this research presents and solves a new mathematical model for school bus routing problem (sbrp). sbrp is a specific case of vehicle routing problem (vrp). despite prevalent models, this model includes location and routing simultaneously. besides, the vehicles are non-homogenous. in addition, instead of locating schools which are the depots, we consider locating bus stops that are mentioned &ap...

Location-Routing Problem (LRP) emerges as one of the hybrid optimization problems in distribution networks in which, total cost of the system would be reduced significantly by simultaneous optimization of locating a set of facilities among candidate locations and routing vehicles. In this paper, a mixed integer linear programming model is presented for a two-echelon location-routing problem wit...

the capacitated location-routing problem (clrp) is a new research area in logistics and distribution management. this problem combines two difficult problems: the facility location problem (flp) and vehicle routing problem (vrp). the goal of the clrp is to open a subset of depots, assign the customers into open facilities, and then design vehicle tours in order to minimize the total cost. the t...

Reliable location routing problem considers a location problem and a vehicle routing problem in order to select the optimal location of facilities and at the same time the optimal routes for vehicles considering the unexpected failure for facilities in which, all facilities may fail with a probability. In this paper, a bi-objective mathematical model has been developed to minimize the total cos...

The location-routing problem is one of the most important location problems for designing integrated logistics systems. In the last three decades, various types of objective function and constraints have been considered for this problem. However, time window constraints have received little attention, despite their numerous real-life applications. In this article, a new 4-index mathematical mod...