Optimizing Inventory Level by Using the VBEOQ Model

In today’s increasingly competitive marketplace, efficient inventory management is crucial for businesses seeking to maximize profits and enhance customer satisfaction. Effective inventory management is crucial for organizations, particularly in the pharmaceutical industry, where balancing supply and demand is essential for operational efficiency. Traditional Economic Order Quantity (EOQ) models have been widely used for optimizing inventory levels; however, they often fail to incorporate financial factors that influence business performance. This study aimed to determine the optimal inventory level for the pharmaceutical supply organization ‘XXX’ using the Value-Based Economic Order Quantity (VBEOQ) model. The ABC classification of 1236 pharmaceutical products at the ‘XXX’ pharmaceutical supply organization revealed six A-stock products: Vemlidy, Lianhua Qingwen, Lutasan, Tabex, Ibuprofen-Denk, and Ketotifen Sopharma. These products collectively represented 80% of the organization’s total revenue, highlighting their critical importance to the company’s financial performance. Using the Economic Order Quantity (EOQ) and Value-Based Economic Order Quantity (VBEOQ) models, we analyzed order lead times and quantities for two critical pharmaceutical products, Vemlidi and Lianhua Qingwen. Our comparative analysis revealed significant differences between traditional and value-based inventory optimization approaches. According to the results of the EOQ model, the order quantity for Vemlidy was 28,556 units, with an order lead time of two orders per year. For Lianhua Qingwen, the order quantity was 43,603 units, and the order lead time was three-four orders per year. However, according to the results of the VBEOQ model, the order quantity for Vemlidy ranged from 1600 to 2000 units, while for Lianhua Qingwen, the order quantity ranged from 2300 to 2800 units per order. The findings indicate that the VBEOQ model provides a more dynamic and financially efficient method for determining optimal order quantities while minimizing inventory-related costs. This study contributes to the ongoing discussion on improving pharmaceutical inventory management through value-based approaches.

Introduction

In today’s fast-paced business environment, effective working capital management is essential for organizational success. A key aspect of this is inventory optimization, which enhances competitive advantage by reducing costs and improving operational efficiency (Liet al., 2022). Since inventory often constitutes the largest portion of working capital, optimizing inventory levels can significantly lower financial costs and improve resource allocation (Tungalaget al., 2015). Poor inventory planning can lead to shortages or excess stock, causing business disruptions and increasing opportunity costs (Debalaet al., 2023; Silaenet al., 2024). Therefore, maintaining optimal inventory levels is critical for sustaining smooth business operations (Munkhzul & Munkhzaya, 2023). Advanced inventory optimization systems help organizations achieve this balance by enhancing operational efficiency, reducing distribution costs, improving customer service, monitoring product expiration dates, and aligning supply with demand (Mayet al., 2017).

In the healthcare sector, effective inventory management is particularly crucial. Proper pharmacy inventory management optimizes drug availability and procurement in public health systems (Fahriatiet al., 2021), enhancing economic efficiency and clinical value through appropriate drug selection, quantity control, and procurement processes.

This study examines the optimal inventory levels for company ‘XXXX’ by analyzing the principles and practical applications of the VBEOQ model.

Literature Review

Inventory Management

Inventory management is a comprehensive system within supply chain management that determines optimal product ordering quantities, timing, and stock levels. Effective inventory management significantly enhances company performance by ensuring product availability to meet customer demand (Asanaet al., 2020).

As a specialized field of business management, inventory management involves strategic planning and control mechanisms to maintain optimal product levels while balancing resource allocation (Mohamed, 2024). This balanced approach enables organizations to respond swiftly to demand fluctuations, minimize excess inventory costs, and improve operational efficiency, customer satisfaction, and financial performance.

The core challenge of inventory optimization lies in managing resources efficiently to meet demand while minimizing costs (Anderssonet al., 2015). Poor management can lead to two major risks: oversupply, which increases holding costs, and shortages, which result in unfulfilled customer needs (Pourhejazy, 2020). By implementing efficient, integrated inventory management systems, organizations can streamline operations, minimize waste, and reduce revenue losses from expired inventory (Kmiecik, 2022).

