Abstract
Goal: This paper aims to implement a periodic capacitated vehicle routing problem with simulated annealing algorithm using a real-life industrial distribution problem and to recommend it to industry practitioners. The authors aimed to achieve high-performance solutions by coding a manually solved industrial problem and thus solving a real-life vehicle routing problem using Julia language and simulated annealing algorithm.
 Design / Methodology / Approach: The vehicle routing problem (VRP) that is a widely studied combinatorial optimization and integer programming problem, aims to design optimal tours for a fleet of vehicles serving a given set of customers at different locations. The simulated annealing algorithm is used for periodic capacitated vehicle routing problem. Julia is a state-of-art scientific computation language. Therefore, a Julia programming language toolbox developed for logistic optimization is used.
 Results: The results are compared to savings algorithms from Matlab in terms of solution quality and time. It is seen that the simulated annealing algorithm with Julia gives better solution quality in reasonable simulation time compared to the constructive savings algorithm.
 Limitations of the investigation: The data of the company is obtained from 12 periods with a history of four years. About the capacitated vehicle routing problem, the homogenous fleet with 3000 meters/vehicle is used. Then, the simulated annealing design parameters are chosen rule-of-thumb. Therefore, better performance can be obtained by optimizing the simulated annealing parameters.
 Practical implications: In this study, a furniture roving parts manufacturing company that have 30 customers in Denizli, an industrial city in the west part of Turkey, is investigated. Before the scheduling implementation with Julia, the company has no effective and efficient planning as they have been using spreadsheet programs for vehicle scheduling solutions. In this study, the solutions with Julia are used in practice for the distribution with higher utilization rate and minimum number of vehicles. The simulated annealing and savings algorithms are compared in terms of solution time and performance. The savings algorithm has produced better solution time, the simulated annealing approach has minimum total distance objective value, minimum number of required vehicles, and maximum vehicle utilization rate for the whole model. Thus, this paper can contribute to small scale business management in the sense of presenting a digitalization solution for the vehicle scheduling solution. Also, Julia application of simulated annealing for vehicle scheduling is demonstrated that can help both academicians and practitioners in organizations, mainly in logistics and distribution problems.
 Originality / Value: The main contribution of this study is a new solution method to capacitated vehicle routing problems for a real-life industrial problem using the advantages of the high-level computing language Julia and a meta-heuristic algorithm, the simulated annealing method.
 Keywords: Capacitated vehicle routing problem, Simulated annealing algorithm, Julia programming language.
Highlights
Nowadays, once starting the rapidly spreading implementations of Industry 4.0 for the companies, the supply chain management 4.0 procedure is developed for which a bibliometric analysis reinforce the growing importance of the topic
As generated from Travelling Salesman Problem with set of constraints, vehicle routing problem (VRP) aims to obtain the minimization of delivery costs of vehicles to customers at different locations from a depot
In VRP solutions, vehicle capacity and/or route distance constraints are taken into consideration
Summary
Once starting the rapidly spreading implementations of Industry 4.0 for the companies, the supply chain management 4.0 procedure is developed for which a bibliometric analysis reinforce the growing importance of the topic. In the operational research area, VRP has numerous applications Both exact and heuristics based solution methods have been proposed to solve VRPs. In VRP solutions, vehicle capacity and/or route distance constraints are taken into consideration. Tavakkoli-Moghaddam et al (2007) developed a mixed integer linear model for CVRP, where a customer’s demands can be divided into more than one vehicle and searched a possible solution with simulated annealing. Tavakkoli-Moghaddam et al (2011) presented a novel mathematical model for a competitive VRPTW to optimize routes considering the minimum travel cost and maximum sale using simulated annealing (SA) algorithm By using both a small and a large dataset, it is shown that the SA algorithm can find useful solutions for VRPTW in a shorter time than exact methods.
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