Fair Profit Allocation Research Articles

Fair collaborative vehicle routing: A deep multi-agent reinforcement learning approach

Collaborative vehicle routing occurs when carriers collaborate through sharing their transportation requests and performing transportation requests on behalf of each other. This achieves economies of scale, thus reducing cost, greenhouse gas emissions and road congestion. But which carrier should partner with whom, and how much should each carrier be compensated? Traditional game theoretic solution concepts are expensive to calculate as the characteristic function scales exponentially with the number of agents. This would require solving the vehicle routing problem (NP-hard) an exponential number of times. We therefore propose to model this problem as a coalitional bargaining game solved using deep multi-agent reinforcement learning, where – crucially – agents are not given access to the characteristic function. Instead, we implicitly reason about the characteristic function; thus, when deployed in production, we only need to evaluate the expensive post-collaboration vehicle routing problem once. Our contribution is that we are the first to consider both the route allocation problem and gain sharing problem simultaneously — without access to the expensive characteristic function. Through decentralised machine learning, our agents bargain with each other and agree to outcomes that correlate well with the Shapley value — a fair profit allocation mechanism. Importantly, we are able to achieve a reduction in run-time of 88%.

Peer-to-Peer electricity trading of interconnected flexible distribution networks based on Non-Cooperative games

With the integration of power electronic devices represented by soft open points (SOPs), distribution networks have gradually evolved into interconnected flexible distribution networks (FDNs). Considering the deregulation of electricity market and user privacy, multiple stakeholders have participated in the operation of FDNs. Peer-to-peer (P2P) electricity trading is promising to alleviate operational problems of interconnected FDNs. As multiple regions pursue the maximum profits individually, non-cooperative game methods can be utilized to realize fair profit allocation in P2P trading. In this paper, a non-cooperative game-based P2P trading method is proposed to meet the electricity trading needs of multi-region interconnected FDNs. First, based on non-cooperative games, a two-layer P2P electricity trading framework is established to realize cost reduction and voltage profile improvement of multi-region interconnected FDNs. Then, a P2P trading adjustment mechanism is designed to improve the operational profits of SOP, in which spatial active power trading adjustment, temporal dispatching of energy storage (ES) link and reactive power support are incorporated. Finally, the effectiveness of the proposed method is verified based on a practical distribution network with four-terminal SOP in Tianjin. The results show that the proposed P2P electricity trading method can promote the economic operation performance of interconnected FDNs and improve the operational profit of SOP.

Optimal coalition formation and maximum profit allocation for distributed energy resources in smart grids based on cooperative game theory

Over the past decades, significant revolutions have occurred on electricity market to reduce the electricity cost and increase profits. In particular, the novel structures facilitate the electricity manufacturers to participate in the market and earn more profit by cooperate with other producers. This paper presents a three-level gameplay-based intelligent structure to evaluate individual and collaborative strategies of electricity manufacturers, considering network and physical constraints. At the Level I, the particle swarm optimization (PSO) algorithm is implemented to determine the optimum power of distributed energy resources (DERs) in the power grid, to maximize the profits. Further, the fuzzy logic algorithm is applied to model the intermittent nature of the renewable sources and implement load demand in the power grid. At the Level II, DERs are classified into two different fuzzy logic groups to secure the fairness between every participant. Finally, at the Level III, the DERs in each group are combined each other by cooperative game theory-based algorithms to increase the coalition profits. Thereafter, Shapley, Nucleolus, and merge/split methods are applied to allocate a fair profit allocation by coalition formation. Ultimately, the results verify the proposed model influence electric players to find effective collaborative strategies under different conditions and environments.

