An allocation rule for connection scheduling problems

This paper studies so-called connection scheduling problems, a type of interactive operations research problem. A connection scheduling problem combines aspects from the minimum cost spanning tree and sequencing problems. Given a graph, we aim to first establish a connection order on the players such that the total cost of connecting them to a source is minimal and second to find a fair cost allocation of such an optimal order among the players involved. We restrict our attention to connection scheduling problems on trees and propose a recursive method to solve these tree connection scheduling problems integrated with an allocation approach. This latter mechanism consistently and recursively uses benchmark endogenous myopic orders to determine potential cost savings, which will then be appropriately allocated. Interestingly, the transition process from a benchmark myopic order to an optimal one will be smooth using the switching of blocks of agents based on the basic notion of merge segments.