ABC Analysis

ABC analysis stands as a cornerstone of modern inventory management methodology. This systematic approach categorizes products based on their strategic importance and economic value, proving instrumental in optimizing operations and inventory management (Chinelloet al., 2020).

The methodology enhances inventory efficiency by identifying items with the greatest impact on total inventory costs (Fahriatiet al., 2021). Through careful evaluation of demand patterns, cost structures, and risk factors, inventory managers can strategically classify items to maximize operational effectiveness. This approach not only enhances profitability but also strengthens market performance by enabling businesses to identify their most financially crucial products and services.

Also known as Pareto analysis, ABC analysis subdivides inventory into three distinct categories:

• Category A: High-value, high-demand items comprising a small percentage of total inventory while generating the majority of revenue. These items demand rigorous monitoring and control protocols to prevent stockouts.

• Category B: Moderate-value and demand items requiring balanced management strategies to optimize cost efficiency while maintaining adequate availability.

• Category C: Low-value, low-demand items that typically constitute the bulk of inventory volume while contributing minimally to revenue.

Regular evaluation and refinement of ABC classifications enable businesses to maintain a competitive advantage and respond effectively to market dynamics (Omaret al., 2019). This ongoing process facilitates operational streamlining, supply chain optimization, targeted marketing strategies, and enhanced after-sales service delivery.

When combined with XYZ classification methodology, ABC analysis provides a comprehensive framework for identifying priority inventory segments and allocating management resources accordingly.

Economic Order Quantity (EOQ)

The Economic Order Quantity (EOQ) model is a fundamental tool for determining optimal inventory levels that maximize profitability. First introduced by Ford W. Harris in 1913 and later refined by R. H. Wilson and K. Andler, it has become a cornerstone of inventory management theory (Senthilnathan, 2019).

EOQ calculates the ideal order quantity that minimizes total inventory costs while ensuring a continuous supply (Tungalaget al., 2015). The model is based on the relationship between two key cost components:

• Ordering costs: Fixed expenses associated with placing and receiving inventory orders, including administrative processes, shipping, and handling.

• Holding costs: Variable expenses incurred in maintaining inventory over time, such as storage, insurance, depreciation, and opportunity costs.

By balancing these cost factors, the EOQ model determines the optimal order quantity, reducing overall inventory costs while ensuring operational efficiency (Sbaiet al., 2022). This data-driven approach helps organizations make informed decisions about order timing and quantity, optimizing inventory investment while maintaining service levels.

Value-Based Optimal Order Quantity (VBEOQ) Model

The Value-Based Optimal Order Quantity (VBEOQ) model represents an evolution in inventory management theory, addressing the limitations of traditional approaches while aligning with businesses’ primary objective of value maximization. This advanced methodology enhances inventory optimization through a dynamic and data-driven approach.

Unlike the traditional EOQ model, which assumes constant demand, VBEOQ incorporates:

• Dynamic Adjustment: Continuously modifies order quantities based on real-time market data and demand patterns.

• Variable Cost Integration: Accounts for fluctuating ordering and holding costs instead of assuming fixed costs.

• Cash Flow Optimization: Prevents capital lock-up in unnecessary inventory while ensuring adequate stock levels.

By adapting to real-world variability, the VBEOQ model enables organizations to:

• Respond effectively to demand fluctuations.

• Minimize stockouts and excess inventory.

• Reduce total inventory costs through more precise ordering.

• Optimize working capital utilization.

This approach represents a significant advancement over traditional inventory management models by integrating financial considerations and market dynamics into the decision-making process. Fig. 1 compares the EEQ and VBEQQ models.

Fig. 1. Research model (Kalberg & Parkinson, 1993, p. 538).

Inventory management involves complex trade-offs that directly impact business performance. While maintaining higher inventory levels increases carrying costs and the risk of obsolescence, it also offers strategic advantages, such as enhanced customer purchasing flexibility, reduced stockout risk, and protection against production disruptions.

The Value-Based Economic Order Quantity (VBEOQ) model helps managers navigate these competing factors. Despite challenges in determining optimal order and production quantities, VBEOQ provides a structured framework for value-driven inventory decisions (Michalski, 2008). This approach enables managers to balance financial constraints with operational needs while maximizing overall business value.

