences at the project schedule design stage. In this paper, we address the issue of designing a project schedule which is not only short in time, but also less vulnerable to disruptions due to reworks and other undesirable conditions. To that aim, we introduce the concept of schedule robustness and we develop a bi-objective resource-constrained project scheduling model. We consider the objectives of robustness maximization along with makespan minimization. We develop a tabu search algorithm in order to generate an approximate set of efficient solutions. Several variants of the algorithm are tested and compared on a large set of benchmark problems. <s> BIB002 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Robustness-Based Objectives <s> Resource-constrained project scheduling problem (RCPSP) is one of the most important problems in the context of project scheduling. Considering a single objective, such as makespan minimization, net present value minimization or cost minimization has been the cornerstone of most studies done so far. At the other hand, taking this problem into account as a multi objective one has not been well studied. In this paper, a bi-objective model of RCPSP is presented. The first objective is makespan to be minimized, and the second one, a recently developed measure, is robustness maximization aimed at floating time maximization to make scheduling more reliable. The problem formed in this way is an NP-hard one forcing us to use simulated annealing algorithm to obtain a global optimum solution or at least a satisfying one. Finally, we have illustrated our new algorithm using a numerical example with different weights for robustness. (As an example, when robustness weight is zero, the problem will be solved as a makespan objective.) <s> BIB003 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Robustness-Based Objectives <s> Abstract The project schedule robustness measure proposed by Al-Fawzan and Haouari is considered. The deficiency of this criterion is proven. Two new criteria are proposed. <s> BIB004
During the execution of a project, delays may occur that could not be foreseen when the schedule was determined. Therefore, a project manager might be interested in a robust schedule, i.e. a schedules in which a delay has only a limited effect. This approach is often referred to as proactive scheduling. (While there are several robustness-oriented approaches that make use of stochastic concepts to capture the uncertainty explicitly, we restrict ourselves to deterministic problems.) Al-Fawzan and Haouari BIB002 define the free slack sl j of activity j as the amount of time the completion of j can be delayed without affecting any other activity. They propose a bi-objective problem incorporating makespan minimization and maximization of total free slack which is used as a measure of robustness. This problem setting is also treated by Abbasi et al. BIB003 . Kobylanski and Kuchta BIB004 provide a discussion of this approach and propose to use maximization of the minimum free slack min i sl i as sole objective. Quality according to the makespan is assured using an additional project deadline constraint. Chtourou and Haouari  follow the approach of Al-Fawzan and Haouari BIB002 and add further measures of robustness. They suggest to weight the free slack of an activity with the number of its immediate successors and/or the sum of its resource requests. Moreover, they outline alternative measures in which the free slack sl j of activity j is replaced with a binary value α j = 0 if sl j = 0 and α j = 1 if sl j > 0. The idea behind the latter approach is to avoid a bias caused by a very large free slack values. Such large slacks might not be particularly important, given that a smaller slack is already a sufficient buffer for typical delays. Icmeli-Tukel and Rom BIB001 assume that activities need to be reworked. RT jt is the expected rework time (i.e., delay) of activity j when completed at time t, while RC jt is the expected rework cost. It is assumed that RT jt and RC jt increase with time. The objective is to find a schedule with minimal sum of rework times and costs.