Multi-item fuzzy-stochastic supply chain models for long-term contracts with a profit sharing scheme

In this study, we develop multi-item multi-objective manufacturer–retailer supply chain models with risk and budget constraints for long-term contracts with a profit sharing scheme in a fuzzy-stochastic environment. The manufacturing costs of the items are fuzzy and the demands for the items are random during each period. We examine two separate models with crisp and probabilistic budget constraints for long-term contracts where the business relationship is repeated, while demand is uncertain in a stochastic sense. The models are formulated as profit maximization problems. Next, the fuzzy compromise programming method, global criteria method, and weighted sum method are used to reduce the multi-objective problems into their corresponding single objective problems. Finally, the problems are solved using a gradient-based nonlinear programming technique: the generalized reduced gradient method. The models are illustrated with numerical examples for different types of stochastic demand and a comparative study is presented.