Heuristic evaluation of the characteristic function in the Cooperative Inventory Routing Game

Abstract

This paper is concerned with the problem of the characteristic function evaluation for the game theory model of horizontal cooperation of carriers on large transportation networks. We consider a mathematical formalization of the Cooperative Inventory Routing Game (CIRG) in the form of characteristic function. Due to non-exact evaluation of the minimal cost for the coalitions, we have the subadditivity property of the characteristic function to be not fulfilled in general case. To calculate the values of characteristic function that satisfy the subadditivity condition, the Direct Coalition Induction Algorithm (DCIA) is used. To solve the multi-depot Inventory Routing Problem for each coalition, the Dynamic Adaptation procedure for Large Neighborhood Search (ALNS) is applied. Calculation of the characteristic function vales, DCIA performance, and advantages of Dynamic Adaptation for ALNS are demonstrated with computational experiments. It is shown that an experimental level of time consistency of the solutions generated by DALNS for given IRP benchmark instances appears to be higher in average in comparison with the solutions generated by ALNS.