A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Determine
Ans:
|
Price Level: |
1 |
2 |
3 |
4 |
||
Minimum quantity for price |
Qmin = |
1000 |
2000 |
5000 |
10000 |
||
Price |
|
|
P = |
1.25 |
1.20 |
1.15 |
1.10 |
Optimal Q (for each price) |
Qopt = |
2400 |
2400 |
5000 |
10000 |
||
Number of orders per year |
D/Qopt = |
7.5 |
7.5 |
3.6 |
1.8 |
||
Average Inventory |
Qopt/2 = |
1200 |
1200 |
2500 |
5000 |
||
Annual carrying cost |
(Qopt/2) * H = |
720 |
720 |
1500 |
3000 |
||
Annual ordering cost |
(D/Qopt) * S = |
720 |
720 |
345.6 |
172.8 |
||
Annual purchase cost |
P * D = |
22500 |
21600 |
20700 |
19800 |
||
Total Annual Cost |
|
TC = |
23940 |
23040 |
22545.6 |
22972.8 |
Annual Demand |
|
D = |
18000 |
||
Ordering cost per order |
S = |
96 |
|||
Annual carrying cost per unit: |
H (fixed) = |
0.6 |
|||
|
TRUE |
H (% of price) = |
|
||
Optimal Q (overall) |
|
Qopt = |
5000 |
||
Actual Order Quantity |
Q = |
||||
Increment |
|
Q = |
|||
Price |
|
|
P = |
1.15 |
|
Number of orders per year |
D/Q = |
3.6 |
|||
Average Inventory |
Q/2 = |
2500 |
|||
Annual carrying cost |
(Q/2) * H = |
1500 |
|||
Annual ordering cost |
(D/Q) * S = |
345.6 |
|||
Annual purchase cost |
P * D = |
20700 |
|||
Total Annual Cost |
|
TC = |
22545.6 |
a.The optimal order quantity.
Ans:
Optimal order quantity = 5000
b.The number of orders per year.
Ans: Number of orders per year = 3.6