A Mathematical Optimization Model for Solving Minimum Ordering Problem with Constraint Analysis and some Generalizations

In this paper, a mathematical method is proposed to formulate a generalized ordering problem. This model is formed as a linear optimization model in which some variables are binary. The constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. On the one hand, these constraints enforce conditions on an arbitrary subgraph and then give sufficient conditions for feasibility, on the other hand, they provide a natural way to generalize the applied aspects of the model without increasing the number of the binary variables.