Individual Project: Unit Operations Management Tools Method
Typeindividual Projectunitoperations Management Tools Methodsdue D
As the production manager, you need to minimize both ordering and inventory costs. You need to provide a recommendation of the optimal order quantity of raw materials to your plant manager. Your objective is to determine the economic order quantity (EOQ). If the annual demand for Ultamyacin at Smitheford is 400,000 units, then the annual carrying cost rate is 15% of the cost of the unit. The product costs $48/unit to purchase, and the product ordering cost is $28.00.
In your report, discuss information based on the following questions: What is the basic EOQ? What is the TC (total cost) at the EOQ? How much would the TC increase if the order quantity must be 1,000 units? How is JIT (just-in-time) ordering methodology different from EOQ methodology? Show all your calculations.
Paper For Above instruction
Introduction
Effective inventory management is crucial for manufacturing firms to minimize costs and enhance operational efficiency. Among various inventory control models, the Economic Order Quantity (EOQ) model is one of the most widely used tools for determining optimal order sizes that balance ordering costs and holding costs. This paper explores the calculation of EOQ for Smitheford Pharmaceuticals, evaluates the total costs at this optimal point, analyzes the impact of alternative order quantities, and compares EOQ with Just-in-Time (JIT) ordering methodology.
Calculating the Basic EOQ
The EOQ model provides the order quantity that minimizes the total inventory costs, which comprise ordering costs and carrying costs. The formula for EOQ is expressed as:
EOQ = √(2DS / H)
where:
- D = Annual demand = 400,000 units
- S = Ordering cost per order = $28
- H = Annual holding cost per unit = 15% of unit cost = 0.15 × $48 = $7.20
Applying these values:
EOQ = √(2 × 400,000 × 28 / 7.20) = √(22,400,000 / 7.20) ≈ √3,111,111.11 ≈ 1763 units
Therefore, the optimal order quantity, or EOQ, is approximately 1,763 units.
Total Cost at EOQ
The total cost (TC) comprises the sum of ordering costs and holding costs at the EOQ level. The formulas are:
- Order Cost = (D / EOQ) × S
- Holding Cost = (EOQ / 2) × H
Calculating each component:
Order Cost = (400,000 / 1,763) × 28 ≈ 226.99 × 28 ≈ $6,355.72
Holding Cost = (1,763 / 2) × 7.20 ≈ 881.5 × 7.20 ≈ $6,349.20
Total Cost (TC) = Order Cost + Holding Cost ≈ $6,355.72 + $6,349.20 ≈ $12,704.92
This total cost reflects the minimal combined expense associated with inventory ordering and holding when using EOQ.
Impact of a Fixed Order Quantity of 1,000 Units
If the order quantity is restricted to 1,000 units, then the total costs change because the ordering and holding costs no longer align with the EOQ. Calculating these costs:
- Order Cost = (400,000 / 1,000) × 28 = 400 × 28 = $11,200
- Holding Cost = (1,000 / 2) × 7.20 = 500 × 7.20 = $3,600
Therefore, total cost at this order quantity is:
TC = $11,200 + $3,600 = $14,800
This indicates an increase of approximately $2,095.08 over the minimal total cost calculated at EOQ, demonstrating the cost impact of non-optimal ordering quantities.
Comparison of EOQ and JIT Methodologies
The EOQ model emphasizes calculating a specific optimal order size that balances ordering frequency and inventory holding costs. It is best suited for firms aiming to maintain a steady inventory level while minimizing cumulative costs. EOQ assumes predictable demand and lead times, and it typically results in larger, infrequent orders to optimize costs.
Conversely, Just-in-Time (JIT) methodology seeks to reduce inventory levels to nearly zero, receiving goods only as needed for production. JIT minimizes warehousing and holding costs significantly and responds quickly to demand changes. It requires robust supply chain coordination, reliable suppliers, and precise demand forecasting.
While EOQ is cost-efficient under stable demand conditions and predictable lead times, JIT favors lean inventory and responsiveness. The primary difference lies in EOQ's focus on minimizing combined costs over a fixed cycle and JIT's focus on eliminating inventory waste and creating a flexible, demand-driven production environment.
Conclusion
Determining the EOQ allows Smitheford Pharmaceuticals to optimize raw material orders, reducing costs and improving efficiency. The calculated EOQ of approximately 1,763 units offers a balance between ordering and holding costs, with a total cost near $12,705. Adjustments from this optimal order size significantly increase total expenses, highlighting the importance of precise demand forecasting and order management. Comparing EOQ with JIT underscores differing operational philosophies: while EOQ aims to balance costs over periodic ordering, JIT emphasizes inventory minimization and responsiveness. Both strategies have their merits and are applicable depending on operational goals, market conditions, and supply chain capabilities.
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