A Comparative Analysis of Inventory Models: Evaluating the Economic Order Quantity (EOQ) Model with Constant Demand versus Variable Demand Rates

Animesh Kumar Sharma*

Department of Mathematics, Faculty of Science and Technology, The ICFAI University Raipur

Abstract: Inventory control management remains a cornerstone of operational efficiency in modern supply chain systems. This study explores the Economic Order Quantity (EOQ) model, a foundational inventory control technique, by comparing its application under two distinct demand scenarios: constant and variable demand rates. This research highlights how demand variability influences optimal order quantities, total inventory costs, and decision-making processes through a detailed theoretical framework, mathematical analysis, and practical implications. From recent literature in operations research and supply chain management, the article provides insights into the adaptability of the EOQ model across diverse demand conditions, offering a comprehensive guide for practitioners and researchers alike.

Keywords: Inventory Management, Economic Order Quantity (EOQ), Constant Demand, Variable Demand, Supply Chain Optimization.

Efficient inventory management is vital for organizations that balance customer satisfaction with cost minimization. Among the numerous inventory models, the Economic Order Quantity (EOQ) model, introduced by Harris (1913), stands out as a widely adopted framework due to its simplicity and effectiveness under specific conditions. The classic EOQ model assumes a constant demand rate, negligible lead time, and no stockouts, providing a baseline for determining the optimal order quantity that minimizes total inventory costs (Choi, 2014). However, real-world scenarios often deviate from these assumptions, with demand exhibiting variability due to seasonality, market trends, or unforeseen disruptions (Taleizadeh et al., 2017).

This research study compares the EOQ model under two demand paradigms: constant demand and variable demand rates. The objective is to assess how these demand patterns affect inventory policies, cost structures, and operational efficiency. By synthesizing findings from recent studies in reputed international journals, this paper contributes to the ongoing discourse on inventory optimization and provides actionable insights for supply chain managers.

2. Literature Review

The EOQ model has been the subject of extensive research since its inception. Chopra and Meindl (2016) describe it as a deterministic model that balances ordering and holding costs to derive an optimal order size. Early studies, such as those by Silver et al. (1998), emphasized its applicability in stable environments with predictable demand. However, the assumption of constant demand has been increasingly challenged as markets become more dynamic (Glock et al., 2019).

Recent literature has explored extensions of the EOQ model to accommodate demand variability. For instance, Sana (2011) developed an EOQ model with time-varying demand, demonstrating its relevance in retail settings with seasonal fluctuations. Similarly, Taleizadeh et al. (2017) proposed an EOQ framework with stochastic demand, incorporating back-ordering costs to address shortages. These studies underscore the need for adaptive inventory models that reflect real-world complexities.

Comparative analyses of EOQ variants have also gained traction. Lau and Lau (2003) compared deterministic and probabilistic demand models, noting that variable demand increases total costs due to uncertainty. More recently, Giri and Sharma (2014) analyzed EOQ models under deteriorating items with fluctuating demand, highlighting the interplay between perishability and order frequency. These findings provide a foundation for this study’s exploration of constant versus variable demand scenarios.

3. Theoretical Framework

3.1 EOQ Model with Constant Demand

The classical EOQ model assumes a constant demand rate (D), fixed ordering cost per order (S), and holding cost per unit per time (H). The total cost (TC) comprises ordering costs and holding costs, expressed as:

Where Q is the order quantity. The optimal order quantity Q* that minimizes TC is derived by taking the derivative of TC with respect to Q, setting it to zero, and solving:

This formula assumes instantaneous replenishment and no shortages (Heizer et al., 2017). The model’s simplicity makes it ideal for industries with stable demand, such as manufacturing raw materials (Choi, 2014).

3.2 EOQ Model with Variable Demand Rates

In contrast, variable demand introduces complexity into the EOQ framework. Demand may vary over time due to seasonality, promotions, or economic factors, necessitating adjustments to the basic model (Sarkar et al., 2015). One approach is to model demand as a function of time, D(t), rather than a constant. For instance, Sana (2011) proposed a linear demand function, D(t) = a - bt , where a is the initial demand and b reflects the rate of decline.

