This research examines a low-carbon power dispatch problem under uncertainty. A hybrid uncertain multi-objective bi-level model with one leader and multiple followers is established to support the decision making of power dispatch and generation. The upper level decision maker is the regional power grid corporation which allocates power quotas to each follower based on the objectives of reasonable returns, a small power surplus and low carbon emissions. The lower level decision makers are the power generation groups which decide on their respective power generation plans and prices to ensure the highest total revenue under consideration of government subsidies, environmental costs and the carbon trading. Random and fuzzy variables are adopted to describe the uncertain factors and chance constrained and expected value programming are used to handle the hybrid uncertain model. The bi-level models are then transformed into solvable single level models using a satisfaction method. Finally, a detailed case study and comparative analyses are presented to test the proposed models and approaches to validate the effectiveness and illustrate the advantages.

Hospital outpatient departments operate by selling fixed period appointments for different treatments. The challenge being faced is to improve profit by determining the mix of full time and part time doctors and allocating appointments (which involves scheduling a combination of doctors, patients, and treatments to a time period in a department) optimally. In this paper, a bilevel fuzzy chance constrained model is developed to solve the hospital outpatient appointment scheduling problem based on revenue management. In the model, the hospital, the leader in the hierarchy, decides the mix of the hired full time and part time doctors to maximize the total profit; each department, the follower in the hierarchy, makes the decision of the appointment scheduling to maximize its own profit while simultaneously minimizing surplus capacity. Doctor wage and demand are considered as fuzzy variables to better describe the real-life situation. Then we use chance operator to handle the model with fuzzy parameters and equivalently transform the appointment scheduling model into a crisp model. Moreover, interactive algorithm based on satisfaction is employed to convert the bilevel programming into a single level programming, in order to make it solvable. Finally, the numerical experiments were executed to demonstrate the efficiency and effectiveness of the proposed approaches.

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