Model Answer
0 min readIntroduction
Effective inventory management is a cornerstone of operational efficiency, directly impacting a company's profitability and customer satisfaction. The Economic Order Quantity (EOQ) model is a fundamental tool used in operations management to determine the optimal order quantity that minimizes the total inventory costs, which include ordering costs and holding costs. This model helps businesses strike a balance between frequent, small orders and infrequent, large orders, ensuring that capital is not unnecessarily tied up in inventory while also avoiding stockouts. Understanding and applying EOQ, along with its variations under real-world constraints like supplier batch sizes or storage limitations, is crucial for optimizing supply chain operations.
3. (a) Inventory Management Analysis
This problem requires us to calculate the Economic Order Quantity (EOQ) and analyze total costs under various ordering constraints. The key is to correctly identify and calculate the annual holding cost and then apply the appropriate formulas.
Given Data:
- Annual Demand (D) = 1600 units
- Unit Cost (C) = ₹70/-
- Ordering Cost per order (S) = ₹100/-
- Annual Holding Cost Components:
- Interest charges = 18% of unit cost
- Insurance = 1% of unit cost
- Allowances for obsolescence = 1.5% of unit cost
- Building overheads = ₹2.50 per unit
- Damage loss = ₹3.40 per unit
- Miscellaneous costs = ₹7.0 per unit
Calculation of Annual Holding Cost per Unit (H):
First, we need to calculate the annual holding cost per unit (H). This includes both a percentage of the unit cost and fixed costs per unit.
- Percentage-based holding costs:
- Total percentage = 18% (interest) + 1% (insurance) + 1.5% (obsolescence) = 20.5%
- Cost from percentage = 20.5% of ₹70 = 0.205 * 70 = ₹14.35
- Fixed holding costs per unit:
- Building overheads = ₹2.50
- Damage loss = ₹3.40
- Miscellaneous costs = ₹7.00
- Total fixed costs = ₹2.50 + ₹3.40 + ₹7.00 = ₹12.90
- Total Annual Holding Cost per Unit (H) = ₹14.35 + ₹12.90 = ₹27.25/-
(i) Calculate Economic Order Quantity (EOQ) and the total costs of stocking the units.
Economic Order Quantity (EOQ) Calculation:
The formula for EOQ is:
EOQ = √[(2 * D * S) / H]
Where:
- D = Annual Demand = 1600 units
- S = Ordering Cost per order = ₹100
- H = Annual Holding Cost per unit = ₹27.25
Substituting the values:
EOQ = √[(2 * 1600 * 100) / 27.25]
EOQ = √[320000 / 27.25]
EOQ = √[11743.119]
EOQ ≈ 108.36 units
Since we cannot order fractional units, we will round EOQ to 108 units for practical purposes. However, for cost calculation, we will use the precise value.
Total Costs of Stocking Units at EOQ:
Total Cost (TC) = (Annual Ordering Cost) + (Annual Holding Cost)
Annual Ordering Cost = (D / Q) * S
Annual Holding Cost = (Q / 2) * H
Where Q = EOQ = 108.36 units
- Annual Ordering Cost = (1600 / 108.36) * 100 = 14.7656 * 100 = ₹1476.56
- Annual Holding Cost = (108.36 / 2) * 27.25 = 54.18 * 27.25 = ₹1476.405
Total Cost at EOQ = ₹1476.56 + ₹1476.405 = ₹2952.965
Rounding to two decimal places, Total Cost at EOQ ≈ ₹2952.97
(ii) If the supplier of the items will only deliver batches of 250 units, how is the total variable cost influenced?
In this scenario, the company is forced to order in batches of 250 units, which is different from the calculated EOQ. We need to calculate the total variable cost (ordering cost + holding cost) for an order quantity (Q) of 250 units.
- Order Quantity (Q) = 250 units
- Annual Demand (D) = 1600 units
- Ordering Cost per order (S) = ₹100
- Annual Holding Cost per unit (H) = ₹27.25
Total Variable Cost (TVC) Calculation for Q = 250 units:
TVC = (Annual Ordering Cost) + (Annual Holding Cost)
- Annual Ordering Cost = (D / Q) * S = (1600 / 250) * 100 = 6.4 * 100 = ₹640
- Annual Holding Cost = (Q / 2) * H = (250 / 2) * 27.25 = 125 * 27.25 = ₹3406.25
Total Variable Cost for Q=250 = ₹640 + ₹3406.25 = ₹4046.25
Influence on Total Variable Cost:
Comparing the total variable cost at EOQ with the total variable cost when ordering 250 units:
- Total Variable Cost at EOQ ≈ ₹2952.97
- Total Variable Cost at Q=250 units = ₹4046.25
The total variable cost increases significantly from ₹2952.97 to ₹4046.25, representing an increase of ₹1093.28. This increase is primarily due to higher holding costs associated with larger inventory levels when ordering in batches of 250 units, which is far greater than the optimal EOQ of 108 units.
(iii) If the supplier relaxes their order size requirements, as the company has limited storage space it can stock a maximum of 100 units at any time. What would be the optimal ordering policy and associated costs ?
In this scenario, the company has a constraint on its maximum inventory level. The storage space limits the maximum stock to 100 units. This means the order quantity (Q) cannot exceed 100 units. We must consider how this constraint interacts with the EOQ.
- Calculated EOQ ≈ 108.36 units
- Maximum Storage Capacity = 100 units
Since the calculated EOQ (108.36 units) is greater than the maximum storage capacity (100 units), the company cannot implement the EOQ policy. The optimal ordering policy under this constraint would be to order the maximum quantity that can be stocked, which is 100 units.
Optimal Ordering Policy:
The company should order 100 units per order.
Associated Costs for Q = 100 units:
- Order Quantity (Q) = 100 units
- Annual Demand (D) = 1600 units
- Ordering Cost per order (S) = ₹100
- Annual Holding Cost per unit (H) = ₹27.25
Total Variable Cost (TVC) = (Annual Ordering Cost) + (Annual Holding Cost)
- Annual Ordering Cost = (D / Q) * S = (1600 / 100) * 100 = 16 * 100 = ₹1600
- Annual Holding Cost = (Q / 2) * H = (100 / 2) * 27.25 = 50 * 27.25 = ₹1362.50
Total Variable Cost for Q=100 = ₹1600 + ₹1362.50 = ₹2962.50
Comparison with EOQ:
- Total Cost at EOQ (108.36 units) ≈ ₹2952.97
- Total Cost at Q=100 units = ₹2962.50
While ordering 100 units (due to storage constraints) results in a slightly higher total variable cost compared to the unconstrained EOQ (₹2962.50 vs. ₹2952.97), it is the optimal policy under the given storage limitation. The increase in cost is marginal (₹9.53), demonstrating that 100 units is close to the optimal unconstrained quantity.
Conclusion
The analysis demonstrates the practical application of the Economic Order Quantity (EOQ) model and its adaptability to real-world operational constraints. Initially, the EOQ was calculated to minimize total inventory costs, offering the most cost-effective ordering strategy. However, the influence of external factors, such as supplier limitations on batch sizes or internal constraints like storage capacity, necessitates deviations from the theoretical EOQ. These deviations, while sometimes unavoidable, lead to an increase in total inventory costs. Therefore, companies must continuously evaluate their inventory policies, considering both theoretical optimality and practical feasibility to achieve efficient supply chain management and maintain competitive advantage.
Answer Length
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