Coordination of humanitarian logistic based on the quantity flexibility contract and buying in the spot market under demand uncertainty using NSGA-II and NRGA algorithms

The extant study aimed to create a kind of coordination in the humanitarian chain by using a quantity flexibility (QF) contract. The QF contract considers a kind of coordination between a relief organization and a producer for inventory management determining order volumes. Due to insufficiency of amenities or time limits during the crisis, an internal producer can outsource a part of its duties to an external producer to produce items and accelerate the relief process. Hence, this study proposed a completely novel bi-objective mathematical model to coordinate relief items' supply and distribution by using QF contracts and buying in the spot market under demand uncertainty conditions to reduce costs and accelerate relief services. The augmented epsilon constraint method was used to solve the small scales of this model and NSGA-II and NRGA algorithms were employed to solve large scales. The results indicated the powerful performance of NRGA in terms of most evaluation indicators.