Project scheduling analysis under time window constraints

Abstract

Project scheduling is used in many fields, such as construction, drug development, and scheduling. Such project scheduling has aperiodic characteristics. The aperiodic project scheduling problem is divided into the scheduling problem of determining the sequence of activities with resource constraints and time constraints or when to execute which activity in the already determined sequence. In particular, many studies have been conducted to determine the start time of activities and the end time of projects in a set sequence in the field of construction, production of large ships or aircraft, and military operation planning. The schedule calculation of this project scheduling problem is easily derived through the Forward & Backward algorithm. This is equally applicable to the problem of the existence of time window constraints. In this study, we prove that the Forward & Backward algorithm can be applied to the problem of time window constraints. In addition, it has been identified and proved that a case of discontinuous slack time may occur when applying the existing Forward & Backward algorithm in project scheduling with time window constraints. To solve this problem, the unique schedule is calculated based only on the target time window. Through this, we present a Scheduling Analysis Method that always derives a feasible schedule by analyzing changes in the schedule of the entire project and changes in activities that require focused management. In addition, through network reconstruction, the setting and effectiveness of the Adaptive Feedback Path that can prevent time window violation even in applying the Earliest Starting Rule, the most intuitive method widely used in the actual field, were mathematically identified and verified through experiments. Finally, research on resource leveling is conducted to minimize the use of renewable resources throughout the project. The resource leveling problem is NP-hard, and the computation time increases exponentially as the size gets larger. In this case, the Modular algorithm for leveling by selecting the most ideal subset through the Scheduling Analysis Method is proposed and utilized. As a result, the performance of any leveling-solving method can be improved. Through this, we derive a schedulable schedule even when the earliest starting rule is not always applied advantageously in the field of production planning, and external or managerial aspects must arbitrarily change the start and end time. In addition, it was possible to derive a schedule that does not violate various and complexly applied time window constraints and to derive an activity to be managed intensively.