This research proposes a new variant of the cyclic inventory routing problem (CIRP) called multi-vehicle CIRP (MV-CIRP). In this problem, there is more than one vehicle available at the supplier site to deliver shipments to customers, and it is not mandatory for the supplier to service all customers. Therefore, a reward is received from each visited customer. Due to the cyclic nature of this problem, the planning horizon is infinite. Thus, the objectives are to find a subset of customers to visit, replenishment quantities and time for each of these customers, and the corresponding vehicle routes for each vehicle such that long-term transportation and inventory costs are minimized and the collected rewards are maximized simultaneously.
In order to solve the problem, we develop a mathematical programming model and propose a simulated annealing (SA) algorithm. The proposed SA is tested on the single-vehicle CIRP (SV-CIRP) datasets. Our proposed SA finds 22 optimal solutions and 15 new best solutions out of 50 test problems. When solving MV-CIRP datasets, SA outperforms BARON and the local search algorithm.

This research proposes a new variant of the cyclic inventory routing problem (CIRP) called multi-vehicle CIRP (MV-CIRP). In this problem, there is more than one vehicle available at the supplier site to deliver shipments to customers, and it is not mandatory for the supplier to service all customers. Therefore, a reward is received from each visited customer. Due to the cyclic nature of this problem, the planning horizon is infinite. Thus, the objectives are to find a subset of customers to visit, replenishment quantities and time for each of these customers, and the corresponding vehicle routes for each vehicle such that long-term transportation and inventory costs are minimized and the collected rewards are maximized simultaneously.
In order to solve the problem, we develop a mathematical programming model and propose a simulated annealing (SA) algorithm. The proposed SA is tested on the single-vehicle CIRP (SV-CIRP) datasets. Our proposed SA finds 22 optimal solutions and 15 new best solutions out of 50 test problems. When solving MV-CIRP datasets, SA outperforms BARON and the local search algorithm.

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