Cooperative game for coordination of a green closed-loop supply chain

This research examines a single-stage green closed-loop supply chain (GCLSC) in which the green manufacturer, retailer, and collector try to reform the environmental effects of their operations, products, and services across the value chain according to their environmental responsibilities. The collector is responsible for performing the take-back program of used green products, recycling, and trading second-hand products. In this paper, the environmental responsibility of all three supply chain members is considered. The demand function of eco-friendly products is defined as a function of retail price, environmental efforts of the green manufacturer and retailer, the sensitivity of environmentally conscious consumers to their efforts, and the worth of off voucher given to the consumer for returning used product. For coordinating this GCLSC, first, the mathematical model of the decentralized model and all possible coalition forms are examined. Then, the cooperative game theory , including Nucleolus solution mechanism (NSM) and Shapley value mechanism (SVM), and different contracting structures, including cost-sharing (CS), revenue sharing (RS), and two-part tariff (TPT) contract, are utilized. Major goal of this research is to compare these two classes of coordination models in terms of economic and environmental dimensions to choose the best strategy for channel coordination. Eventually, computational and practical investigations reveal that forming the grand coalition yields better results than contracts in terms of achieving environmental goals and total profit. Also, the economic advantages are different for each coordination model. Besides coordination mechanisms explored in this research, as a future study, one can incorporate the effect of competition between green and traditional manufacturers on supply chain performance. Finally, managerial insights of this research guide the managers towards desirable practices to promote coordination and achieve a fair allocation of profit. • Develops a green closed-loop supply chain (GCLSC) including green manufacturer, retailer, and collector. • Obtains the optimal pricing, environmental responsibilities, and rate of return decisions. • The environmental responsibility of all three supply chain members is considered. • Grand coalition yields better results than contracts in terms of achieving environmental goals and total profit. • The economic advantages are different for each coordination model.

Queuing-Based Federation and Optimization for Cloud Resource Sharing

Resource sharing can gain economies of scale and increase utilization of cloud infrastructure, a critical challenge of which is how to design efficient resource sharing solutions among self-interested cloud providers. Cloud federation can realize resource sharing, but the existing methods of forming federation need complex computation to guarantee the stability of federation. To address this shortcoming, after analyzing an optimal allocation approach of service requests among clouds, we propose a pareto optimal resource sharing solution named Cloud Light-Federation Sharing (CLFS), in which each cloud can choose its own optimal strategies individually and federation can be formed without complex computation for allocation of service requests and profits. In addition, an optimal resource sharing solution named Cloud Cooperative-Federation Sharing (CCFS) was also designed, in which cloud providers are fully cooperative and have fair profit allocation. The experimental results show that the two federation methods can significantly improve the total utility and decrease the number of dropped jobs. Although the federation rules of Cloud Light-Federation Sharing are simple, its performance is still very close to that of Cloud Cooperative-Federation Sharing.

Development of Community-Based Peer-to-Peer Energy Trading Mechanism Using Z-Bus Network Cost Allocation

Community-based peer-to-peer (P2P) energy trading is applied to manage local market transactions to maximize the social welfare of the community. However, the increasing number of distributed energy resources in distribution systems affects the performance of community-operators in P2P energy trading. Hence, this study develops a community-based P2P energy trading mechanism to ensure fair profit allocation and reduce computation cost, even with numerous participants. To achieve this, the P2P participants were aggregated into smaller groups using the K-means clustering method, allowing the community manager to perform market transactions in a hierarchical manner. In the hierarchical P2P market, social welfare maximization is performed in the higher layer and profit distribution in the lower layer. Furthermore, the Z-bus network cost allocation method was applied to determine the network usage cost and was thus considered as a parameter to ensure fair profit allocation based on the Shapley value. The proposed method was simulated in South Korean P2P energy trading at various market scales. The results showed an improvement in the proposed method compared with conventional single-layer community-based P2P energy trading.

