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This study considers a project scheduling model to assess the project risks and the impacts on project sustainability when subcontractors collaborate under uncertainty. Moreover, some allocation methods are applied for fair allocating utility of the project and supper-additivity, stability and satisfaction level of each coalition. Finally, sustainability concept is considered in risk assessment in all coalitions.

The proposed mathematical programming model evaluates project risks when the subcontractors cooperate with each other by sharing their limited resources. Then, some cooperative game theory methods are applied for fair allocation of net present value, of the cooperation and finally sustainability aspects (economic, social and environmental) are investigated in risk assessment for each possible coalition.

The results of the proposed model indicate that the subcontractors can increase their profit by 10 per cent ($14,028,450 thousand) and save the equilibrium between sustainability aspects especially in grand coalition. It means that subcontractors do not have incentive to leave the coalition and the supper-additive property is feasible. Furthermore, risk assessment shows that project risks have less impact on subcontractor profits when they cooperate with each other.

Sustainability aspects may be investigated in project management in previous studies, but the authors study sustainability indicators when subcontractors form a coalition and share their resources in response to the risks of availability to resources and delay in completing the project under uncertainty.

Production of waste has been increased exponentially due to world industrialization and urban and machine life expansion. On the other hand, the outbreak of the COVID-19 coronavirus quickly became a global crisis. This crisis has added a large amount of waste to urban waste. The purpose of this study is to create cooperation between municipal waste collector contractors.

Thus, a mathematical model is proposed under uncertain conditions, which includes the volume of municipal waste and infectious waste including personal protective equipment and used equipment for patients. To reduce total costs, the results are evaluated with four cooperative game theory methods such as Shapley value, t value, core center and least core. Ultimately, the saved cost by cooperation in each coalition is allocated fairly among the contractors. Finally, a comparison was made between the solution methods based on the value of the objective function and the solution time.

The results indicate that the proposed cooperative method increases cost savings and reduces the fine of residual waste. Therefore, it can be mentioned that this kind of cooperation would finally result in more incentives for contractors to form larger coalitions. Genetic algorithms were used to solve the large-scale model.

The proposed model boosts the current understanding of waste management in the COVID-19 pandemic. The paper adds additional value by unveiling some key future research directions. This guidance may demonstrate possible existing and unexplored gaps so that researchers can direct future research to develop new processes.

Globalization of markets and pace of technological change have caused the growing importance of paying attention to supplier selection problem. Therefore, this study aims to choose the best suppliers by providing a mathematical model for the supplier selection problem considering the green factors and stochastic parameters. This paper aims to propose a multi-objective model to identify optimal suppliers for a green supply chain network under uncertainty.

The objective of this model is to select suppliers considering total cost, total quality parts and total greenhouse gas emissions. Also, uncertainty is tackled by stochastic programming, and the multi-objective model is solved as a single-objective model by the LP-metric method.

Twelve numerical examples are provided, and a sensitivity analysis is conducted to demonstrate the effectiveness of the developed mathematical model. Results indicate that with increasing market numbers and final product numbers, the total objective function value and run time increase. In case that decision-makers are willing to deal with uncertainty with higher reliability, they should consider whole environmental conditions as input parameters. Therefore, when the number of scenarios increases, the total objective function value increases. Besides, the trade-off between cost function and other objective functions is studied. Also, the benefit of the stochastic programming approach is proved. To show the applicability of the proposed model, different modes are defined and compared with the proposed model, and the results demonstrate that the increasing use of recyclable parts and application of the recycling strategy yield more economic savings and less costs.

This paper aims to present a more comprehensive model based on real-world conditions for the supplier selection problem in green supply chain under uncertainty. In addition to economic issue, environmental issue is considered from different aspects such as selecting the environment-friendly suppliers, purchasing from them and taking the probability of defective finished products and goods from suppliers into account.

This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game.

First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game.

The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness.

In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.

