This paper deals with an integrated routing problem in which a supplier delivers a commodity to its customers through a two-echelon supply network. Over a planning horizon, the commodity is first sent from a single depot to a set of Distribution Centers (DCs). Then, from the DCs, it is delivered to customers. Two sources of flexibility are analyzed: flexibility in network design and flexibility in due dates. The former is related to the possibility of renting any of the DCs in any period of the planning horizon, whereas the latter is related to the possibility of serving a customer between the period an order is set and a due date. The objective is to minimize the total cost consisting of the sum of the shipping cost from the depot to the DCs, the traveling cost from the DCs to the customers, the renting cost of DCs, and the penalty cost for unmet due dates. A mathematical programming formulation is presented, together with different classes of valid inequalities. Moreover, an exact method is proposed that is based on the interplay between two branch-and-bound algorithms. Computational results on randomly generated instances show the value of each of the two kinds of flexibility. Their combination leads to average savings of up to about 30%.
DARVISH, M., ARCHETTI, C., COELHO, L.C. et SPERANZA, M.G. (2019). Flexible two-echelon location routing problem. European Journal of Operational Research, 277(3), pp. 1124-1136.