Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine "fair" shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important and complicated problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the constrained equal contribution rule, the (truncated) proportional rule and the (truncated) constrained equal reduction rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the tau-value generate delay cost sharing rules. In the second approach the delays of the paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs to each path are divided proportionally w.r.t. the individual delays among the activities in the path.