Single Machine Sequencing Situations with Position-Based Costs

In this paper, we discuss single machine sequencing situations with position-based costs. For these sequencing situations, the costs of agents on different positions are given by a matrix. Solving a sequencing situation means choosing a final processing order and deciding the related payment scheme. We focus on the payment scheme under the optimal processing order. When there is an initial order we design a simple cost allocation rule, and without initial order we make the payment scheme by an assignment game.