# A two-phase heuristic method for the multi-depot location routing problem taking inventory control decisions into consideration

• S. C. Liu
• S. B. Lee
Original Article

## Abstract

The multi-depot location-routing problem (MDLRP) combines depot location and vehicle routing decisions, in order to determine the locations of depots and find the optimal set of vehicle schedules and routes. Inventory control decisions are interrelated with vehicle routing and depot location. However, the inventory control decisions are always ignored in MDLRP. In this paper, a mathematical model for the single-product multi-depot location-routing problem taking inventory control decisions into consideration is proposed. Since finding the optimal solution(s) for this model is an NP (non-polynomial) problem, we propose a two-phase heuristic method to find solutions for this problem. In phase 1, the initial solution using a route-first, location-allocation second approach based on the minimal system cost (including location, transportation, and inventory costs) is determined. In phase 2, an improvement heuristic search for a better solution based on the initial solution in phase 1 is developed. One sample description is presented for demonstration purposes. At last, the proposed heuristic method is tested and evaluated via simulation. The results show the proposed heuristic method is better than those existing methods without taking inventory control decisions into consideration.

## Keywords

Heuristic methods Multi-depot location-routing problem (MDLRP) Inventory control NP problem

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