# Linear Project-Scheduling Optimization Considering a Reverse Construction Scenario
## 1 Introduction  
Throughout the lifecycle of a construction project, several complex engineering and management challenges can arise [1], particularly in large-size infrastructure, such as railways and expressways, owing to their extensive construction period. Among the myriad issues these projects face, scheduling optimization is a significant concern [1, 2]. This problem has attracted substantial attention from the academic community in recent years and is considered one of the most formidable challenges in construction project management [3, 4]. Given this, the scheduling optimization of construction projects is particularly important. Typically, scheduling forms the backbone of project management decision making [5] and ensures successful management, notably in the area of resource management [4, 6]. The fundamental aspect of construction project management can be viewed as the organization and distribution of activities and resources [7]. Construction projects can be classified into linear-repetitive and nonrepetitive projects [8]. Linear projects are characterized by numerous repetitive activities with the same type [9] and are continuously pushed forward on the mileage line during construction [10, 11]. Activities of nonrepetitive projects, such as hospitals and libraries, do not have obvious repetitive characteristics. Detailed comparison for such two types of projects is referred to in [12, 13]. In such a context, resource wastage due to construction delays must be eliminated by ensuring as much continuity of resources as possible [10]. Discontinuousresource allocation typically leads to decreased staff morale, reduced productivity, increased costs, and extended construction periods [14; 15; 16]. These negative effects are magnified in the linear project scenario owing to the continuous repetition of construction. Conversely, the continuous use of resources enhances the learning curve utility, minimizes resource idle, and improves productivity and cost efficiency [17; 18; 19]. Additionally, it enhances the accuracy of project duration and resource usage predictions [20]. In addition, the linear project's repetitive as well as large-span characteristics inevitably lead to the demand for multi-crew strategies, construction continuity, and various special constraints such as spatiotemporal constraints, crew assignment constraints, construction sequence constraints, etc., which are important distinctions from nonrepetitive construction scheduling. These constraints are difficult to describe by traditional network scheduling methods. Overall, owing to the repetitive nature of linear activities, traditional network scheduling methods prove ineffective. Over the past decade, numerous academic studies have highlighted defects in these methods when applied to linear projects. Among these, the two most critical issues are that they fail to guarantee resource continuity and lack the representation of spatial information. Traditional \"activity-based\" scheduling methods, such as network planning, fall short in these areas. Consequently, the linear scheduling method (LSM), a new spatial location-based [16] and resource-driven [21; 22] scheduling technique, tailored for linear projects, has been garnering increased attention from both academia and industry. A comparison between LSM and CPM is referred to in [23]. In recent years, the scheduling optimization of linear projects has been extensively researched and discussed. However, certain research gaps still exist, especially research on incorporating reverse construction activities and other practical scenarios, such as flexible activity-section-crew assignment demands, in linear project-scheduling optimization where research remains insufficient. This has further spurred research on practical scenario-based linear project-scheduling optimization. In response to these gaps, this study developed a scheduling optimization model under the LSM framework to incorporate reverse construction activities and a more flexible crew application mode.