Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players

Abstract EN

This paper extends an existing cooperative multi-objective interaction programming problem with interaction constraint for two players (or two agents).

First, we define an s-optimal joint solution with weight vector to multi-objective interaction programming problem with interaction constraint for two players and get some properties of it.

It is proved that the s-optimal joint solution with weight vector to the multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem.

Then, we define another s-optimal joint solution with weight value to multi-objective interaction programming problem with interaction constraint for two players and get some of its properties.

It is proved that the s-optimal joint solution with weight vector to multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem.

Finally, we build a pricing multi-objective interaction programming model for a bi-level supply chain.

Numerical results show that the interaction programming pricing model is better than Stackelberg pricing model and the joint pricing model.