# Minimization of Material Waste Through Maintenance Interval Optimization in Transport Systems
## 1 Introduction
### Origin of the Research Problem  
Effective planning and management of transport operations are essential across all types of transportation to ensure reliability, efficiency, and sustainability. Operators in road, air, maritime, and rail transport face similar challenges, such as optimizing resource use, reducing downtimes, and adapting to changing conditions in service demands. However, each mode of transport also has its own unique characteristics and specific requirements, which impact the types of tools and systems that can effectively support these needs. For railway operators, expectations regarding the functionality of software supporting the process of planning and managing rolling stock and train crew operations are focused on the need to create a new, integrated system equipped with advanced optimization tools. Potential users expect solutions tailored to both the specific nature of their work and the constantly changing demands and conditions of transport services. Due to the specific nature of railway transportation and the much larger and functionally more complex requirements compared to road transport, the range of software systems is much more limited than in other branches of transportation. Currently, there are IT solutions globally that cover the area of railway transport services. Most of these tools do not use mathematical optimization tools to support decision-making processes. Only a few of them use optimization algorithms, and even then, these are mostly classical algorithms limited to linear, integer, or binary programming. Given the scale of real-world problems, leading to a very large number of decision variables and constraints in the mathematical model, these have limited practical application (they are inflexible, slow, and complicated to implement and use). The result of using such tools is far-from-optimal solutions. The main issues with using more effective and advanced optimization algorithms are primarily performance problems (unrealistic data processing times), as well as their effective implementation in IT tools, and the significant expertise required for proper configuration and use. The solution presented in this publication minimizes the downtime of rail vehicles from effective operation, which includes technical travel time to repair stations, waiting time for repair (available slots), waiting to be incorporated into the timetable, and other factors directly or indirectly related to vehicle maintenance. A very important issue is forecasting the wear of individual components of the rail vehicle to determine when and to what extent it should be serviced. The required time until the next technical review, according to safety principles of operation, will be determined based on the optimization of time intervals between the boundary values of analyzed indicators and will be determined by the values of the weakest component indicator, which may be characterized by the system's sensitivity to external forcing factors. Requirements for technical inspections of aircraft are defined by national regulations and the European Union Aviation Safety Agency (EASA). Legal regulations include the Commission Implementing Regulation (EU) 2019/947 of 24 May 2019 regarding rules and procedures for the operation of unmanned aircraft. These regulations aim to ensure airworthiness and flight safety. Regular Technical Inspections: Aircraft must undergo periodic technical inspections according to schedules set by manufacturers and regulatory requirements. These inspections cover the examination of technical condition, onboard systems, and equipment. Inspection Frequency: The frequency of technical inspections depends on several factors, such as the type of aircraft, its purpose, classification, and applicable regulations. In general, technical inspections are divided into:  
* Pre-flight Inspection (Daily Check): Conducted before each flight or once daily, depending on usage.