Virtual power plants (VPPs), as a novel integrated energy aggregation model, can effectively realize peak shaving and valley filling in the power system. This paper mainly investigates the model of a VPP consisting of distributed energy resources (DERs) as energy producers and converters, and an electric vehicle parking lot (EVPL) serving as both a battery storage system and an energy consumer. To mitigate the risks associated with uncertainties, a downside risk constraint method is concerned, which has not yet been applied to this model with multiple uncertainties. We concentrate on the risk-embedded scheduling of the VPP with EVPL, taking into account key uncertain factors, such as, the arrival and departure times of the EVs. Numerical results reveal that the primary factor affecting VPP profits is the instability of renewable energy. In our model, compared to risk-neutral strategies, risk-averse strategies lead to a reduction in average profits by 5.66% , highlighting the trade-off between minimizing risk and maximizing profits.
Due to its numerous applications in social marketing and crowdsourcing, the classical topic of designing a budget-feasible mechanism for a submodular valuation function has been well-studied. In this paper, we consider a generalization of this topic: budget-feasible mechanism design for a k-submodular function in the clock auction model. In our problem, each agent has a private cost, and the auctioneer, composed of k departments, attempts to maximize his k-submodular valuation subject to a budget constraint. For the monotone objective, we propose a randomized mechanism with an approximation ratio of 1/5+√(13) . Additionally, the randomized mechanism can also achieve an approximation ratio of 2/15+3√(13) for the non-monotone objective. Our mechanism only requires O(kn) value oracle queries, making it more practical.
An acyclic edge coloring of a graph G colors the edges in G such that adjacent edges receive distinct colors and the subgraph induced by the edges of any two colors is acyclic. It is conjectured that every simple graph with maximum degree can be acyclically edge ( + 2) -colored. The conjecture has been proven true on triangle-free planar graphs, but is unknown true or not for general planar graphs. We make a step forward to acyclically edge color triangle-free toroidal graphs in + 2 colors. This improves the latest ( + 3) -coloring scheme by Chen and Hou, and completely resolves affirmatively the conjecture on such a super class of triangle-free planar graphs. We achieve the result by first showing that every triangle-free toroidal graph has one of the five specified groups of local structures, and then inductively coloring the edges at the presence of each local structure.
We consider m identical machines scheduling problems with fully parallel jobs. Each job J_j requires processing time p_j and can be executed on any machine at any time unit. In this paper, four scheduling problems are considered: (1) minimize the maximum cost, (2) minimize the total completion time, (3) minimize the weighted number of tardy jobs, and (4) minimize the total weighted tardiness. For the first two problems, we develop optimal polynomial-time algorithms to solve them, respectively. For the third problem, we design a polynomial-time algorithm if all weights are equal to one; we propose a pseudo-polynomial-time algorithm for the general case. For the last problem, we design polynomial-time algorithms for solving some special cases of this problem, respectively.
We consider two scheduling problems with rejection and resource matching on m identical parallel-batch machines. A job is either rejected with a rejection cost or accepted for processing. Accepted jobs are processed on parallel-batch machines with a batch capacity of b. There are multiple kinds of resources, one of which could be matched with an accepted job. Each accepted job must consume exactly one kind of resource and each kind of resource can be consumed by at most one accepted job. Job’s processing time may be different when it consumes a different kind of resource. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection cost of the rejected jobs. When the batch capacity is bounded, we give two approximation algorithms with worst case ratios mb and 2-1/mb , respectively. When the batch capacity is unbounded, we give a polynomial time optimal algorithm.
