Optimizing logistics processes is a key topic in industrial engineering. Increasing market competition and the need to reduce costs have driven companies to adopt scientific approaches to optimize distribution and transportation processes [1]. One of the fundamental challenges in this field is the optimal management of product distribution from manufacturers to consumers, with the objectives of reducing logistics costs and preventing inventory shortages at distribution centers [2], [3]. In real-world conditions, the optimal product distribution problem typically involves constraints such as factory and warehouse capacity, transportation fleet capacity, distribution center unloading and storage capacity, and the timely fulfillment of branch demand [4], [5].

A manufacturing company producing Fast-Moving Consumer Goods (FMCG) faces the challenge of optimizing product distribution and reducing logistics costs [6]. One of the key transportation performance indicators in this factory is the transportation cost per kilogram and the cost of transporting one carton of product, which varies depending on capacity, total freight cost, distance, and the type of transportation fleet [7]. The company aims to reduce overall supply chain costs. At the same time, the demand of each distribution branch must be fully satisfied [8]. Accordingly, a mathematical model has been designed that, by considering constraints such as factory warehouse capacity, distribution center storage capacity, and vehicle type, seeks to optimize product distribution and reduce transportation costs. The manufacturing plant produces goods daily and distributes them to branches according to demand.

Vendor-Managed Inventory (VMI) is an important coordination mechanism in Supply Chain Management (SCM), in which the supplier manages inventory according to agreed-upon quantities at specified retail locations [9]. The VMI system can reduce inventory levels and stockouts by using data retrieval systems [10]. Moreover, because the vendor manages inventory and demand under mutual agreements, both suppliers and distributors can maximize their benefits [11]. In this paper, logistics and distribution costs are reduced for a system comprising one manufacturer, five distribution warehouses, and four product types, while accounting for the problem's existing constraints. Due to internal company policies and confidentiality considerations, the names of products and distribution branches have not been disclosed in this study. The present study focuses on a two-echelon supply chain comprising a manufacturer and distribution branches and investigates the problem of distribution and logistics optimization. The primary objective of this research is to reduce logistics costs while ensuring the complete fulfillment of distribution centers’ demand. To this end, a mathematical model has been developed that not only determines the optimal quantity of products to be distributed but also identifies the most appropriate type of transportation fleet. The proposed model not only reduces transportation costs but also achieves optimal product distribution. The case study in this research focuses on the distribution of products from the factory warehouse to various branches of a distribution company. The results from this model can support effective decision-making in logistics and distribution and help optimize supply chain operations. This research can also be applied to other industries and organizations facing similar SCM challenges.

One of the most important challenges for companies and organizations is decision-making in production and inventory planning. To date, various models for production and inventory control systems have been developed and discussed to address these issues, using different approaches and scenarios. Among traditional supply chain models, a dominant approach holds that each tier of the supply chain (e.g., suppliers, manufacturers, distributors, or retailers) is solely responsible for its own inventory and production control activities [12].

As a result of these conditions, each tier has access only to information on the inventory levels or demand of its immediate upstream and downstream neighbors. In particular, the downstream tier plays a leading role in this type of SCM system. In contrast, the upstream tier merely receives production order quantities and must fulfill orders in response to downstream requests. The upstream member perceives market demand only indirectly through the downstream tier's ordering activities. In fact, the supplier bears no responsibility for decisions regarding the buyer’s order quantities or their consequences. Fig. 1 illustrates a schematic representation of a traditional supply chain [13].

This type of traditional relationship among the tiers of the supply chain led to various problems in traditional SCM. Consequently, many industries decided to share more information within the supply chain to improve overall supply chain performance [14].

VMI is an industrial approach in which the supplier manages the customer’s inventory. Today, VMI is widely used and has contributed significantly to improvements in supply chain performance [15].

