Today, supply chain management is a fundamental principle of business infrastructure implementation in the world. One of the most important pillars of the supply chain management is distribution network design. A distribution network with appropriate structure reduces costs and enhances customer-perceived service level, thereby improving competitive advantages of the company. In supply chain analysis, it is essential to focus on customers, as they great affect the formation of chain. This requires a balance between associated costs and the level of service provided. Variable-radius and gradual-radius maximal covering problem focuses on the service levels in relation to the costs incurred to the system. In this study, a bi-objective mixed-integer nonlinear programming model was presented to determine optimal number, location and capacity of factories, distribution centers, and retailers, select transportation modes between the chain elements, and evaluate coverage radius of retailers, in such a way to minimize total transportation costs, maximize the covered demand, and achieve gradual coverage of facilities in a variable-radius scheme. The proposed model was validated on a number of sample problems produced and solved by GAMS optimization software. Being NP-Hard, the problem was proposed to be solved via NSGA-II algorithm when its dimensions go large. Analysis of the computational results and respective comparisons indicated good performance of the presented algorithm.
