This paper studies the Multi-Vehicle Cyclic Inventory Routing Problem (MV-CIRP) as the extension of the Single-Vehicle CIRP (SV-CIRP). The objective is to minimize both distribution and inventory costs at the customers and to maximize the collected rewards simultaneously. The problem is treated as a single objective optimization problem. A subset of customers is selected for each vehicle including the quantity to be delivered to each customer. For each vehicle, a cyclic distribution plan is developed. We construct a mathematical programming model and propose a simulated annealing (SA) metaheuristic for solving both SV-CIRP and MV-CIRP. For SV-CIRP, experimental results on benchmark instances show that SA is comparable to the state-of-the-art algorithms and it is able to improve 12 best known solutions. For the MV-CIRP, the results show that SA performs better than an Iterated Local Search algorithm.

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Cross-docking is a logistics strategy that aims at less transportation costs and fast customer deliveries. Incorporating an efficient vehicle routing could increase the benefits of the cross-docking. In this paper, the vehicle routing problem with reverse cross-docking (VRP-RCD) is studied. Reverse logistics has attracted more attention due to its ability to gain more profit and maintain the competitiveness of a company. VRP-RCD includes a four-level supply chain network: suppliers, crossdock, customers, and outlets, with the objective of minimizing vehicle operational and transportation costs. A two-phase heuristic employs an adaptive large neighborhood search (ALNS) with various destroy and repair operators is proposed to solve benchmark instances. The simulated annealing framework is embedded to discover a vast search space during the search process. Experimental results show that our proposed ALNS obtains optimal solutions for 24 out of 30 problems of the first set of benchmark instances while getting better results for all instances in the second set of benchmark instances compared to optimization software.

This paper studies the integration of the Vehicle Routing Problem with Cross-Docking (VRPCD). The aim is to find a set of routes to deliver products from a set of suppliers to a set of customers through a cross-dock facility, such that the operational and transportation costs are minimized, without violating the vehicle capacity and time horizon constraints. A two-phase matheuristic based on column generation is proposed. The first phase focuses on generating

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