Bi-level multi-objective optimization model for last mile delivery using a discrete approach.

*(English)*Zbl 1376.90057Summary: To reduce traffic congestion as well as to improve workforce productivity, a bi-level multi-objective model is proposed for an urban logistics metropolis, in which there are two decision-makers, one is the center operator (leader) of an urban consolidation center at the upper level and the other is the logistics party (follower) who manages the delivery at the lower level. In this model, we suppose the supply side risk and the demand side risk exist simultaneously and the decision-makers at both levels are risk-averse. The leader makes his decision by considering the demand from the follower and his own economic efficiency, environmental emissions, and highly dependent time windows with penalties for late delivery. The follower arranges his transportation plan by considering the cost for the order from retail stores and the time window set by the center operator at the upper level. To solve the resulting bi-level multi-objective model, a new solution method is constructed. Numerical tests are given to show the efficiency of our method.

##### MSC:

90C29 | Multi-objective and goal programming |

90C15 | Stochastic programming |

90C22 | Semidefinite programming |

90B06 | Transportation, logistics and supply chain management |

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\textit{Y. Ji} et al., J. Difference Equ. Appl. 23, No. 1--2, 179--190 (2017; Zbl 1376.90057)

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