University of Tehran Press Advances in Industrial Engineering 2783-1744 60 1 2026 06 01 Integrated Multi-Agent Problem of Vehicle Routing and Cross-Dock Scheduling Considering Group Purchasing Strategies, Perishability of the Commodities and Requirements of the Customers 1 29 103583 10.22059/aie.2025.395242.1946 EN Hadi Sarmadi Ph.D. Candidate, Department of Industrial Engineering, Kish International Campus, University of Tehran, Tehran, Iran. 0009-0000-9754-2559 Mohammad Mahdi Nasiri Professor, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran. 0000-0001-9813-1233 Journal Article 2025 05 13 During the recent years, the companies in a wide range of industries have to design their activities in such a way to reduce the costs. A most popular way to reduce the costs in logistics is cross-docking. It is a strategy which is used to serve different purposes including the fast consolidation of received volume of commodities from suppliers, improving the responsiveness by shortening delivery lead time, reducing the inventory holding costs, eliminating spoilage costs of commodities, reducing transportation costs by employing full truck loading policy etc. The objective of this paper is to develop a mixed integer linear programming (MILP) model considering supplier selection and order allocation, perishability of commodities, group purchasing strategy and multi-agent scheduling into the well-known vehicle routing problem with cross-docking. Some small-sized test instances are applied to validate the new proposed model. A weighted-sum method is applied to solve small-sized instances. Then sensitivity analysis of the new proposed model is performed on the key parameters of the objective functions so that the supply decisions are evaluated while the parameters of the distribution costs are changed. Due to NP-hardness of the new proposed problem, two meta-heuristic algorithms including NSGA-II and MOPSO are applied to solve a wide range of instances. The obtained results by applying statistical hypothesis tests are compared through six different criteria. Also, an ordering technique that is called Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is applied to rank the meta-heuristic approaches. https://aie.ut.ac.ir/article_103583_4e9134f3c0bb3bff3ead88d4faa73b83.pdf