VMI is one of the mechanisms that have recently been employed as integration and coordination systems in SCM. Under VMI, the downstream entity (distributors) no longer manages its own production and inventory control system and instead delegates this responsibility to the upstream entity (supplier). Moreover, by implementing the VMI policy, the downstream entity allows the upstream entity to access demand and inventory information and to receive market data directly. Unlike traditional SCM approaches, upstream and downstream entities operate as a single unit under a VMI contract. They follow an agreed-upon policy that holds the upstream entity responsible for receiving demand data directly from the market and managing production and inventory policies at both upstream and downstream levels [13]. Fig. 2 illustrates the supply chain structure under the VMI system.

Subsequently, research on and application of this approach expanded. Although VMI was initially popular in the food sector, its applications have extended to other industries such as steel, publishing, and petrochemicals [16]. Disney and Towill [17] demonstrated that sharing demand and inventory information within a supply chain minimizes total supply chain costs while meeting customer service levels.

VMI is a widely implemented approach in supply chains that coordinates replenishment decisions among multiple buyers to reduce inventory-related costs [18].

SCM generally aims to reduce costs, improve customer satisfaction, and achieve a competitive advantage for all chain members. When decisions are made independently, there is no guarantee that the network members as a whole will reach an optimal decision. In integrated buyer–vendor optimization models, decision-making is centralized, and different components are integrated and coordinated [19].

Today, supply chains and production systems must be responsive, agile, and flexible to adapt to market changes and requirements. Globalization and intense market competition impose additional challenges on such systems and increase their complexity. One of the main objectives of SCM is coordinating different levels and related planning decisions, such as procurement, manufacturing, inventory management, and distribution [20]. Furthermore, because mutual agreements on inventory levels guide vendor, fill rate, and transaction costs, both suppliers and customers can maximize their benefits [11].

VMI is an industrial approach to supply chain collaboration in which the manufacturer assumes responsibility for customers’ inventories and determines the timing and quantity of replenishment. Established in the late 1980s, VMI is now widely used and is considered one of the most successful approaches for enhancing supply chain integration [15]. VMI has been adopted by 84% of companies with revenues exceeding one billion dollars and by two-thirds of medium-sized companies [21]. This model, which emphasizes integration and coordination in SCM, involves VMI, where the supplier is responsible for monitoring and maintaining inventory levels at the customer’s location. The model can reduce inventory levels, minimize associated costs, and prevent supply chain stockouts. In the VMI framework, inventory and routing decisions are optimized. The supplier must ensure that no stockouts occur for the customer while simultaneously minimizing total inventory and routing costs [22].

Over the years, various forms of VMI have been proposed. A model presented by Yao et al. illustrates how implementing VMI between a single supplier and a single buyer in a single-product setting can reduce supply chain costs [23]. In recent years, many researchers have attempted to extend VMI to more realistic conditions. Tarhini et al. [24] developed a model for a single supplier and multiple buyers under a VMI policy. Hariga et al. [25] proposed a VMI-based model for a supply chain consisting of a single supplier and multiple retailers, subject to environmental constraints, in a single-product setting. However, previous studies have not examined the role of transportation mode selection in reducing FMCG costs while ensuring that no warehouse experiences stockouts.

This study addresses the optimization of distribution and logistics in a two-echelon supply chain consisting of one manufacturer, five distribution warehouses, and four product types. Products are transported from the manufacturer’s warehouse to distribution warehouses in different cities using two modes of transportation: single trucks and trailers. Transportation costs vary across cities, products, and transportation fleet types. The primary objective of this research is to prevent inventory shortages and ensure adequate product availability at all distribution warehouses, such that no warehouse experiences a stockout. At the same time, distribution activities are planned to reduce logistics costs by selecting appropriate transportation fleet types. The mathematical model developed in this study aims to provide an optimal distribution plan that accounts for differences in transportation costs per kilogram of product across cities, product types, and transportation fleets. In real-world conditions, the optimal product distribution problem is subject to various operational constraints. These constraints include unloading capacity at distribution branches, storage capacity at distribution warehouses, storage capacity at the manufacturing warehouse, transportation fleet capacity, and the satisfaction of branch demand. By minimizing total costs, the proposed mathematical model can provide an optimal decision-support solution for distribution and logistics planning. In practice, logistics systems must also account for heterogeneous transportation fleet capacities, varying fixed and variable transportation costs, and additional considerations such as penalty costs and delivery times [26]. In this research, a distribution model focused on reducing logistics costs is proposed

