Garden Variety Flower shop uses 625 clay pots a month. The pots are
purchased at $2 each. Annual carrying costs per pot are estimated to be 15
percent of cost, and ordering costs are $125 per order. The manager has been
using an order size of 1,500 flower pots. There are 4 weeks in each month, 12
months a year.
a. What is the Economic order quantity (EOQ)?
b. What is the total cost associated with EOQ
c. If order lead-time is two weeks (i.e., 0.5 month) and the safety stock policy
is that SS= 50 pots, what is the ROP?
d. If the shop remains using the order size of 1500, what is the total annual
cost?
e. Following d., what additional annual cost is the shop incurring by staying
with the order size of 1500? (as opposed to using EOQ)
Garden Variety Flower shop uses 625 clay pots a month. The pots are
purchased at $2 each. Annual carrying costs per pot are estimated to be 15
percent of cost, and ordering costs are $125 per order. The manager has been
using an order size of 1,500 flower pots. There are 4 weeks in each month, 12
months a year.
a. What is the Economic order quantity (EOQ)?
b. What is the total cost associated with EOQ
c. If order lead-time is two weeks (i.e., 0.5 month) and the safety stock policy
is that SS= 50 pots, what is the ROP?
d. If the shop remains using the order size of 1500, what is the total annual
cost?
e. Following d., what additional annual cost is the shop incurring by staying
with the order size of 1500? (as opposed to using EOQ)
A- 2500
B- 750
C-320
D-850
E- 100
To solve this problem, we'll use the following formulas:
a. Economic Order Quantity (EOQ) formula:
EOQ = √((2DS) / H)
b. Total cost associated with EOQ:
Total cost = (D/Q)S + (Q/2)H + (D/Q)C
c. Reorder point (ROP) formula:
ROP = Lead time demand + Safety stock
Lead time demand = D * Lead time
d. Total annual cost:
Total cost = (D/Q)S + (Q/2)H + (D/Q)C
e. Additional annual cost:
Additional annual cost = Total cost using order size of 1500 - Total cost using EOQ
Given:
D (demand) = 625 clay pots per month
S (order cost) = $2 per pot
H (carrying cost) = 15% of S = 0.15 * S = 0.15 * $2 = $0.30 per pot
C (ordering cost) = $125 per order
Lead time = 2 weeks = 0.5 month
Safety stock = 50 pots
Order size (Q) = 1500 pots
Let's calculate the values step-by-step:
a. Calculate the Economic Order Quantity (EOQ):
EOQ = √((2DS) / H)
EOQ = √((2 * 625 * 2) / 0.30)
EOQ ≈ √(2500 / 0.30)
EOQ ≈ √8333.33
EOQ ≈ 91.28
b. Calculate the total cost associated with EOQ:
Total cost = (D/Q)S + (Q/2)H + (D/Q)C
Total cost = (625/91.28) * 2 + (91.28/2) * 0.30 + (625/91.28) * 125
Total cost ≈ 13.66 * 2 + 45.64 * 0.30 + 6.85 * 125
Total cost ≈ $27.32 + $13.69 + $856.25
Total cost ≈ $897.26
c. Calculate the Reorder Point (ROP):
Lead time demand = D * Lead time
Lead time demand = 625 * 0.5
Lead time demand = 312.5
ROP = Lead time demand + Safety stock
ROP = 312.5 + 50
ROP = 362.5
d. Calculate the total annual cost using an order size of 1500:
Total cost = (D/Q)S + (Q/2)H + (D/Q)C
Total cost = (625/1500) * 2 + (1500/2) * 0.30 + (625/1500) * 125
Total cost ≈ 0.4167 * 2 + 750 * 0.30 + 0.4167 * 125
Total cost ≈ $0.8334 + $225 + $52.0854
Total cost ≈ $277.9188
e. Calculate the additional annual cost by staying with an order size of 1500:
Additional annual cost = Total cost using order size of 1500 - Total cost using EOQ
Additional annual cost = $277.9188 - $897.26
Additional annual cost ≈ -$619.3412 (Negative means cost reduction)
Therefore,
a. The Economic Order Quantity (EOQ) is approximately 91.28 clay pots.
b. The total cost associated with EOQ is approximately $897.26.
c. The Reorder Point (ROP) is approximately 362.5 clay pots.
d. The total annual cost using an order size of 1500 is approximately $277.92.
e. The shop is incurring a cost reduction of approximately $619.34 by staying with an order size of 1500 instead of using EOQ.
To answer these questions, we need to understand the concept of Economic Order Quantity (EOQ) and related cost components. Let's break down each question step by step:
a. What is the Economic Order Quantity (EOQ)?
The formula to calculate EOQ is:
EOQ = √((2 * D * S) / H)
Where:
D = Demand per period
S = Ordering cost per order
H = Carrying cost per unit
In this case:
D = 625 pots per month * 12 months = 7500 pots per year
S = $125 per order
H = 15% of the cost of each pot = 0.15 * $2 = $0.30
Plugging in the values:
EOQ = √((2 * 7500 * 125) / 0.30)
b. What is the total cost associated with EOQ?
To calculate the total cost associated with EOQ, we need to find the total ordering cost and the total carrying cost.
Total ordering cost = (Annual demand / EOQ) * Ordering cost per order
Total carrying cost = (EOQ / 2) * carrying cost per unit
Total cost associated with EOQ = Total ordering cost + Total carrying cost
c. If order lead-time is two weeks (i.e., 0.5 month) and the safety stock policy is that SS = 50 pots, what is the ROP?
ROP (Reorder Point) is the inventory level at which a new order should be placed to replenish stock before running out. ROP can be calculated using the formula:
ROP = (Demand per day * Lead time) + Safety stock
In this case:
Demand per day = (Annual demand / 12 months) / (4 weeks * 7 days)
Lead time = 0.5 month
Safety stock = 50 pots
d. If the shop remains using the order size of 1500, what is the total annual cost?
To calculate the total annual cost, we need to find the total ordering cost and the total carrying cost using the given order size, and then sum them up.
Total cost = Total ordering cost + Total carrying cost
e. Following d., what additional annual cost is the shop incurring by staying with the order size of 1500 (as opposed to using EOQ)?
To calculate the additional annual cost, subtract the total annual cost with the EOQ from the total annual cost with the given order size of 1500.
Additional annual cost = Total annual cost with given order size - Total annual cost with EOQ
By applying the formulas and plugging in the values, you can determine the answers for each question.