# Coalition-Formation Problem for Cooperative Inventory Routing Game

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Abstract

This paper studies stability of carrier coalitions in a cooperative inventory routing game (CIRG). Difficulty of this study is not only in a computational complexity of the class of routing problems, but also in the task of constructing a characteristic function, since heuristic solutions that are usually used in routing problems can’t guarantee the subadditivity property in the general case. In its turn, violation of subadditivity can lead to instability of a coalition, because a player could get more profit in a different coalition or individually. To solve routing problems, Adaptive large neighborhood search (ALNS) and its modification with the Dynamic adaptation method, DALNS, are used in this work. A special Direct coalition induction algorithm (DCIA) is used to construct a subadditive characteristic function, and four different concepts of cooperative game solutions are considered. The analysis of extensive computational experiments allows to illustrate the dependence of the stability of a grand coalition on such factors as a routing algorithm, an algorithm for a characteristic function construction, and a solution concept for a cooperative game.