In this study, an optimization model for product distribution is developed to minimize distribution costs by optimizing decisions on shipping products to different distribution branches. This model is particularly suitable for companies in the FMCG industry that face daily distribution challenges and substantial logistics costs. In this research, the model determines the following key decisions:

I. Selection of the type of transportation fleet.

II. Determination of the quantity of products to be distributed to each branch.

The proposed model reduces transportation costs by considering the operational and distribution-related constraints. In this section, the model's main parameters are presented and described.

In this paper, we examined the impact of vehicle type on logistics costs in a VMI-based supply chain. The analyses indicate that selecting an appropriate transportation fleet can significantly reduce transportation costs, particularly logistics costs. According to the proposed model, optimal load distribution across branches not only reduces transportation costs but also improves the supply chain's overall efficiency. By adjusting distribution and optimizing the use of different vehicles' capacities, additional costs can be avoided. For example, choosing heavier, higher-capacity vehicles for longer distances typically reduces costs, while for shorter distances, lighter vehicles may be a better option. These choices are also optimized by considering the specific characteristics of each distribution branch. The model developed in this study was solved using LINGO. The problem is an integer programming type designed to achieve optimal distribution and cost reduction. The solution process took less than 1 minute, demonstrating the model and software's high efficiency in analyzing and finding the optimal solution. The results show that the proposed model is effective not only in reducing costs but also in delivering an efficient, practical solution. The findings of this study can help logistics and supply chain managers make better decisions about selecting the type of transportation fleet and distributing loads, thereby improving overall supply chain performance and reducing costs. Previous studies in this area have mostly focused on reducing logistics costs, but, in the context of fast-moving goods and transportation optimization, they have not addressed the problem as presented in this research. In this study, a real-world industrial problem has been modeled to analyze the specific conditions and complexities of a real supply chain. This approach ensures that the results obtained from the proposed model have greater practical applicability and can be implemented in real systems. The results of the model solution are presented in Table 1. In the proposed model, branch demand is assumed fixed, but the model can be extended to account for probabilistic demand. The model considers one factory, five distribution branches, and four product types; to extend this model, the number of factories, distribution branches, and product types can be increased.

Table 2 shows the number and type of fleet for different branches. For Branch 3, which has a significant difference in the ratio of trailer costs to single-truck costs and is the largest in terms of operational volume, five trailer fleets were used to meet demand for more products and achieve cost savings. Table 3 shows the number of shipping cartons for each product separately.

This study addresses the optimization of distribution and logistics in a two-level supply chain consisting of one manufacturer, five distribution warehouses, and four types of fast-moving consumer products. Products are transported from the factory to warehouses in different cities using two types of transportation fleets (single trucks and trailers), with transportation costs varying by city and fleet type. The model aims to prevent warehouse inventory shortages and reduce logistics costs by optimizing fleet selection. By accounting for constraints such as warehouse capacity, fleet capacity, and demand fulfillment, the model provides a practical approach to reducing costs and improving decision-making in distribution. In this research, a VMI-based transportation optimization model was designed and implemented to reduce logistics costs in the supply chain. The results indicate that selecting the right vehicles can significantly reduce costs and improve supply chain efficiency. In particular, the proposed model, based on per-kilogram transportation cost analysis and load distribution optimization across branches, reduces overall system costs. In the model, single trucks, which are more cost-effective for nearby cities, were used to fully meet the needs of all branches. For distant cities, trailer fleets, which are more economical than single trucks, were deployed, and the model correctly applied this allocation while considering distribution constraints. The use of LINGO software to solve the problem demonstrated that the proposed model not only finds optimal solutions quickly but also effectively reduces costs and is feasible for real-world implementation. These characteristics make the model a practical and operational tool for supply chain and logistics managers.