Guest Editorial: Situational awareness of integrated energy systems

Guest Editorial: Situational awareness of integrated energy systems

Sharing carbon permits in industrial symbiosis: A game theory-based optimisation model

The emerging effects of climate change caused by the rise of carbon dioxide (CO2) and equivalent greenhouse gas (GHG) emissions to the atmosphere have prompted policymakers to revise current emission reduction schemes. One of the schemes is a carbon permit scheme which places a restriction on the CO2 or equivalent GHG emissions to the atmosphere. However, limited literature explores the effectiveness of sharing carbon permits in an IS system to optimise and reduce waste emissions in a system. Therefore, this research presents an optimisation-based framework for plants in an industrial symbiosis (IS) system with a carbon permit scheme. The critical success factor for an IS system is the collaboration and synergistic possibilities between participating plants within geographical proximity. This paper takes a different approach from the typical physical resource sharing in IS. This research considers carbon permits as a shared resource between the plant operators. The sharing of carbon permits creates a cooperative environment between the plant operators in the IS system. Through this system, cooperative game theory (CGT) was used to determine the fair allocation of profit to each participating plant operator based on their marginal contribution in the IS system. A case study has been implemented for three process plants: palm oil mill (POM), palm oil-based biorefinery (POB) and combine heat power (CHP) plant that are operated under a carbon permit scheme. Results from the base case study illustrates that each plant operator receives an average of 12% higher profit when sharing their carbon permits relative to working individually under the carbon permit scheme. A further analysis has been conducted to investigate the framework′s economic feasibility at different emission cuts. With differing emission cuts, the results indicated plant operators obtained an increase in their profit margin by 25% when working in a coalition relative to working independently.

Explanation of machine learning models using shapley additive explanation and application for real data in hospital

Background and ObjectiveWhen using machine learning techniques in decision-making processes, the interpretability of the models is important. In the present paper, we adopted the Shapley additive explanation (SHAP), which is based on fair profit allocation among many stakeholders depending on their contribution, for interpreting a gradient-boosting decision tree model using hospital data. MethodsFor better interpretability, we propose two novel techniques as follows: (1) a new metric of feature importance using SHAP and (2) a technique termed feature packing, which packs multiple similar features into one grouped feature to allow an easier understanding of the model without reconstruction of the model. We then compared the explanation results between the SHAP framework and existing methods using cerebral infarction data from our hospital. ResultsThe interpretation by SHAP was mostly consistent with that by the existing methods. We showed how the A/G ratio works as an important prognostic factor for cerebral infarction using proposed techniques. ConclusionOur techniques are useful for interpreting machine learning models and can uncover the underlying relationships between features and outcome.

A multi-agent game based joint planning approach for electricity-gas integrated energy systems considering wind power uncertainty

To improve the effective planning of electricity-gas integrated energy systems (EGIES) among various stakeholders with distinct interests, a multi-agent game based joint long-term planning approach considering wind power uncertainty is proposed in this paper. First, the planning profit models of individual stakeholders are constructed. Then, the robust optimization approach is employed to deal with uncertainties of wind power outputs, and a virtual player ”nature” is introduced to represent uncertainties in the game process. Moreover, based on the analysis of the game mechanism among various stakeholders, a bi-level dynamic game based planning model for EGIES is proposed, conducting security checks through an integrated electricity-gas energy flow model. Finally, the proposed planning model is solved by an iterative search algorithm. Simulation results illustrate superiority of the proposed approach via two aspects: first, it guarantees the equity and provide fair profit allocation of all players in the game; second, it ensures security of the integrated energy system by effectively mitigating violations on voltage and nodal gas pressure limits.

Capacity pooling games in crowdsourcing services

In crowdsourcing services, employers often post some complex (or difficult) tasks that individual workers cannot complete independently. In this paper, we investigate that a group of independent workers willingly form a workers coalition by pooling their capacities together to jointly complete a crowdsourcing task, with the goal of being to obtain a reward from an employer. The capacity pooling games in the crowdsourcing service setting are formulated as optimization problems. Using the duality theory of a linear program, we not only establish that the core of the capacity pooling game is nonempty but also provide a simple way to compute a fair profit allocation policy in the bidding mode, employment mode and contrast mode of crowdsurcing services, respectively. Then, we further analyze the capacity pooling games with concave investment cost and convex quality reward structures, which exhibit the economies of scale and quality incentives. More interestingly, we give a constructive proof to the nonemptiness of the core of the resulting capacity pooling game with nonlinear structures.

