Supply chain is usually represented by a network (which is called supply chain network) that contains some nodes. In a supply chain network these nodes are suppliers, plants, distribution centers and customers which are some facilities connected by some arcs to each other. The arcs connect the nodes in the direction of their production flow, meaning that each arc shows a route between the facilities for transporting the products. A multi-stage supply chain network (MSCN) is defined as a sequence of multiple supply chain network stages. This paper addresses a typical supply chain network problem which is based on a two-stage single-product system under uncertain conditions such that both cost and constraint parameters are interval numbers. The combination of these uncertain parameters are considered in this typical problem for the first time. In this case, two different order relations (the order relations UC ≤ and HW ≤ ) for interval numbers are considered. Then, two solution procedures are developed in order relations for the interval two-stage supply chain network design problem. The efficiency of the proposed method is illustrated by a numerical example where it is proved that the relation HW ≤ shows better performance than the relation UC ≤ .

Abstract
I. Introduction
II. Basic definitions
    2.1. Order relation between intervals
III. Problem description and mathematical model
    3.1. Standard representation of the MSCN
    3.2. Interval representation of the MSCN
IV. A relevant multi-objective problem
    4.1. The order relation UC ≤ 
    4.2. The order relation HW ≤
V. Numerical example
VI. Conclusion
References

• Masoud SANEI(Department of Mathematics, Central Tehran Branch, Islamic Azad University)
• Ali MAHMOODIRAD(Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University) Corresponding Author
• Sadegh NIROOMAND(Departments of Industrial Engineering, Firouzabad Institute of Higher Education)