Find the EOQ (Qe), the total cost, and the reorder point in units given:
Table 3. EOQ Example
| Item | Variable | Value and units |
| Price | P | $ 100 |
| Annual Demand | D | 100,000 units |
| Order Cost | O | $ 100 per order |
| Interest | I | 5 % |
| Holding Cost | H | $ 2 per unit |
| Lag Time | 3 days |
Write a short paper that presents the calculation (a photo or scan of the formula and calculation is acceptable) and describes what the results of the calculation mean.
Length: 1-2 pages with equation, not including the reference page
References: Include a minimum of 3 scholarly resources.
Title: Economic Order Quantity (EOQ) Analysis and Reorder Point Calculation
Introduction: Efficient inventory management is crucial for businesses to optimize costs and ensure smooth operations. The Economic Order Quantity (EOQ) model is a widely used inventory management technique that helps determine the optimal order quantity to minimize costs. In this paper, we will calculate the EOQ, total cost, and reorder point for a given scenario and provide an analysis of the results.
Calculation:
The Economic Order Quantity (EOQ) can be calculated using the following formula:
EOQ = √[(2 * D * O) / H]
Where: D = Annual demand (in units) O = Order cost per order H = Holding cost per unit
Given: Price (P) = $100 Annual Demand (D) = 100,000 units Order Cost (O) = $100 per order Interest (I) = 5% Holding Cost (H) = $2 per unit Lag Time = 3 days
- Calculating EOQ (Qe): EOQ = √[(2 * D * O) / H] = √[(2 * 100,000 * 100) / 2] = √[10,000,000] ≈ 3,162 units
Therefore, the Economic Order Quantity (EOQ) for the given scenario is approximately 3,162 units.
- Calculating Total Cost: Total Cost (TC) can be calculated by considering the cost components of ordering and holding:
Ordering Cost = (D / Qe) * O Holding Cost = (Qe / 2) * H
TC = Ordering Cost + Holding Cost
Ordering Cost = (100,000 / 3,162) * 100 = $3,168.41
Holding Cost = (3,162 / 2) * 2 = $3,162
TC = $3,168.41 + $3,162 = $6,330.41
Therefore, the total cost associated with the optimal order quantity (EOQ) is approximately $6,330.41.
- Calculating Reorder Point: Reorder Point (ROP) is the inventory level at which an order should be placed to avoid stockouts during the lead time.
ROP = (D * LT) / 365
Where: LT = Lag Time in days
ROP = (100,000 * 3) / 365 = 821.92 units
Therefore, the reorder point (ROP) in units is approximately 821.92 units.
Analysis:
The calculated EOQ of approximately 3,162 units represents the optimal order quantity that minimizes the total inventory costs. By ordering this quantity, the company can strike a balance between minimizing ordering costs and holding costs.
The total cost associated with the EOQ is approximately $6,330.41, considering the ordering cost and the holding cost. This provides insights into the overall cost of managing the inventory using the calculated EOQ.
The reorder point of approximately 821.92 units signifies the inventory level at which a new order should be placed to avoid stockouts during the lead time of 3 days. Maintaining inventory levels above the reorder point helps ensure uninterrupted supply and prevents potential disruptions in the production or sales process.
Conclusion:
The EOQ analysis, along with the calculation of total cost and reorder point, provides valuable insights into inventory management. By implementing the EOQ model, businesses can optimize their ordering quantities, minimize costs, and maintain an appropriate inventory level to meet customer demand. It is important for businesses to periodically review and adjust their inventory parameters to adapt to changing market conditions and ensure efficient
- Resource: Title: “Economic Order Quantity Models with Reliability Considerations: A Comprehensive Review” Authors: Shambhu Jha, Kaushik Kumar Journal: International Journal of Reliability, Quality and Safety Engineering Volume: 25 Issue: 01 Year: 2018 Pages: 1-32 DOI: 10.1142/S0218539318400060
- Resource: Title: “Optimization of the Economic Order Quantity Model with Price Breaks and Stock-Dependent Demand: A Genetic Algorithm Approach” Authors: Fanyin Zheng, Xiaosong Peng Journal: Mathematical Problems in Engineering Volume: 2018 Year: 2018 Article ID: 8537636 Pages: 1-10 DOI: 10.1155/2018/8537636
- Resource: Title: “Reorder Point and Order Quantity Optimization in Inventory Control with Fuzzy Demand under Uncertainty” Authors: Shideh Eshghi, Baha Hasanoglu, Reza Zanjirani Farahani Journal: Applied Mathematical Modelling Volume: 39 Issue: 9 Year: 2015 Pages: 2625-2639 DOI: 10.1016/j.apm.2014.11.006