Materials and Methods

This analysis was conducted using inventory data from the pharmaceutical supply organization “XXX,” the subject of our study. The evaluation included calculations based on both traditional and extended models for two types of Category A resources identified through ABC analysis.

For the extended model, we applied Grzegorz Michalski’s Value-Based Economic Order Quantity (VBEOQ) model (Michalski, 2008) to determine the optimal order quantity based on the organization’s financial value. While the traditional model focuses on minimizing inventory costs, the VBEOQ model incorporates financial factors such as capital used for financing and tax rates. This approach assumes that inventory level fluctuations influence the organization’s overall value (Michalski, 2008).

Traditional model for calculating optimal inventory stock:

(1) $$\begin{array}{r}EOQ=\sqrt{\frac{2\times P\times K_z}{C\times v}}=\sqrt{\frac{2\times P\times K_z}{K_u}}\end{array}$$

(2) $$\begin{array}{r}TCI=\frac{P}{Q}\times K_z+(\frac{Q}{2}+Z_b)\times C\times v\end{array}$$

Extended model for calculating the optimal inventory level:

(3) $$\begin{array}{r}VBEOQ=\sqrt{\frac{2\times (1-T)\times K_z\times P}{v\times (k+C\times (1-T))}}\end{array}$$

Research Results

We conducted an ABC analysis on 1236 pharmaceutical products from the Pharmaceutical Supply Organization “XXX.” The results of the analysis are as follows: The results are presented in Fig. 2.

Fig. 2. Research model.

From the ABC analysis, A-resources include key pharmaceutical products such as Vemlidy, Lianhua Qingwen, Lutasan, Tabex, Ibuprofen-Denk, and Ketotifen Sopharma. These products contribute to 80% of the organization’s total revenue and should be considered critical for policy decisions that will influence the future growth or decline of the organization’s revenue.

Given their significance, factors such as inventory replenishment and withdrawal, price, agreement of purchase, and continuity of these resources are crucial indicators that can significantly impact the organization. Consequently, these resources require close monitoring and careful management.

Table I presents the results of calculating the optimal order quantity (EOQ) for the Vemlidy and Lianhua Qingwen pharmaceutical products from the list above. It also includes the total cost of inventory (TCI), total sales (54,362 units), and the impact of specific growth points on scenarios using traditional methods.

Table I. Order Options-Vemlidy (Eoq)

Required resources per year/unit/	54362.0	60000.0	65000.0	70000.0	75000.0
Order cost per unit/₮/	400000.0	400000.0	400000.0	400000.0	400000.0
Holding cost per unit/₮/	120.0	120.0	120.0	120.0	120.0
Economic Order Quantity (EOQ)/unit/	19037.2	20000.0	20816.7	21602.5	22360.7
Order quantity per year/times/	3.0	3.0	3.0	4.0	4.0
Time Between Orders (TBO)/day/	84.0	84.0	84.0	63.0	63.0
Required resources per year/unit/	54362.0	60000.0	65000.0	70000.0	75000.0
Order cost/₮/	1200000.0	1200000.0	1200000.0	1600000.0	1600000.0
Holding cost/₮/	1142229.4	1200000.0	1248999.6	1296148.1	1341640.8
Total cost TCI min/₮/	2342229.4	2400000.0	2448999.6	2896148.1	2941640.8

According to the 2023 sales data of the “XXX” pharmaceutical supply organization, the sales volume of Vemlidy was 54,362 units. The order volume was determined by increasing this amount by 10,000 units. With an ordering cost of 1,200,000₮ per order and a holding cost of 160₮ per unit, the optimal order volume is 28,556 units, resulting in a total inventory cost of 4,568,000₮.

The analysis suggests that orders should be placed twice a year, with the next order scheduled after 132 working days, on the 133rd day.

Similarly, Table II presents the calculated optimal order volume and total inventory cost for Lianhua Qingwen, which had a sales volume of 126,749 units.

