bender decomposition algorithm

The purpose of this paper is to introduce a more integrated and specialized approach to address the challenging issues known as the "Last-Mile Transportation" and to provide a conceptual-mathematical framework for making a synergy and integration between theoretical concepts and classic urban logistics optimization issues. This is a two-echelon routing-location network consisting of an urban distributor (or warehouse), customers and potential locations to install two types of facilities (automated parcel locker and micro-distributor). After ordering based on their desirability, customers are able to receive their product at the door or at 24-hour parcel locker. A modified Bender decomposition algorithm is used to solve the proposed model, which is amplified by the strategy of rounding of master problem’s variables and local search. To prove the efficiency, we compared the properties obtained from the proposed algorithm with the results obtained from the epsilon-constraint method in the Python software environment, the CPLEX library and ILOG CPLEX Optimization Studio and the results confirms the absolute dominance of this method in large-sized instances. The results of the sensitivity analysis of the role of automated parcel lockers on the network’s cost and produced pollution indicate the efficiency and validity of the proposed model.