# A Memetic Algorithm for an External Depot Production Routing Problem
## 5 Conclusions  
This paper focuses on the comparative study of the results obtained with a memetic algorithm (MA) and a two-phase decomposition heuristic (TPDH) for the management of an external depot in a production routing problem (EDPRP). In the MA developed in this work, three local search algorithms (LS) were used to intensify the search for the best solution on each instance adapted from the work of [PERSON] and al. [17]. The results have shown an improvement in the production cost computed with MA compared to TPDH ranging from 0% to 16.64% with an overall average rate of 5.18%. Similarly, there has been an improvement in the cost of transport ranging from 17.08% to 51.26% with an overall average rate of 35.60%. However, the inventory cost increased from 5.69% to 32.10% with an overall average increase rate of 15.38%. As regards the overall cost of production, inventory and distribution, there was a reduction ranging from 3.65 to 16.73% with an overall rate of 11.07%. Such a finding highlights the effectiveness of MA in relation to TPDH.  
Beyond the contributions developed in this work, many avenues of research remain to be examined. MA using the local search method BI is the only one that provides a reduction (36.85%) in MA computation time compared to TPDH with an overall average time of 12.87 s. This implementation of the MA allowed to obtain two better results with a  
Figure 4: Behavior of the proposed MA for the EDPRP.  
decrease of 8.94% of the total global average cost compared to the TPDH. The use of MA with local search BI thus appears as a very good algorithm in the search for a good initial solution in the global scheme of a branch-and-cut algorithm.  
In the model studied in this paper, the supply chain consists of a factory and a depot. Studies of versions with several factories and/or depots will help to reflect certain realities in supply chain practice and management. Similarly, considering certain characteristics such as the use of heterogeneous vehicles, dynamic (stochastic) demands or delivery from the plant during production days would also make it possible to highlight other aspects of realities in supply chain management.  
A comparative study on the management of MA parameters could reveal other potentials of this algorithm. For example, this study would allow to compare the strategy of parameter tuning by the three methods of parameter control which are: deterministic parameter control, adaptive parameter control, and self-adaptive parameter control.  
Conceptualization, B.K.B.K. and M.D.; Data curation, B.K.B.K. and M.K.; Formal analysis, B.K.B.K., M.D. and M.K.; Investigation, B.K.B.K., M.D. and M.K.; Methodology, B.K.B.K.; Project administration, B.K.B.K. and S.O.; Resources, B.K.B.K., M.D. and M.K.; Software, B.K.B.K. and M.D.; Supervision, B.K.B.K. and S.O.; Validation, B.K.B.K., M.D., M.K. and S.O.; Visualization, B.K.B.K., M.D. and M.K.; Writing--original draft, B.K.B.K.; Writing--review and editing, M.D., M.K., and S.O. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding. The authors declare no conflict of interest.