Risk and value-added balancing model for a sustainable industry’s supply chain

Industry’s supply chain faces obstacles in maintain sustainability, especially in fair profit allocation, increase value added processing and manage risk. The research aimed to formulate risk and value-added balancing model to determine an ideal price in each supply chains stakeholder of sugar industry. Value added was analyzed through Hayami approach while risk was assessed through House of Risk framework. Risk and value added were optimized by using Multi-objective particle swarm optimization (MOPSO) and LINMAP to find an ideal solution of Pareto. A balanced risk and value added was applied to determine an ideal and fair price of supply chain product in each stage stakeholders. The result shows that upstream stakeholders suffer with higher risk while downstream savors major value added and profit. MOPSO algorithm fires well in finding alternative solutions of risk and value-added optimization and LINMAP succeed to find an ideal solution. The research successfully determines the ideal price of product in each stakeholder and distributes profit with considering a balanced risk and value added, product quality, and current product price. For further research, it requires a predicted and sensitivity model to enrich the price scheme of the supply chain.

Supply Chain Fair Profit Allocation Based on Risk and Value Added for Sugarcane Agro-industry

Supply Chain Fair Profit Allocation Based on Risk and Value Added for Sugarcane Agro-industry

Bilateral Coordinated Dispatch of Multiple Stakeholders in Deep Peak Regulation

Driven by high penetration renewable energy roadmaps, making full use of wind power is still an important work for wind industry and the goal of China. Considering the multiple stakeholders in power supply side and the unbalanced development of them, coordinated dispatch can maximize the wind power utilization. Deep peak regulation (DPR) market in China now has facilitated the coordination. However, wind farms in the market are involved passively for the cost sharing which is not conducive to wind farms to make full play of it advantages. Besides, the electricity of wind farm benefiting from deep peak regulation market cannot be clearly calculated. To solve this problem, a bilateral coordinated dispatch of wind power and other power generation companies (GENCOs) can be introduced in deep peak regulation. In this paper, the bilateral coordination of wind power and other GENCOs in DPR is studied. The potential economic feasible regions in bilateral coordination are analyzed and the compensation pricing ranges are given according to the individual rationality (IR) constraints. The contributions of different participants are clearly calculated using Shapley value, according to which the fair profit allocation is ensured. An affine decision rule is utilized for the simplification and fast computation. A real system in northeast China is utilized for case study to verify the potential economic feasible region. The results can provide reference for the implement and profit allocation of bilateral coordination.

Profit allocation analysis among the distributed energy network participants based on Game-theory

To overcome the supply-demand imbalance problem within a conventional distributed energy system, the distributed energy network (DEN) based on electricity and heat interchanges is proposed. With rational design and operation, the DEN may achieve satisfied economic performance compared with the situation without energy interchange. However, the maximum of overall economic benefits does not necessarily lead to satisfied economic performance for each consumer. Therefore, to promote the consumers' participation in the DEN, an effective and fair allocation mechanism for the additional profit is necessary. In this study, firstly, a mixed-integer linear programming (MILP) model is proposed to deal with the optimal technique selection, lay-out of the energy transmission line and running strategy of the DEN. Then, a mathematical model for fair benefit allocation amongst the participants is presented based on the core method of the cooperative Game-theory. As an illustrative example, three buildings located in Tokyo, Japan have been selected for analysis. According to the simulation results, total annual cost is reduced by 14.5% thanks to the energy interchange within the DEN. Moreover, fair profit allocation mechanism is determined by employing the core method. In this way, a win-win solution is achieved for both group interests and individual interests.

