Calculate Quantities And Annual Costs

Calculate Quantities And Annual Costs To

For this assignment, you will calculate quantities and annual costs to answer two supply chain questions. When you are finished, submit your answers for review by your instructor.

1. A distribution center sells Sony televisions to retailers at a constant demand rate of 20,000 units per year. It costs the distribution center $500 to place an order. The price the distribution center pays the manufacturer for each unit is $350. The inventory holding cost is $30 per unit per year. The material cost is $250 per unit. Assume the lead time from the manufacturer to the distribution center is zero years, and that the initial inventory at the distribution center is zero units. Calculate the economic order quantity and the total annual cost.

2. Calculate the total annual cost change if the order quantity had to be decreased to 250 units per order.

Paper For Above instruction

The efficient management of inventory is crucial for supply chain effectiveness, particularly in retail operations. In this context, determining the optimal order quantity and understanding the implications of changing this quantity are vital for minimizing costs and ensuring product availability. This paper addresses two primary questions: calculating the economic order quantity (EOQ) for Sony televisions and assessing the change in total annual costs when the order quantity decreases to 250 units per order.

Calculating the Economic Order Quantity (EOQ)

The EOQ model is a fundamental tool used to identify the most cost-effective order quantity that minimizes total inventory costs, which comprise ordering costs, holding costs, and sometimes material costs. The classical EOQ formula is expressed as:

EOQ = √(2DS / H)

Where:

• D = Demand rate (units per year) = 20,000 units
• S = Ordering cost per order = $500
• H = Holding cost per unit per year = $30

Substituting the known values into the formula:

EOQ = √(2  20,000  500 / 30) = √(20,000,000 / 30) = √666,666.67 ≈ 816.50 units

Thus, the EOQ is approximately 817 units per order, indicating that ordering this quantity each time balances the ordering and holding costs effectively, minimizing total inventory costs.

Total Annual Cost Calculation

The total annual cost (TAC) in an EOQ system incorporates three components:

1. Ordering costs: The total number of orders per year is D/EOQ = 20,000 / 817 ≈ 24.5 orders.

   Total ordering cost = number of orders ordering cost = 24.5 $500 = $12,250.

2. Holding costs: The average inventory level is EOQ / 2 ≈ 817 / 2 = 408.5 units.

   Total holding cost = average inventory holding cost per unit = 408.5 $30 ≈ $12,255.

3. Material costs: The total units purchased per year = demand unit cost = 20,000 $250 = $5,000,000.

   (Note: Material cost is typically considered variable, but the total material cost for purchased units remains constant regardless of order quantity in this analysis.)

Summing the costs (excluding the material costs since they are fixed in procurement decisions):

Total Cost (excluding material) = Ordering costs + Holding costs = $12,250 + $12,255 ≈ $24,505.

Including material costs, total annual procurement expenditure is:

Material costs = 20,000 units * $250 = $5,000,000.

Therefore, total annual costs encompassing procurement, ordering, and holding are approximately $5,024,505, with the majority stemming from material costs.

Assessing Cost Change When Order Quantity Decreases to 250 Units

If the order quantity is decreased to 250 units per order, the impact on total annual costs needs evaluation.

First, recalculate the number of orders per year:

Number of orders = D / new order size = 20,000 / 250 = 80 orders.

Then, compute the new total ordering cost:

Ordering cost = 80 * $500 = $40,000.

The average inventory now is 250 / 2 = 125 units, leading to new holding costs:

Holding cost = 125 * $30 = $3,750.

The material costs remain unaffected at $5,000,000 for the year's procurement.

Hence, the total annual cost with reduced order size becomes:

Total cost = procurement + ordering + holding = $5,000,000 + $40,000 + $3,750 = $5,043,750.

Comparing this with the original total costs, the increase in annual costs due to the smaller order size is:

$5,043,750 - $5,024,505 = $19,245.

This analysis illustrates that decreasing order size significantly boosts ordering costs despite reducing holding costs, leading to an overall increase in total costs. Such trade-offs are critical in supply chain decision-making, emphasizing the importance of strategic choice of order quantities to balance cost efficiency and inventory levels.

Conclusion

The EOQ for Sony televisions at this distribution center is approximately 817 units, optimizing supply chain costs by balancing ordering and holding expenses. When the order quantity decreases to 250 units, total costs increase primarily due to elevated ordering frequency, reaffirming the importance of identifying optimal order quantities via EOQ calculation. This detailed analysis underscores the importance of analytics in inventory management and cost reduction strategies, which are vital for maintaining competitive advantage in retail supply chains.

References

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