Location routing problems (LRP) are utilized to solve situations in which locations and routes concurrently refer to specific performance criteria such as minimizing total costs. LRP consists of decisions regarding the location of the facilities and the route from the depot to the consumer. The primary components of LRP model are the depot, the vehicle, and the consumer. In its implementation, LRP evolves in accordance with the underlying assumptions and the circumstances.
This study was inspired by differences between depots and vehicles as LRP components. The minimum number of depots in a region affects LRP. Existing depot facilities also affect the decision to open a new one. Heterogeneous vehicles will increase the model complexity in practice. The model meets the minimum depot requirements of a business or government institution, such as representations, licensing, satisfaction, and consumer protection.
This work introduces three LRP models that contain the regional factor: the regional LRP (RLRP), the multi-depot regional location routing issue (MRLRP), and the heterogeneous-fleet-multi-depot regional location routing problem (HFMRLRP). The goal is to establish the optimal depot locations and vehicle routes for each region to meet demand at the lowest possible cost. This research illustrates the model with numerical examples based on actual data and implements an algorithm to resolve the issue. The results demonstrate that the technique effectively resolves the RLRP, MRLRP, and HFMRLP.

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