A company requires 5,000 units of a product in a single year. It costs them $100 per order for expenses such as transportation and communication. If the product is carried in inventory, the carrying cost equals 1% of the price of the product for every month that a single unit of the product is held in inventory. This cost is realized primarily from the costs associated with rental and utility costs for the warehouse that stores the inventory. The product costs $200 per unit, and the company works for a total of 300 days in the year. The company currently orders 500 units in each order for a total of 10 orders in the year, but they feel that this order level is not the most economical. They feel that the total inventory costs (the sum of the ordering and the inventory-carrying costs) can be reduced further if they change the order quantity. They also use the continuous inventory system for the product; they want to evaluate whether this is the right system for the product.
Analyze whether the company can further reduce the total inventory costs. If so, what would you recommend the new order quantity to be, and what would be the annual savings in the total inventory costs with the new order quantity? Then evaluate whether the continuous inventory system is the correct inventory management system for this product.
To analyze whether the company can further reduce total inventory costs, we need to consider the ordering costs and inventory-carrying costs for the current order quantity of 500 units per order.
1. Ordering Costs:
The company currently places 10 orders in a year, with each order costing $100. Therefore, the total ordering cost is $100 * 10 = $1000.
2. Inventory-Carrying Costs:
The carrying cost is 1% of the price of the product for every month that a single unit is held in inventory. Since the company works for a total of 300 days in a year, the average inventory holding period can be calculated as 300/2 = 150 days.
The carrying cost per unit per month is 0.01 * $200 = $2.
The carrying cost per unit per year is $2 * 12 = $24.
Therefore, the total carrying cost for 500 units is $24 * 500 = $12,000.
Now, let's calculate the Total Inventory Costs for the current order quantity:
Total Inventory Costs = Ordering Costs + Inventory-Carrying Costs
= $1000 + $12,000
= $13,000.
To find a new order quantity that minimizes total inventory costs, we can use the Economic Order Quantity (EOQ) formula:
EOQ = √((2 * D * S) / H)
Where:
D = Annual demand (5000 units)
S = Ordering cost per order ($1000)
H = Inventory-carrying cost per unit ($24)
EOQ = √((2 * 5000 * 1000) / 24)
≈ √(416667)
Therefore, the recommended new order quantity, rounded to the nearest whole number, would be approximately 646 units.
To calculate the annual savings in total inventory costs with the new order quantity, we need to compare the total inventory costs with the current order quantity to the total inventory costs with the new order quantity:
Total Inventory Costs with new order quantity = Ordering Costs + Inventory-Carrying Costs with new order quantity.
Ordering Costs with new order quantity = (Annual demand / New order quantity) * Ordering cost per order.
= (5000 / 646) * $100
= $773.34 (rounded to the nearest whole number)
Inventory-Carrying Costs with new order quantity = (New order quantity / 2) * H
= (646 / 2) * $24
= $7744.
Total Inventory Costs with new order quantity = $773 + $7744
= $8517.
Annual savings in total inventory costs = Total Inventory Costs with current order quantity - Total Inventory Costs with new order quantity
= $13,000 - $8517
= $4,483.
Therefore, the annual savings in total inventory costs with the new order quantity is approximately $4,483.
Now, let's evaluate whether the continuous inventory system is the correct inventory management system for this product. The continuous inventory system assumes that inventory is continuously monitored and reordered whenever the stock level reaches a predetermined reorder point.
Since the company already has a fixed order quantity and a predetermined reorder point for this product, the continuous inventory system may not be the most suitable. The fixed order quantity and predetermined reorder point suggest that the company is using the periodic inventory system, where orders are placed at fixed intervals regardless of the inventory level.
To further optimize inventory management, the company may consider implementing a Just-In-Time (JIT) inventory system or explore other inventory management techniques, depending on the specific needs and characteristics of the product.
To analyze whether the company can further reduce the total inventory costs and recommend a new order quantity, we need to calculate the total cost for the current order quantity first.
The current order quantity is 500 units per order, and there are a total of 10 orders in a year. So the total number of units ordered in a year is 500 * 10 = 5000 units, which matches the company's requirement.
Let's calculate the various costs for the current order quantity:
1. Ordering costs: The company incurs a cost of $100 per order. Since there are 10 orders in a year, the total ordering cost for the current order quantity is 10 * $100 = $1000.
2. Inventory carrying costs: The carrying cost for each unit of the product is 1% of its price for every month held in inventory. The product costs $200 per unit, so the carrying cost per unit per month is 1% of $200, which is $2. The carrying cost for a year is $2 * 12 = $24 per unit.
Now, we need to determine how many units are held in inventory on average. Assuming a continuous inventory system, we can use the Economic Order Quantity (EOQ) formula to find the optimal order quantity that minimizes the total inventory costs.
The EOQ formula is:
EOQ = sqrt((2 * D * S) / H),
where:
D = annual demand (total units required in a year)
S = ordering cost per order
H = carrying cost per unit per year
In this case, D = 5000 units, S = $100, and H = $24 per unit per year.
Calculating the EOQ:
EOQ = sqrt((2 * 5000 * 100) / 24) = sqrt(41666.67) = 204.08 (approximately)
Since the EOQ gives a decimal value, we need to round it to the nearest whole number. The new order quantity should be 204 units per order.
To calculate the annual savings in total inventory costs, we compare the costs for the current order quantity to the costs for the new order quantity.
For the current order quantity, the total cost is the sum of the ordering costs ($1000) and the carrying costs ($24 * 5000 units) = $1000 + $120,000 = $121,000.
For the new order quantity of 204 units per order, the number of orders in a year would be 5000 units / 204 units per order = 24.51 (approximately). Again, we round it to the nearest whole number, so there would be 25 orders.
The total cost for the new order quantity can be calculated as follows:
- Ordering costs: $100 * 25 orders = $2500
- Carrying costs: $24 * 5000 units = $120,000
Total cost for the new order quantity = $2500 + $120,000 = $122,500.
The annual savings in total inventory costs with the new order quantity would be $121,000 - $122,500 = -$1500 (approximately).
Based on this analysis, it appears that the new order quantity does not result in a reduction in total inventory costs. Therefore, the company should stick with the current order quantity of 500 units per order.
As for whether the continuous inventory system is the correct inventory management system for this product, since the current order quantity aligns with the annual demand and does not result in savings, it suggests that the continuous inventory system might not be the most suitable for this product. The company may consider evaluating alternative inventory management systems like a periodic review system or a Just-In-Time (JIT) system, which might be more effective in minimizing inventory costs.