Application of fuzzy goal programming and genetic algorithm is considered in this paper. We extend a multi-objective model for integrated inventory-production-distribution planning in supply chain (SC). We consider a supply chain network which consists of a manufacture, with multiple plants, multiple distribution centers (DCs), multiple retailers and multiple customers. The manufacturer produces several items. Decision maker's imprecise aspiration levels of goals are incorporated into model using fuzzy goal programming approach. Due to the complexity of problem in large size and in order to get a satisfactory near optimal solution with great speed, a new genetic algorithm is proposed to solve constrained problems. To show the efficiency of the used model and fuzzy goal programming approach and genetic algorithm for the collaborative inventory-production-distribution problem, computational experiments are performed on a hypothetically constructed case problem.