In this paper, we study a compensation scheme for linear sequencing situations proposed by Curiel et al. (1989). Instead of focusing on the allocation of the total cost savings among players, we concentrate on the actual monetary transfers arising from each neighboring switch. First, inspired by the split core introduced by Hamers et al. (1996), we introduce a compensation scheme that accounts for the losses incurred by players who are moved to later positions in the queue. Second, we propose two properties to characterize the compensation scheme, namely the Compensation Balance property and the Proportional Balanced Net Payoff property. The former implies that for any neighboring switch of two players, the compensation loss of the forward-moving player is exactly balanced by the compensation gain of the backward-moving player. The latter implies that for any two inverse players, their net payoffs are proportional to their bargaining abilities. Moreover, we construct a cooperative compensation game and demonstrate that the Shapley value of this game coincides with the proposed compensation scheme. Finally, we extend the compensation scheme from linear sequencing situations to a broader class of sequencing situations with general cost structures by proposing a path-based compensation scheme.
