3. Mathematical modeling

The collection and delivery problem we have just presented is a well-known operations research problem known as the VRP vehicle tour problem. It can be modeled in different ways, depending on the objective to be optimized (maximization or minimization) and the constraints imposed.

Several mathematical models have been proposed . After testing a number of them, we finally settled on the three-index vehicle flow formulation. This model uses binary variables x _ijk to indicate whether a vehicle k passes through an arc (i, j) (from site i to site j) or not. Based on this formulation, we have developed two models: one for laundry collection, the other for distribution. In the following paragraph, we present the model...