Achieving Stable and Fair Profit Allocation with Minimum Subsidy in Collaborative Logistics

With the advent of e-commerce, logistics providers are faced with the challenge of handling fluctuating and sparsely distributed demand, which raises their operational costs significantly. As a result, horizontal cooperation are gaining momentum around the world. One of the major impediments, however, is the lack of stable and fair profit sharing mechanism. In this paper, we address this problem using the framework of computational cooperative games. We first present cooperative vehicle routing game as a model for collaborative logistics operations. Using the axioms of Shapley value as the conditions for fairness, we show that a stable, fair and budget balanced allocation does not exist in many instances of the game. By relaxing budget balance, we then propose an allocation scheme based on the normalized Shapley value. We show that this scheme maintains stability and fairness while requiring minimum subsidy. Finally, using numerical experiments we demonstrate the feasibility of the scheme under various settings.

Proportional egalitarian core solution for profit allocation games with an application to collaborative transportation planning

For a profit allocation game, one key issue is to find a fair allocation of profit among its players. In this paper, a proportional egalitarian core solution is proposed, which defines in the core of a game an allocation that takes account of each player’s contribution to the grand coalition. This solution concept generalises the egalitarian core solution for cooperative games. To efficiently compute the new solution, a row generation method is developed. The applicability of this new solution concept and the row generation method is demonstrated by an application to a carrier collaboration problem with numerical experiment results.

Fair profit allocation in supply chain optimization with transfer price and revenue sharing: MINLP model and algorithm for cellulosic biofuel supply chains

A mixed‐integer nonlinear programming (MINLP) formulation to simultaneously optimize operational decisions as well as profit allocation mechanisms in supply chain optimization, namely material transfer prices and revenue share policies among the supply chain participants is proposed. The case of cellulosic bioethanol supply chains is specifically considered and the game‐theory Nash bargaining solution approach is employed to achieve fair allocation of profit among the collection facilities, biorefineries, and distribution centers. The structural advantages of certain supply chain participants can be taken into account by specifying different values of the negotiation‐power indicators in the generalized Nash‐type objective function. A solution strategy based on a logarithm transformation and a branch‐and‐refine algorithm for efficient global optimization of the resulting nonconvex MINLP problem is proposed. To demonstrate the application of the proposed framework, an illustrative example and a state‐wide county‐level case study on the optimization of a potential cellulosic bioethanol supply chain in Illinois are presented. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3211–3229, 2014

Vertical integration with endogenous contract leadership: Stability and fair profit allocation

This paper studies vertical integration in serial supply chains with a wholesale price contract. We consider a business environment where the contracting leader may be endogenously changed before and after forming the integration. A cooperative game is formulated to normatively analyze the stable and fair profit allocations under the grand coalition in such an environment. Our main result demonstrates that vertical integration is stable when all members are pessimistic in the sense that they are sure that they will not become the contracting leader if they deviate from the grand coalition. We find that in this case, the grand coalition’s profit must be allocated more to the retailer and the members with higher costs. Nevertheless, we also show the conditions under which the upstream manufacturer can have strong power as in traditional supply chains.

Integrated Resource and Cost Management Scheme for Computational Grids

Problem statement: Autonomous decision making and resource scheduling are the main objectives of market-life computational grid. Resource providers and consumers make the scheduling decisions with cost and incentive factors. The two objectives are to maximize the success rate of job execution and to minimize fairness deviation among resources. The challenge is to develop a grid-scheduling scheme that enables individual participants to make autonomous decision while producing a desirable emergent property in the grid system. Approach: An incentive-based scheduling scheme is presented to utilize a peer-to-peer decentralized scheduling framework a set of local heuristic algorithms and three market instruments of job announcement, price and competition degree. The incentive based scheme is enhanced with priority based pricing schemes. The resource availability, job priority and network delay are used for the cost and incentive decisions. Results: The performance of this scheme is evaluated via extensive simulation using synthetic and real workloads. The system achieves efficient cost and incentive optimization for both providers and consumers. Conclusion: The approach outperforms other scheduling schemes in optimizing incentives for both consumers and providers, leading to highly successful job execution and fair profit allocation.