Fair and Rational Schemes for Payoff Allocation in Supply Chain Design Problems

Supply chain design problems can be analyzed as cooperative linear production games. The maximal total payoff and the optimal coalition of a “market responsive” supply network can be obtained from the solution of the mixed-variables Linear Programming problem. Then, using duality theory, the “Owen set” can be constructed in order to allocate the payoff among the members of the optimal coalition. However, it is shown that for a classical aggregate planning model, such an allocation scheme may be unfair and its stability critical. Two techniques are proposed to correct this defect. The first one consists in introducing transfer payments among the players of the optimal coalition. Then, as this technique is not always feasible, a second technique is proposed. It relies on an improved representation of capacitated resources through clearing functions. It is shown that a better payoff allocation mechanism can then be computed through an appropriate tuning of clearing functions.