Solving a Two-Level Location Problem with Nonlinear Costs and Limited Capacity: Application of Two-Phase Recursive Algorithm Based on Scatter Search

Abstract This study examines the issue of distribution network design in the supply chain system. There are many production factories and distribution warehouses in this issue. The most efficient strategy for distributing the product from the factory to the warehouse and from the warehouse to the customer is determined by solving this model. This model combines location problems with and without capacity limits to study a particular location problem. In this system, the cost of production and maintenance of the product in the factory and warehouse is a function of its output. This increases capacity without additional costs, and ultimately does not lose customers. This algorithm is a population-based, innovative method that systematically combines answers to obtain the most accurate answer considering quality and diversity. A two-phase recursive algorithm based on a scattered object has been developed to solve this model. Numerical results show the efficiency and effectiveness of this two-phase algorithm for problems of different sizes.