## 1 Introduction  
Industry 4.0 has become a revolutionary industrial paradigm that can endow enterprises with the ability to fulfill challenging industrial and business requirements flexibly [1]. Cyber-Physical Systems (CPSs) offer a paradigm for realizing the vision of Industry 4.0 and support the daily operations of enterprises in the Industry 4.0 era [2]. Due to its capability to enable enterprises to monitor, manage and supervise resources and activities, the CPS becomes an important paradigm today. CPS refers to smart systems consisting of entities in cyber space and physical space. The entities in cyber space are computational components and the entities in physical space are physical components in the systems. CPS relies on interactions between the cyber-space computational components and physical-space components to achieve its goals through properly sensing, planning, control and monitoring. In the literature, a lot of studies concerning CPSs are available. Key research issues such as modeling [3; 4; 5], control [6], planning [7; 8], security [9], development of context-aware applications [10] and resilience/robustness properties [11] have been studied in the context of CPSs. With the development of the Sustainable Development Goals (SDGs) aiming to achieve a more sustainable future [12], many countries around the world and companies in different sectors have been taking actions to achieve these SDGs. Therefore, the design of CPSs should take into account its sustainability factors. In the literature, sustainability in CPSs has been studied in [13; 14; 15]. Among the 17 SDGs, Goal 7, Goal 9, Goal 12, Goal 13 and Goal 17 are relevant to manufacturing. The challenges are the design and development of effective, energy-efficient and sustainable self-adaptive CPSs [16; 17]. Recent studies on the energy efficiency and energy consumption of machine tools pave the way for the development of energy-efficient CPSs. Existing studies on the energy efficiency and energy consumption of machine tools can be found in the review papers [18; 19]. The above studies provide the underpinning knowledge for developing effective, energy-efficient and sustainable self-adaptive CPSs. Although Cyber-Physical Systems (CPSs) provide a flexible architecture for enterprises to respond to changing demand and achieve the Sustainable Development Goals, an effective method to plan processes and allocate resources must be developed to realize these advantages in the Industry 4.0 era. An important related research subject in the context of CPSs is the sustainable development of the self-adaptive CPS [16]. Although a variety of approaches for the sustainable development of self-adaptive CPSs have been proposed in the literature [16], there lacks a sustainable development methodology that covers all the stages in the development of solvers for realizing self-adaptive CPSs, from modelling CPSs and problem formulation to the development of solution algorithms. The requirements of such a sustainable development methodology not only must be able to deal with a specific type of production process, achieving a specific goal of production using a specific solution algorithm, but also need to accommodate the changes in production processes, goals of production, and solution algorithms. To bridge this gap, this study focuses on developing a solution methodology to support the sustainable development of self-adaptive CPSs based on formal models, a general problem formulation and a solution algorithm for the general problem. We will illustrate the proposed framework by applying it to deal with the case of sequential production processes. Self-organization and self-adaptation are two research issues related to exploiting the flexible architecture of a CPS to achieve production objectives [20; 21; 22] in the presence of unexpected changes or disturbances. The design of a CPS must consider issues in order to allow the system to self-organize and self-adapt to satisfy requirements dynamically [23].