| Summary: | Optimal profits for third-party logistics providers (3PLs) can be analyzed using the networks model to determine decision-making processes within transshipment and logistics, distribution networks, etc. Increasing academic attention is currently being focused upon fields examining 3PLs' operations within logistics networks. This paper studies cooperative game theory (CGT) of retailers-3PLs that make an alliance with each other with a specified demand function. The logistics network involves several suppliers and retailers-3PLs alliances, a distribution graph consisting of several nodes and arcs as well as multiple customers. Retailers-3PLs purchase the same goods from suppliers and sell to customers after shipping via the network; they also consider environmental issues to reduce pollutants and emissions fines. The proposed nonlinear programming (NLP) model aims to find the best flow and price of goods under cooperation conditions among retailers-3PLs by analyzing their risk levels. Controlling uncertainty in the models is accomplished by Mulvey's robust approach. In a general coalition, fair profit distribution methods are applied to share the profits among retailers-3PLs under different risk situations. We conduct a numerical analysis to present the application of our proposed model and find whether coalitions and cooperation between retailers-3PLs reduce costs and increase profits. Finally, we report the sensitivity analysis results regarding the penalties imposed for pollutant emissions, along with suggestions for future research. The results reveal that since their profit is greater in the coalition mode, they tend to cooperate with each other, whatever the amount of pollution fines be. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.
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