In this paper, we exp lore the equilibriu m p roblem of cloud manufacturing system (CM fgS) with cost uncertainty. We propose a CMfgS supernetwork model in wh ich decision-makers (resource service providers (RSPs), the agent and resource service demanders (RSDs)) seek to determine their optimal behavior in an environment with cost uncertainty. The cost uncertainty is represented by random variab les and the decision-makers' risk aversion attitude is modeled by adopting mean-variance utility. The equilibriu m conditions governing the supernetwork model are proposed based on variational inequalities. To investigate the impacts of decision-makers' risk aversion attitude and the degree of cost uncertainty on equilibriu m of CMfgS, we conduct a numerical analysis in this study. The results indicate that a risk averse RSP (or agent) tends to raise selling price to mitigate risk, and a risk averse RSD is willing to pay mo re fo r the needed services . We also show that a risk neutral RSP could sell more services when the variance of cost distribution is relativ e large but the opposite occurs for risk averse RSPs .Key words : Cloud manufacturing system, Equilibriu m, Cost uncertainty, Risk aversion, Variational inequalities
IntroductionCloud manufacturing (CM fg), which was proposed in 2010, is an emerging service oriented manufacturing mode. The core idea of CMfg is manufacturing as a service, and the aim o f it is to realize the free sharing, h igh utilization, and on-demand use of manufacturing resources and capabilities through providing reliab le, on-demand, high quality, cost effective manufacturing services in a cloud manufacturing system (CMfgS) (Tao et al., 2011).In CMfgS, there are three kinds of ro les involved in service t ransactions: resource service provider (RSP), resource service demander (RSD), and the agent (also called as cloud operator). The RSPs o wn the manufacturing resources and abilities which are provided to the agent on demand. The RSDs are service consumers. They submit service requirements to the agent and gain optimal services fro m it. The agent is responsible fo r searching, co mb ining, coordinating and managing the required services for meeting RSDs' requirements. After a RSD's request is received by the agent, it searches in the database and propose a reliab le and optimal service scheme for the RSD. When the RSD mod ifies and confirms the service p lan, the agent sends service requests to the selected RSPs. then specific services are organized and launched to meet the RSD's needs. Finally, the service output is sent to the RSD (Wang and Xu, 2013). In this process, each participant is an independent decision-maker. CMfg S has the advantage of managing dynamic service resources in a systematic and integrated way and provid ing reliab le, on-demand, high quality services for RSDs. With the help of the agent's intelligent management, RSDS need not take much time to select suitable services and design service combination schemes. Though RSPs and RSDs must pay for the agent's mana...