The total cost function under variable demand becomes more intricate, often requiring numerical methods or approximations. A simplified version assumes demand varies cyclically within a planning horizon (T), with average demand  used to approximate:

However, this approximation overlooks peak demand periods, potentially leading to stockouts or overstocking (Glock et al., 2019). Advanced models incorporate stochastic elements or time-dependent parameters to enhance accuracy (Taleizadeh et al., 2017).

4. Methods and Methodology

This study adopts a theoretical and comparative approach, analyzing the EOQ model under constant and variable demand scenarios. Mathematical derivations are supported by numerical examples to illustrate cost differences. Data and assumptions are drawn from existing literature, ensuring consistency with established research. Fifteen peer-reviewed articles from international journals, published between 1998 and 2023, form the basis of the analysis, adhering to APA citation standards.

5. Comparative Analysis

5.1 Assumptions and Parameters

For the constant demand EOQ model, we assume:

Annual demand (D) = 10,000 units

Ordering cost (S) = $50 per order

Holding cost (H) = $2 per unit per year

For the variable demand model, demand fluctuates between 8,000 and 12,000 units annually, with an average of 10,000 units. Other parameters remain identical.

5.2 EOQ with Constant Demand

Using the classic EOQ formula:

Total cost:

Number of orders per year = .

5.3 EOQ with Variable Demand

Assuming average demand ():

However, during peak demand (12,000 units), the order quantity may be insufficient, leading to potential stock outs. Adjusting for peak demand:

Total cost (peak demand):

During low demand (8,000 units):

5.4 Results and Discussion

The constant demand model yields a stable Q* of 707 units and a total cost of $1,414.21 annually. In contrast, the variable demand model shows a range of Q* (632–775 units) and costs ($1,264.91–$1,549.19), reflecting sensitivity to demand fluctuations. The wider cost range suggests higher risk of overstocking or stockouts, aligning with findings by Lau and Lau (2003).

The comparative analysis reveals distinct outcomes between the EOQ model under constant demand and its variable demand counterpart. The constant demand scenario yields a stable optimal order quantity (Q*) of 707 units, with a total annual cost of $1,414.21. This consistency stems from the model’s assumption of a uniform demand rate (10,000 units/year), making it predictable and straightforward for planning purposes (Silver et al., 1998). In contrast, the variable demand model exhibits a range of Q* values (632–775 units) and total costs ($1,264.91–$1,549.19), reflecting its sensitivity to demand fluctuations. This variability introduces risks such as stockouts during peak demand or overstocking during low demand periods, corroborating findings by Lau and Lau (2003) that uncertainty amplifies inventory costs.

To further elucidate the mathematical implications of variable demand, Table 1 below summarizes the calculations from Section 5.3. The table contrasts the optimal order quantities and total costs under average, peak, and low demand scenarios, providing a clear visual representation of how demand variability alters inventory outcomes.

Table 1: Summary of EOQ Calculations under Variable Demand Scenarios

Note:  ​

The graph visually confirms that as demand increases from Low to Peak, both Q*and TC rise. The Peak Demand scenario shows the tallest bars for both metrics, while Low Demand shows the shortest. The relative heights of the bars within each group highlight the proportional relationship between order quantity and cost, with TC consistently about twice the Q* value due to the EOQ cost structure ().

6. Practical Implications

The constant demand EOQ model suits industries with predictable consumption, such as utilities or staple goods (Silver et al., 1998). However, variable demand models are more applicable to retail or fashion sectors, where demand shifts rapidly (Sana, 2011). Managers must weigh the trade-offs between simplicity and adaptability, potentially integrating forecasting tools to refine variable demand estimates (Glock et al., 2019).

7. Conclusion

This study demonstrates that while the EOQ model with constant demand offers a cost-effective and straightforward solution, its variable demand counterpart provides flexibility at the expense of increased complexity and cost variability. Future research could explore hybrid models combining deterministic and stochastic elements to bridge these paradigms, enhancing inventory management in dynamic environments.

References

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