Table II. Order Options-Lianhua Qingwen (EOQ)

Required resources per year/unit/	126749.0	150000.0	160000.0	170000.0	180000.0
Order cost per unit/₮/	400000.0	400000.0	400000.0	400000.0	400000.0
Holding cost per unit/₮/	120.0	120.0	120.0	120.0	120.0
Economic Order Quantity (EOQ)/unit/	29068.8	31622.8	32659.9	33665.0	34641.0
Order quantity per year/times/	3.0	3.0	3.0	4.0	4.0
Time Between Orders (TBO)/day/	84.0	84.0	84.0	63.0	63.0
Required resources per year/unit/	126749.0	150000.0	160000.0	170000.0	180000.0
Order cost/₮/	1200000.0	1200000.0	1200000.0	1600000.0	1600000.0
Holding cost/₮/	1744126.1	1897366.6	1959591.8	2019901.0	2078461.0
Total cost TCI min/₮/	2944126.1	3097366.6	3159591.8	3619901.0	3678461.0

According to the calculation results, to meet the demand for 120,000–160,000 tablets of Lianhua Qingwen, it is necessary to place orders three times a year, with a reorder point of 84 working days. However, if the inventory of Lianhua Qingwen is expected to increase to 170,000–180,000 tablets, the number of orders will rise to four times a year, with the reorder point adjusted to 63 working days.

Further analysis was conducted using an extended model called Value-Based Economic Order Quantity (VBEOQ) to evaluate the value of both stock types. This study examined how the optimal order quantity and total cost would differ from the traditional model. Additionally, financial indicators such as the tax rate, the amount of funds required to finance the organization, and the proportion of costs were considered in the analysis. The results are shown in Table III.

Table III. Order Options-Vemlidy (VBEOQ)

Required resources per year/P/	54362.0	60000.0	65000.0	70000.0	75000.0
Order cost per unit/Kz/	25000000.0	25000000.0	25000000.0	25000000.0	25000000.0
Purchase price per unit/v/	16000.0	16000.0	16000.0	16000.0	16000.0
Holding cost factor/C/	0.40	0.40	0.40	0.40	0.40
Tax rate/T/	0.100	0.100	0.100	0.100	0.100
Cost of capital financing the firm/K/	0.30	0.30	0.30	0.30	0.30
Value-Based Optimal Order Quantity (VBEOQ)/unit/	10045.4	10553.4	10984.4	11399.0	11799.1
Order quantity per year/times/	5.4	5.7	5.9	6.1	6.4
Time Between Orders (TBO)/day/	46.6	44.3	42.6	41.0	39.6
Order cost/₮/	135291181.2	142133810.9	147937560.8	153522062.2	158910431.5
Holding cost/₮/	80362961.6	84427483.7	87874911.1	91192104.9	94392796.3
Total cost TCI min/₮/	215654142.8	226561294.6	235812471.9	244714167.1	253303227.9

The optimal order quantity for the two resources, as calculated using the extended VBEOQ model, differed significantly from the traditional Economic Order Quantity (EOQ) model. Based on the value-based order quantity model, the optimal order quantity was estimated to be 1600–2000 units for Vemlidy and 2300–2800 units for Lianhua Qingwen, ensuring the lowest inventory cost. The results are shown in Table IV.

Table IV. Order Options-Lianhua Qingwen (VBEOQ)

Required resources per year/P/	126749.0	150000.0	160000.0	170000.0	180000.0
Order cost per unit/Kz/	25000000.0	25000000.0	25000000.0	25000000.0	25000000.0
Purchase price per unit/v/	21000.0	21000.0	21000.0	21000.0	21000.0
Holding cost factor/C/	0.40	0.40	0.40	0.40	0.40
Tax rate/T/	0.100	0.100	0.100	0.100	0.100
Cost of capital financing the firm/K/	0.30	0.30	0.30	0.30	0.30
Value-Based Optimal Order Quantity (VBEOQ)/unit/	13388.8	14565.1	15042.8	15505.8	15955.3
Order quantity per year/times/	9.5	10.3	10.6	11.0	11.3
Time Between Orders (TBO)/day/	26.6	24.5	23.7	23.0	22.3
Order cost/₮/	236670267.8	257464325.3	265908011.7	274091704.8	282038037.4
Holding cost/₮/	140582139.1	152933809.2	157949359.0	162810472.6	167530594.2
Total cost TCI min/₮/	377252406.9	410398134.5	423857370.7	436902177.4	449568631.6

When comparing these two models, it is crucial to maintain business continuity in the pharmaceutical supply industry, which relies on foreign markets. This can be achieved by making fewer but larger withdrawals of resources. However, the results obtained from the extended VBEOQ model suggest that, in this industry, the impact of resource decision-making on overall costs is relatively minor.

