A developed nonlinear model for the location-allocation and transportation problems in a cross-docking distribution network

The paper addresses the location-allocation and transportation problems in designing a cross-docking distribution network that consists of suppliers, cross-docks, and plants. A developed mixed-integer non-linear model is proposed for a post-distribution cross-docking strategy with multiple cross-docks and products that cross-docks can be connected. The objective function is to minimise the total cost comprising the cost of established cross-docks and transportation costs. To obtain this model, first, two models are introduced and compared (basic non-linear model 1 and non-linear model 2 with the possibility of connections between cross-docks). Results indicate that the total cost is decreased when the connection between cross-docks exists. So, model 2 is more efficient and suitable than model 1. Then, consolidation of plant orders is added to model 2, and the developed model is formulated. Finally, some problems with different sizes are generated randomly and solved by GAMS software to evaluate the model accuracy.