Supply network design with uncertain demand: Computational cooperative game theory approach using distributed parallel programming

In this work we investigate a supply chain design problem with uncertain final demands for the end products produced by a set of manufacturers. This network of manufacturers has the organizational decisions made internally by pooling resources in a cooperative manner and externally by determining the dominant strategic actors that are characterized by the retailer. A non-linear production game (NLPG) is formulated as a mathematical programming problem to describe coalition formation among the manufacturers based on initial contractual agreements. We show that NLPG is a grand coalition game when demand distribution has an increasing generalized failure rate. The conditions that impact the profit allocation in the game including core set, fairness, stability, superadditivity, least-core and ∊-core are defined. A core allocation solution is generated by using an algorithmic approach. This algorithmic solution is tested in a distributed work station network and resulted in attaining strong computational results for the proposed mathematical programming problem; optimization results with 1000 players are determined in 6 min 40 s on a university computer network using parallel programming with 52 powerful work stations. The numerical results indicated O(log(-N|)) complexity of the algorithmic solution up to 800 players. To the best of our knowledge, this work is the first of its kind in which distributed parallel processing is implemented in a university work station network with distributed parallel programming and processing for solving a production cooperative game.