The purpose of this study is to propose a decentralized multi-party cross-trading scheme based on a certificate transaction mechanism for the transaction of excess consumption certificates (ECCs) of renewable energy. The aim is to address the problems associated with the existing centralized transaction mode and to promote the development of the green electricity industry.

The proposed scheme involves calculating the quotation difference for the same type of certificate transaction based on the quotations of all users of both buyers and sellers. The transaction volume is then determined based on the order of quotation difference from large to small, and the total interests of cooperation are calculated. The nucleolus method is adopted to allocate the total interests to each member of the alliance and calculate the final transaction price. The blockchain technology is used for the transaction to achieve accurate traceability and efficient supervision, and a corresponding smart contract is designed and simulated in the Ethereum consortium chain.

The results of the simulation show the rationality and effectiveness of the proposed scheme. The decentralized multi-party cross-trading scheme can overcome the problems associated with the existing centralized transaction mode, such as low transaction efficiency, difficulty in obtaining the optimal transaction strategy and efficient supervision. The proposed scheme can promote the development of the green electricity industry by stimulating users' demand potential for green electricity.

The proposed scheme is original in its use of a certificate transaction mechanism to facilitate the trading of ECCs of renewable energy. The scheme adopts a decentralized multi-party cross-trading approach that overcomes the problems associated with the existing centralized transaction mode. The use of the nucleolus method for the allocation of total interests to each member of the alliance is also original. Finally, the use of blockchain technology for accurate traceability and efficient supervision of the transaction is an original contribution to the field.

This paper examines the profit distribution of engineering projects in the integrated project delivery (IPD) mode. IPD is a new delivery method that can ameliorate many of the disadvantages of traditional delivery methods and improve project results. In the implementation of IPD, the profit distribution is key for ensuring the success of IPD projects.

This paper described a new method for characterizing profit distribution in the IPD mode. The payment function and Shapley value of the cooperative fuzzy game of fuzzy alliance were defined by considering the Choquet integral of the fuzzy measure. The participation of each player was considered, and the influence of participation on the profit distribution was discussed. Lastly, changes in the profit distribution of core participants under different alliance combinations were studied.

A case from a report of The American Institute of Architects (AIA) was used to verify the fuzzy alliance model. There was a significant correlation between the degree of participation of the owner, architect and builder and the profit distribution among these three participants.

The theoretical research in this paper has some limitations. Initially, this paper selects a case with only three key participants in order to simplify the research. When there are many core participants, how to establish the alliance in the IPD mode and how to establish the corresponding profit distribution model, further work is certainly required to disentangle these complexities in models. Second, in this case, BIM technology has little impact on the income of the whole project. Therefore, this paper does not consider the impact of BIM technology on the marginal effect of the IPD project. Third, the contract type in the case is a custom tri-party based on IFOA. There is no classified discussion of the impact of different contracts on the profit distribute in the paper.

Based on the in-depth study of cooperative game with alliance structure, this paper promotes the classic cooperative game with alliance structure. The authors define the payoff function of fuzzy cooperative games by Choquet integral of fuzzy measure, and introduce the idea into the field of IPD. It aims at extending the solution to a cooperative game without a core. It can be obtained through a simple calculation. In the IPD alliance, the fuzziness and uncertainty of the participation degree of each participant will affect the profit of the whole project. The authors find that the higher the participation rate of players, the more profit each participant has. The greater the influence weight of the designer on the alliance, the lower the influence weight of the contractor on the alliance, the lower the participation of the contractor and the designer, and the lower the income distribution value of the three core participants. It shows a monotonous decline status.

For any construction enterprise, it can make more profits if it joins the grand alliance. In the IPD alliance, each participant can maximize their own interests, which can also promote the enthusiasm of construction enterprises to participate in the alliance and increase the application of IPD mode in AEC industry. This research method provides a new fast, effective, and more realistic solution method for cooperative countermeasures. It can be further extended to other cooperative game fields and advance a new research perspective and solution for the distribution of cooperative interests.

The contribution of this paper is the development of a fuzzy alliance model that provides a tool for measuring the profit distribution in IPD. This is the first quantitative model to connect the degree of participation with the profit distribution in IPD using fuzzy alliance.

