Cooperative inventory planning in a distribution network

This study addresses the problem of optimal ordering and collaborative inventory management in a distribution network as a two-stage decision problem. In the first stage, when demand is uncertain, the retailers (sellers) order the products from a warehouse. Then, when demand becomes known with certainty, retailers may exchange their products to better match local demands. Sellers should determine their optimal order quantities for the first stage, and quantities and prices of products exchanged in the second stage. This paper proposes to build sellers’ coalitions and solve the two-stage decision problem as a cooperative game. Stability of a sellers’ coalition can be achieved only if the benefits resulting from collaboration are maximised and distributed according to an allocation policy that is both efficient and rational. The profit maximisation problem is formulated as a stochastic optimisation problem with recourse. Using the scenario method, this problem is approximated by a deterministic linear problem for which the existence of a solution is guaranteed. The proposed pricing policy guarantees the rational allocation of benefits under the scenario approximation. An industrial example supports the modelling approach and is used to evaluate the profitability of the exchange practice in the case of real data.