In recent years, with the support of new information technology and national policies, cloud manufacturing (CMfg) has developed rapidly in China. About CMfg, scholars have conducted extensive and in-depth research, among which multi-objective service selection and scheduling (SSS) attracts increasing attention. Generally, the objectives of the SSS problem involve several aspects, such as time, cost, environment and quality. In order to select an optimal solution, the preference of a decision maker (DM) becomes key information. As one kind of typical preference information, objective priorities are less considered in current studies. So, in this paper, a multi-objective model is first constructed for the SSS with different objective priorities. Then, a two-phase method based on the order of priority satisfaction (TP-OPS) is designed to solve this problem. Finally, computational experiments are conducted for problems with different services and tasks/subtasks, as well as different preference information. The results show that the proposed TP-OPS method can achieve a balance between the maximum comprehensive satisfaction and satisfaction differences, which is conducive to the sustainable development of CMfg. In addition, the proposed method allows the preference information to be gradually clarified, which has the advantage of providing convenience to DM.Sustainability 2019, 11, 4767 2 of 24 common feature of these models is that multiple factors need to be considered in the objectives, for example, time [14][15][16], cost [14][15][16][17], reliability [14-16] and energy consumption [14,[17][18][19], risk [17], service [20], trust [21], availability [22], value [23], reputation [19,24] and workload [25]. Some scholars integrate these factors into a single objective through weight values and design effective algorithms, such as the: parallel method [8], workload-based method [9], two-level method [10], cooperative method [26], chaos control optimal algorithm [16] and improved niche immune algorithm [27]. Some focus on the game theory models [11,12]. Some others pay attention to multi-objective models and algorithms; for instance, Pareto group leader algorithm [14], cloud-entropy enhanced genetic algorithm [23], hybrid artificial bee colony algorithm [18,19], adaptive multi-population differential artificial bee colony algorithm [24], modified particle swarm optimization algorithm [25] and ε-dominance multi-objective evolutionary algorithm [28].In the above studies, novel objective functions attract more attention, and DM's preference for different objectives is rarely considered or simply expressed as a set of weight values [8,17]. In the decision-making process, preference information is critical due to the fact that only one solution needs to be selected as the final scheme. Therefore, considering preference information in the model or algorithm becomes a new research direction, which can provide convenience for DM to choose satisfactory solutions. So, in our previous paper [29], linguistic preference is taken into...