Toward the fair sharing of profit in a supply network formation

The design of a supply chain network can be interpreted as a coalition formation problem in a cooperative game theory and formulated as a linear production game (LPG). The companies that are members of the optimal coalition share their manufacturing assets and resources to produce a set of end-products and globally maximize their profits by selling them in a market. This paper investigates the possibility of combining the requirement of coalition stability with a fair allocation of profits to the participants. It is shown that, in general, the purely competitive allocation mechanism does not exhibit the property of fairness. A technique is proposed to construct a stable and fair allocation system when the core of the game does not exclusively contain a set of competitive allocations.