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The two-stage supply chain problem with fixed costs consists of designing a mimimum distribution cost configuration of the manufacturers, distribution centers and retailers in a distribution network, satisfying the capacity constraints of the manufacturers and distribution centers so as to meet the retailers specific demands. The aim of this work is to pinpoint some inaccuracies regarding the paper entitled "A two-stage supply chain problem with fixed costs: An ant colony optimization approach" by Hong et al. published in International Journal of Production Economics, Vol. 204, pp. 214-226 (2018) and to propose a valid mixed integer programming based mathematical model of the problem. The comments are related to the mathematical formulation proposed by Hong et al. and the considered test instances. [ABSTRACT FROM AUTHOR]

Nowadays, routing problems arise in different contexts of distribution of goods, transportation of commodities and people. Routing problems deals with traveling along a given network in an optimal way. One of the major goals in optimization, including optimization of routing problems, is to reduce the time of stagnation by finding an exit state. The current work is a study about the ability of ants to escape from solution stagnation on a particular routing problem, the Traveling Salesman Problem. [ABSTRACT FROM AUTHOR]