## 1 Introduction  
### Background and Motivation  
New digital technologies have grown to empower the advantages of advanced manufacturing machinery and smarter control [1]. The cloud-based technology of remote data collection, intelligent machine interconnectivity, and sensor monitoring provide the opportunity for pattern modification across all manufacturing divisions [2, 3]. Cloud manufacturing is receiving increasing attention as a product of new digital technologies and the industrial Internet of Things. Cloud manufacturing refers to a service-oriented networked manufacturing model in which service consumers are able to configure, select, and utilize resources on demand in order to complete customized manufacturing tasks. Compared with traditional information manufacturing technology, cloud manufacturing systems have the typical technical characteristics of digitalization, interconnection of objects, virtualization, service, collaboration, and intelligence [4]. Cloud manufacturing comprises a novel manufacturing business model that aims to provide a shared and collaborative pool of manufacturing resources for users [5]. The idea behind the cloud manufacturing concept is establishing a cloud manufacturing platform that aggregates distributed manufacturing resources and then transforms them into manufacturing services while managing them in a centralized manner. This centralized management allows for the handling of multiple tasks simultaneously [6]. One of the critical aspects of centralized management is the scheduling of tasks to achieve optimal system performance. In a cloud manufacturing environment, customers benefit from lower whole-life equipment costs, no upfront capital investments, and flexible services for personalized demands [7]. The customers purchase the service in a pay-per-use paradigm, wherein a customer only pays for what they actually use, regardless of the specific service provider. This is a common pricing plan in the cloud manufacturing environment. The cloud manufacturing industry involves a significant amount of intelligent equipment that serves as an important basis for the development of the manufacturing industry [8; 9; 10]. In cases of equipment failure, users will send a task request for equipment maintenance to the cloud manufacturing platform. Consequently, the cloud manufacturing platform needs to allocate resources effectively to complete equipment maintenance, in order to ensure that users can resume production as soon as possible. With the continuous improvement of equipment, in terms of formalization and complexity, the professional scope of maintenance technology involved in maintenance equipment widens, and operational and resource allocation processes become more complex. A large number of resources are involved in the process of equipment maintenance, including material resources, human resources, information resources, and so on. How to effectively schedule and optimize maintenance resources to meet the needs of users and balance the benefits of cloud manufacturing platforms is an important problem that must be solved. In a cloud computing platform, the cloud service center only provides virtual resources. Cloud manufacturing platforms also provide material resources, human resources, information resources, and virtual or physical resources. These resources may differ in location, cost, and completion performance. Price plays an important role in resource allocation. In addition, how to improve the service quality of cloud manufacturing platforms is also an important aspect. Task scheduling and resource allocation schemes are key factors that affect the efficiency and service satisfaction of cloud manufacturing platforms. Reducing the completion time of each task submitted by users can improve the satisfaction of cloud manufacturing service platforms. In addition, price is also an important factor affecting user satisfaction.