Company Aan Electronic Retail Chain Wishes To Minimize Costs
Company Aan Electronic Retail Chain Wishes To Minimize Costs For A Pa
Company Aan Electronic Retail Chain wishes to minimize costs for a particularly popular model of laptop computer. This retail chain has a line of credit to finance its inventory and the current holding rate is 5%. The chain estimates it can sell $70,000 units per year and it pays $400 dollars per unit. It costs $34 dollars to place each order. How many units should it order each time?
Company B: A Manufacturer of laptop computers operates a plant with an annual capacity of 15,470,000 laptop units. One of its models is expected to sell 910,000 units in the coming year. How large should each product lot be if it costs $400 to change production for one model to another? Assume that the manufacturer values each laptop unit at $200 dollars and it has a holding rate of 6%. You should round your answer to the nearest laptop unit.
Paper For Above instruction
The task involves determining the optimal order quantity for two distinct entities—one being an electronic retail chain and the other a manufacturing plant—by applying inventory management principles. The classical approach to tackle such problems is the Economic Order Quantity (EOQ) model, which aims to minimize the total inventory costs, including ordering and holding costs.
Part 1: Retail Chain's Optimization
The retail chain's scenario posits a demand (D) of 70,000 units annually, an ordering cost (S) of $34 per order, and a holding or carrying cost (H) derived from a unit cost value and a holding rate. Each unit costs $400, and the holding rate (i.e., the proportion of the unit cost held per year) is 5%. Therefore, the annual holding cost per unit (H) can be calculated as:
H = unit cost × holding rate = $400 × 0.05 = $20 per unit per year.
The EOQ formula for order quantity (Q) is:
Q = √(2DS / H)
Substituting the known values:
Q = √(2 × 70,000 × 34 / 20)
Calculating step-by-step:
- Numerator: 2 × 70,000 × 34 = 4,760,000
- Divide by H: 4,760,000 / 20 = 238,000
- Square root: √238,000 ≈ 487.96
Since the answer must be rounded up to the nearest unit:
Q ≈ 488 units.
Thus, the retail chain should order approximately 488 laptops each time to minimize the total inventory costs.
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Part 2: Manufacturer's Lot Size Calculation
The manufacturer has an annual capacity of 15,470,000 units and expects to sell 910,000 units next year. The setup or changeover cost (S) for switching production between models is $400 per changeover. Additionally, the manufacturer values each unit at $200, and the holding rate (i) is 6%. The first step is to determine the holding cost per unit (H):
H = unit value × holding rate = $200 × 0.06 = $12 per unit per year.
The EOQ model applies here as well:
Q = √(2DS / H),
where D is 910,000 units, S is 400, and H is 12.
Calculating:
Q = √(2 × 910,000 × 400 / 12)
Step-by-step:
- Numerator: 2 × 910,000 × 400 = 728,000,000
- Divide by H: 728,000,000 / 12 ≈ 60,666,666.67
- Square root: √60,666,666.67 ≈ 7,791.34
Rounding to the nearest unit:
Q ≈ 7,792 units.
In conclusion, the manufacturer should produce approximately 7,792 units per lot to optimize production costs and inventory holding costs.
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Implications and Strategic Considerations
Applying EOQ models helps both retail and manufacturing firms to streamline their inventory management, reduce costs, and improve operational efficiency. For the retail chain, purchasing approximately 488 units per order balances ordering costs and holding costs, thus preventing excess inventory and stockouts. For the manufacturer, batch sizes of around 7,792 units optimize changeover and holding costs, allowing efficient use of plant capacity while minimizing costs associated with production adjustments.
It is noteworthy that while the EOQ provides an effective baseline, real-world factors such as fluctuating demand, supplier reliability, and capacity constraints might necessitate adjustments. Nonetheless, these calculations illustrate a systematic approach for inventory management optimization grounded in financial and operational considerations.
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