Short-run cost-based pricing model for a supply chain network

We have studied a short-run cost-based pricing model of a supply chain network with multiple production and operation units. First, we discussed the cost-based pricing model of a production unit and explained the distinguishing feature of the cost function, an average cost decreases as the output increases. Second, we extended the model to include multiple production and operation units, and then presented a short-run cost-based pricing model of a supply chain network with multiple production and operation units. The cost function is considered as a monotonic multi-dimensional mapping. Third, we discussed the existence and uniqueness of the solution of the above model. We found if the system is profitable, there is at least a meaningful solution, and the solution usually is not unique. That is to say, the low-cost price solution can be found by an iterative method according to the Kantorovich Theorem and it is possible that there is another high-cost price solution. Finally, we illustrated the model with an example.