You manage inventory for your company and use a continuous review inventory system to control reordering items for stock. Your company is open for business 310 days per year. One of your most important items experiences demand of 24 units per day, normally distributed with a standard deviation of 5 units per day. You experience a lead time on orders from your supplier of 7 days with a standard deviation of 4 days. If you order 1,000 units or less, you pay the supplier $7 per unit. Orders of 1,000 or more can be bought at a unit price of $6.70. Your ordering cost is $10. Your inventory carrying cost is 22 percent. You have established a service level policy of 97.5 percent on this item.
What is the
Optimal order quantity units
Reorder point units
Safety stock units
Average inventory
Why did the inventory manager go to the comedy show? Because they needed to improve their "stock" of jokes!
Now let's calculate the answers to your questions:
1. Optimal order quantity: The optimal order quantity can be calculated using the Economic Order Quantity (EOQ) formula: EOQ = √(2DS/H), where D is the average demand per year, S is the ordering cost, and H is the holding cost per unit per year.
Plugging in the values:
D = 24 units per day * 310 days = 7,440 units per year
S = $10
H = 22% of the cost per unit = 0.22 x $7 = $1.54
Using the formula: EOQ = √(2 * 7,440 * 10 / 1.54) = √(144,800) = 380.17
So the optimal order quantity is 380 units.
2. Reorder point: The reorder point can be calculated by multiplying the lead time of 7 days by the average demand per day and adding the safety stock:
Reorder point = Lead time demand + Safety stock
Lead time demand = 24 units per day * 7 days = 168 units
Safety stock = Z * √(Lead time * variance in demand), where Z is the number of standard deviations required to achieve the desired service level (97.5% in this case).
Using the Z value for a 97.5% service level (Z = 2.24, obtained from a standard normal distribution table):
Safety stock = 2.24 * √(7 * 5^2) = 2.24 * √(7 * 25) = 2.24 * 5 * √7 = 15.76 * √7 ≈ 15.76 * 2.65 ≈ 41.71
Reorder point = 168 + 41.71 ≈ 210.71
So the reorder point is approximately 211 units.
3. Safety stock: The safety stock is the buffer stock maintained to account for uncertainties in demand and lead time.
Safety stock = Z * √(Lead time * variance in demand)
Using the same Z value and calculations as before:
Safety stock = 2.24 * √(7 * 5^2) = 41.71
So the safety stock is approximately 42 units.
4. Average inventory: The average inventory can be calculated using the formula:
Average inventory = Reorder point + (EOQ / 2)
Average inventory = 210.71 + (380 / 2) = 210.71 + 190 = 400.71
So the average inventory is approximately 401 units.
To determine the optimal order quantity, reorder point, safety stock, and average inventory, we can use the continuous review inventory system formula. Here's how you can calculate each of these:
1. Optimal Order Quantity:
The optimal order quantity can be calculated using the economic order quantity (EOQ) formula. The EOQ formula is:
EOQ = √((2DS) / H)
Where:
D = Annual demand (in this case, it is 24 units per day * 310 days)
S = Ordering cost ($10)
H = Carrying cost (22% of the unit cost)
Substituting the values into the formula:
D = 24 units/day * 310 days = 7,440 units per year.
H = 22% * $7 = $1.54 per unit
EOQ = √((2 * 7,440 * $10) / $1.54) ≈ 173 units
Therefore, the optimal order quantity is approximately 173 units.
2. Reorder Point:
The reorder point is calculated by multiplying the lead time demand by the number of days in lead time. The lead time demand is the average daily demand multiplied by the lead time.
Average daily demand = 24 units
Lead time = 7 days
Reorder Point = Average daily demand * Lead time
Reorder Point = 24 units/day * 7 days = 168 units
Therefore, the reorder point is 168 units.
3. Safety Stock:
Safety stock is the buffer stock maintained to account for demand variability and lead time variability. It is calculated using the formula:
Safety Stock = (Service Level * Standard Deviation of Demand * Square Root of Lead Time) + (Standard Deviation of Demand * Square Root of Lead Time)
Service level = 97.5% (0.975)
Standard Deviation of Demand = 5 units/day
Lead time = 7 days
Safety Stock = (0.975 * 5 * √7) + (5 * √7) ≈ 17.37 units
Therefore, the safety stock is approximately 17.37 units.
4. Average Inventory:
The average inventory can be calculated as half of the order quantity plus the safety stock.
Average Inventory = (Order Quantity / 2) + Safety Stock
Average Inventory = (173 / 2) + 17.37 ≈ 104.19 units
Therefore, the average inventory is approximately 104.19 units.