Discussion

Determining the appropriate inventory level enables organizations to allocate financial resources effectively, reducing unnecessary costs. To ensure the continuous availability of medicines within the healthcare system, pharmaceutical organizations must implement optimal inventory management. Since pharmaceutical budgets are limited, pharmacies must carefully select medicines and determine appropriate stock levels during the drug planning and procurement process.

A lack of necessary drug stock can result in patients being unable to access essential medicines, compromising continuous availability. Conversely, unplanned drug purchases can lead to unexpected costs in procurement (Bachrun, 2017). To mitigate these risks, pharmaceutical organizations can utilize ABC analysis and the Value-Based Economic Order Quantity (VBEOQ) model to determine the optimal stock levels and selection of medicines.

In 2023, our country imported pharmaceuticals worth a total of 528.2 billion tugriks ( https://mmra.gov.mn), highlighting the industry’s reliance on foreign markets. The research findings varied depending on the models and resources used in the analysis. The results and their practical applications are outlined below, considering the characteristics of the pharmaceutical market:

1. Traditional EOQ model results: Based on 2023 sales data, the optimal order quantity for each 10,000-unit increase in demand for Vemlidy and Lianhua Qingwen was calculated using the traditional Economic Order Quantity (EOQ) model. The results indicate:

• Vemlidy EOQ = 28,556 units

• Lianhua Qingwen EOQ = 43,603 units

Under this model, it is appropriate to order Vemlidy twice a year and Lianhua Qingwen three to four times. In an industry heavily reliant on foreign markets and imports due to an underdeveloped domestic pharmaceutical sector, placing larger but less frequent orders can improve operational efficiency. Therefore, the traditional EOQ model is relatively suitable for our country’s pharmaceutical supply organizations.

2. Extended VBEOQ model results: When calculating the optimal order quantity using the extended VBEOQ model, the results significantly differed from those of the traditional EOQ model. According to the value-based approach, the optimal order quantities were estimated as follows:

• Vemlidy VBEOQ = 1600–2000 units

• Lianhua Qingwen VBEOQ = 2300–2800 units

Organizations that adopt circular economy principles and lean manufacturing systems, particularly those sourcing key resources (Type A) from domestic pharmaceutical manufacturers, may benefit from the VBEOQ model. This approach helps enhance efficiency by reducing warehousing costs, pharmaceutical waste, and financial losses associated with premium pricing.

Conclusion

Inventory optimization plays a critical role in ensuring the efficiency and sustainability of pharmaceutical supply chains. This study compared the EOQ and VBEOQ models to determine their effectiveness in managing pharmaceutical inventory. While the EOQ model provides a structured approach to minimizing inventory costs based on fixed parameters, the VBEOQ model offers a more adaptive framework that integrates financial constraints and dynamic cost factors.

The results indicate that the VBEOQ model is particularly beneficial for organizations operating in industries heavily dependent on foreign markets, such as pharmaceuticals. By optimizing order quantities based on financial considerations, the VBEOQ model can help reduce excess inventory, improve capital allocation, and minimize financial risks. However, for organizations with stable demand and predictable procurement cycles, the traditional EOQ model remains a viable option.

Ultimately, implementing an inventory management strategy that aligns with financial and operational objectives is essential for pharmaceutical organizations. Future research should explore further enhancements to the VBEOQ model by incorporating real-time market fluctuations and supply chain disruptions.

Limitations and Future Research

This study focuses on two Type A products from a single pharmaceutical supply organization. It is based on sales data for 2023, which may not necessarily predict future trends. Additionally, several limitations must be considered, including the use of a VBEOQ model based on specific financial indicators and the exclusion of external market fluctuations.

Future research would be more effective if it expanded the study to multiple organizations, developed more sophisticated predictive models, and created a more dynamic framework for inventory optimization.