In the process of group decision-making, there may be multilayer subjects. In other words, members of the decision-making group may come from different layers and there is interest game among decision experts. Therefore, it is an extremely important topic to aggregate the information of decision experts who are involved in hierarchical relations and gaming relations so as to effectively address game conflicts and reach game cooperation.

First, a programming model is established to minimize the difference of expert opinions in hierarchical decision-making, and the method to solve the optimal solution is given. Second, the cooperative game model and its properties are discussed by using cooperative game and Shapley value, and the method to determine the weight vector between layers is also proposed.

This model can quickly aggregate information and achieve game equilibrium among decision-makers with hierarchical relationships. It can be widely used in decision evaluation with hierarchy structure and has certain practical value.

In order to solve the problem that experts at different levels may have conflicts of interest in multilayer grey situation group decision-making process, cooperative game and Shapley value theory are introduced into the study, and a multilayer grey situation group decision-making model based on cooperative game is constructed. The validity and practicability of the model are illustrated by an example.

An abundance of literature suggests that organisations adopting a cooperative approach achieve greater rewards than those that act in opposition or isolation. An emerging body of work also highlights the multiple actors involved in servitization. Despite this, in some contexts the benefits of servitization are not apparent. This paper examines business relationships in the oil industry and how they affect levels of servitization.

A mixed method study employing qualitative and quantitative methods was used to fully explore the context. In the quantitative phase, 48 oil industry specialists responded to a scenario based on game theory. This aimed to determine if the relationships between their respective organisations are cooperative or adversarial. Abduction drove a second qualitative phase. This consisted of a series of semi-structured interviews used to explore the servitization level and influence of servitization on relationships and vice versa.

The statistical results suggest that all parties used adversarial strategies despite the publicised intent to work cooperatively. The interviews suggested that increasing (decreasing) servitization could increase (decrease) cooperation and, in turn, value co-creation but revealed nuances to this effect. It also adds to our understanding of the darker side of servitization by illustrating the impact of mimetic isomorphism.

The findings add to understanding of the complex dynamics around servitization by showing that it is only at advanced levels of servitization that cooperative behaviour is observed, and base and intermediate levels result in non-cooperative behaviour and thus illustrate the importance of adopting a multi-actor lens to explore servitization.

This paper aims to study the establishment of cooperative supply game model considering transportation hub location, and design the profit allocation rule of the cooperative supply coalition.

Based on the economic lost-sizing (ELS) game model and considering the location of transportation hub and the topology design of basic traffic network, we build a supply game model to maximize the profit of cooperative supply coalition. Based on the principle of proportion and the method of process allocation, we suppose the procedural proportional solution of the supplier cooperative supply game.

Through numerical examples, the validity and applicability of the proposed model and the procedural proportional solution were verified by comparing the procedural proportional solution with the weighted Shapley value, the equal division solution and the proportional rule.

This paper constructs a feasible mixed integer programming model for cooperative supply game. We also provide the algorithm of the allocation rule of cooperative supply game and the property analysis of the allocation rule.

The purpose of this paper is to extend the results of Meca et al. (2004) depending on the grey information revealed by the individual firms.

The authors introduce cooperative grey games and focus on sharing ordering cost rule (SOC-rule) to distribute the joint cost.

In this study, the authors introduce a model, where inventory costs are assumed as grey numbers instead of crisp or stochastic ones studied in literature. At first, grey numbers and classical cooperative inventory games are recalled. Then, cooperative grey games are introduced and related results are given. Finally, an application is performed for three shotgun companies in Turkey.

It is an effective approach for theoretical analysis of systems with imprecise information and incomplete samples. Therefore, grey system theory, rather than the traditional probability theory and fuzzy set theory, is better suited to model the inventory problems by using cooperative game theory. To the best of the knowledge no study exists modeling inventory situations by using cooperative grey games. From this point of view this study is a pioneering work on a promising topic.