149. The annual demand for an item is 40,000 units. The cost to process an order is $40 and the annual
inventory holding cost is $3 per item per year. What is the optimal order quantity, given the
following price breaks for purchasing the item?
Quantity
Price
1-1,499
$2.50 per unit
1,500 - 4,999
$2.30 per unit
5,000 or more
$2.25 per unit
a. What is the optimal behavior?
b. Does the firm take advantage of the lowest price available? Explain.
a.
Purchase 1500 units at a time, paying $2.30 each.
b.
It is not advantageous to pay $2.25 if that requires ordering 5000 units. The annual cost is
$97,820.00 at the $2.25 price versus $95,316.67 annual cost at the $2.30 price.
Q* (Square root formula)
Range
1
1032.796
Range
2
1032.796
Range
3
1032.796
Order Quantity
1032.796
1500
5000
Holding cost
$1,549.19
$2,250.00
$7,500.00
Setup cost
$1,549.19
$1,066.67
$320.00
Unit costs
$100,000.00
$92,000.00
$90,000.00
Total cost, T
c
$103,098.39
$95,316.67
$97,820.00
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
150.
Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16. Carrying
costs are $1 per pound per week because space is very scarce. It costs the firm $8 to prepare an
order. Assume the basic EOQ model with no shortages applies. Assume 52 weeks per year, closed
on Mondays.
a. How many pounds should Groundz order at a time?
b. What is total annual cost (excluding item cost) of managing this item on a cost-minimizing
basis?
c. In pursuing lowest annual total cost, how many orders should Groundz place annually?
d. How many days will there be between orders (assume 310 operating days) if Groundz practices
EOQ behavior?
a.
Q
*
=
2
⋅
4
⋅
52
⋅
8
=
8
. Groundz should order 8 pounds per order.
1
⋅
52
b.
TC
=
4
⋅
52
⋅
8
+
8
⋅
1
⋅
52
=
208
+
208
=
416
. The firm will spend $416 annually.