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Salehi Sarbijan M. Modeling Multi-Product Inventory Routing and Production with Outsourcing Orders and Solving It with The Hybrid Metaheuristic Algorithm PSO-VNS. jor 2026; 23 (1)
URL: http://jamlu.lahijan.iau.ir/article-1-2334-en.html
Modeling Multi-Product Inventory Routing and Production with Outsourcing Orders and Solving It with The Hybrid Metaheuristic Algorithm PSO-VNS
M. Salehi Sarbijan *
Department of Mechanical Engineering, Faculty of Engineering, University of Zabol, Zabol, Iran , m.salehisarbijan@uoz.ac.ir
Abstract:   (74 Views)
This research addresses an integrated problem consisting of production routing, vehicle routing, and stack size determination under a vendor-managed inventory system, and examines production and inventory decisions in an integrated manner. In this study, the production routing problem considering outsourcing is modeled with the aim of minimizing production, holding, and outsourcing costs. Based on the proposed mixed-integer linear programming (MILP) model, a hybrid algorithm combining particle swarm optimization and variable neighborhood search (PSO-VNS) is proposed, and its performance is compared with the PSO optimization algorithm and the exact solution method on problem instances of small, medium, and large sizes. The results indicate that all three methods perform satisfactorily in solving small instances, in terms of the average value of the objective function and execution time. However, in medium- and large-sized instances, the hybrid PSO-VNS algorithm shows significantly better performance compared to the standard PSO algorithm in terms of simultaneously reducing runtime and the value of the objective function.
 
Keywords: Multi-Item Production Routing Problem, Outsourcing, Particle Swarm Optimization Algorithm - Variable Neighborhood Search (PSO-VNS).
     
Type of Study: Research | Subject: Special
Received: 2025/05/7 | Accepted: 2025/11/11
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