A new mathematical model for a multi-product location-arc routing problem

This paper addresses a multi-product location-arc routing problem by developing two mathematical models under two assumptions, namely all types of products of a required arc must be supplied by a tour and each type of products of a required arc must be supplied by a tour. Regarding the complexity of the models, this paper provides lower bounding (LB) models using the method exist in the related background. These bounds will help the decision makers to develop quality heuristics. The numerical results demonstrate the true performance of the developed models.