Robust Optimization of Multiple Logistics Nodes Location Problem with Curved Demands

In the construction of traffic line, the materials are continuously distributed along the curve and have the characteristics of uncertainty. The location problem of material supply facilities plays an important role to control the transportation costs. In this paper, the demand density is used to describe continuous demands. Considering the demand uncertainty which often appear during the construction, it is assumed that the demand density fluctuates within a given ellipsoidal uncertainty set. The total freight is described by definite integral, so the Robust optimization model is proposed. According to the robust optimization theory, the problem is simplified into a robust counterpart model. Based on the analysis of the model properties, the iterative algorithm is designed. The case study shows that the solution of the robust optimization model can be more stable. According to the correspondence between robust budget and cost, decision makers can weigh them and choose the robust budget reasonably.