یک الگوریتم ژنتیک برای مشکل زمانبندی پروژه با محدودیت منابع پیشگیرانه با تقسیم فعالیت A Genetic Algorithm for the Proactive Resource-Constrained Project Scheduling Problem With Activity Splitting

I. INTRODUCTION IT IS a well-known fact that project activities are subject to considerable uncertainties, such as accidents, resource breakdowns, and bad weather conditions, which may lead to numerous schedule disruptions during project execution and therefore incur some costs when project managers adjust the starting times of the activities to deal with them. Accordingly, proactive scheduling has been the subject of many research efforts that aim to generate robust baseline schedules that are protected against schedule disruptions. The more robust the baseline schedules are, the lower the adjustment costs will be during project execution. These research efforts have led to many models and algorithms, which are summarized in [1]–[4]. Two robustness approaches are considered in this field, i.e., quality robustness and solution robustness [5]. For quality robustness, the robust multimode discrete time/cost tradeoff problem is introduced and solved by exact and heuristic algorithms [6], [7]. Regarding solution robustness, various approaches are developed to cope with multiple disruptions, including activity duration disruptions [8], stochastic activity durations [9], [10], and stochastic resource availabilities [11], [12]. In contrast to the literature that addresses quality robustness or solution robustness separately, several studies have concentrated on the potential tradeoff between these two types of robustness. Al-Fawzan and Haouari develop a bi-objective model with an aggregation function in the absence of available information regarding the nature or size of the uncertain events [13]. With the composite objective of maximizing both schedule stability and timely project completion probability, Van de Vonder et al. develop a heuristic algorithm for minimizing a stability cost function [14] and they discuss the results obtained by a large experimental design that is established to evaluate several predictive-reactive resource-constrained project scheduling procedures [15]. Furthermore, Chtourou and Haouari present a two-stage algorithm in which the first stage is designed to minimize the project makespan, while the second one aims to maximize schedule robustness [16]. Deblaere et al. propose an objective to minimize a cost function that consists of the weighted expected activity starting time deviations and the penalties or bonuses that are associated with late or early project completion [17].