Mudra Fabricators Ltd (MFL) produces
an item required for industrial consumption. The monthly forecast
for year 2004 is given below. MFL has a normal production capacity
of 2200 units per month and a current inventory of 1000 left
as part of inventory in December 2003.
| Month
Forecast |
(units) |
| Jan |
1500 |
| Feb |
1000 |
| Mar |
1900 |
| Apr |
2600 |
| May |
2800 |
| Jun |
3100 |
| July |
3200 |
| Aug |
3000 |
| Sep |
2000 |
| Oct |
1000 |
| Nov |
1800 |
| Dec |
2200 |
| Total |
26100 |
|
Production cost is Mu 70 per unit, inventory
holding cost is Mu 1.4 per month per unit of ending inventory,
overtime costs Mu 6.5 additional per unit and there is Mu 5
per unit charge to change the production rate. Cost of under-time
(production below full capacity) is Mu 3 per unit. The demand,
which is not satisfied, is charged at Mu 9 per unit.
Evaluate the cost of the following two production plans:
a) produce uniformly at full capacity per month
b) produce 1500 units in Jan to Mar, 2800 units in April- Aug,
2200 units in Sep- Nov and 1500 units in Dec.
Option (a) : Uniform production of 2200
units per month
| Month |
Demand |
Cumulative demand |
Production |
Cumulative
prod availability |
End-of-month
Inventory
= Beginning Inventory + prodn-demand |
| (1) |
(2) |
(3) |
(4) |
(5) |
(6)=(5)-(3) |
| Jan |
1500 |
1500 |
2200 |
1000+2200=3200 |
1700 |
| Feb |
1000 |
2500 |
2200 |
5400 |
2900 |
| Mar |
1900 |
4400 |
2200 |
7600 |
3200 |
| Apr |
2600 |
7000 |
2200 |
9800 |
2800 |
| May |
2800 |
9800 |
2200 |
12000 |
2200 |
| June |
3100 |
12,900 |
2200 |
14200 |
1300 |
| July |
3200 |
16,100 |
2200 |
16400 |
300 |
| Aug |
3000 |
19,100 |
2200 |
18600 |
0(Lost
sales of 500 units) |
| Sept |
2000 |
21,100 |
2200 |
21300 |
200 |
| Oct |
1000 |
22,100 |
2200 |
23500 |
1400 |
| Nov |
1800 |
23,900 |
2200 |
25700 |
1800 |
| Dec |
2200 |
26,100 |
2200 |
27900 |
1800 |
|
Production cost per month = 2200 units x Mu 50 = Mu 154,000
Total production cost Mu 154,000 x 12 months = Mu 1848,000
Total inventory = 1700 +2900 +…. +1800 = 19600 units
Total Inventory cost = 19600 units x Mu 1.4 = Mu 27,440
Total Lost sales cost = 500 units x Mu 90 = Mu 45,000
Total cost of this plan = Mu 1848,000 + Mu 27,440 + Mu 45,000
=Mu 1920,440
Option (b).
| Month |
Demand |
Cumulative demand |
Production |
Cumulative
prod availability |
End-of-month
Inventory= Beginning Inventory + prodn-demand |
| (1) |
(2) |
(3) |
(4) |
(5) |
(6)=(5)-(3) |
| Jan |
1500 |
1500 |
1500 |
1000+1500=2500 |
1000 |
| Feb |
1000 |
2500 |
1500 |
4000 |
1500 |
| Mar |
1900 |
4400 |
1500 |
5500 |
1100 |
| Apr |
2600 |
7000 |
2800 |
8300 |
1300 |
| May |
2800 |
9800 |
2800 |
11,100 |
1300 |
| June |
3100 |
12,900 |
2800 |
13,900 |
1000 |
| July |
3200 |
16,100 |
2800 |
16,700 |
600 |
| Aug |
3000 |
19,100 |
2800 |
19,500 |
400 |
| Sept |
2000 |
21,100 |
2200 |
21,700 |
600 |
| Oct |
1000 |
22,100 |
2200 |
23,900 |
1800 |
| Nov |
1800 |
23,900 |
2200 |
26,100 |
2200 |
| Dec |
2200 |
26,100 |
1500 |
27,600 |
1500 |
|
Cost computations under Option (b)
| Month |
Production |
Prodn
cost (in Mu) |
End-of-month Inventory= Beginning Inventory + prodn-demand |
Inv
cost (in Mu) |
Capacity
change cost (in Mu) @ Mu 5 per unit |
OvertimeCost@
Mu 6.5 per unit |
Under
time cos@ Mu 3 per unitt |
| (1) |
(2) |
(3)
= (2) x Mu 70 |
(4) |
(5)
= (4) x Mu 1.4 |
(6) |
(7) |
(8) |
| Jan |
1500 |
105,000 |
1000 |
1400 |
|
|
700 x 3 =2100 |
| Feb |
1500 |
105,000 |
1500 |
2100 |
|
|
700 x 3 =2100 |
| Mar |
1500 |
105,000 |
1100 |
1540 |
|
|
700 x 3 =2100 |
| Apr |
2800 |
196,000 |
1300 |
1820 |
1300*5=6500 |
600 x 6.5 =x 3900 |
|
| May |
2800 |
196,000 |
1300 |
1820 |
|
600 x 6.5 =x 3900 |
|
| Jun |
2800 |
196,000 |
1000 |
1400 |
|
600 x 6.5 =x 3900 |
|
| July |
2800 |
196,000 |
600 |
840 |
|
600 x 6.5 =x 3900 |
|
| Aug |
2800 |
196,000 |
400 |
560 |
|
600 x 6.5 =x 3900 |
|
| Sept |
2200 |
154,000 |
600 |
840 |
600*5=3000 |
|
|
| Oct |
2200 |
154,000 |
1800 |
2520 |
|
|
|
| Nov |
2200 |
154,000 |
2200 |
3080 |
|
|
|
| Dec |
1500 |
105,000 |
1500 |
2100 |
700*5=3500 |
|
700 x 3 =2100 |
| Total coats |
|
1862,000 |
|
20,020 |
13,000 |
19,500 |
8,400 |
|
Total cost of Option B
Mu 1862,000 + Mu 20,020 + Mu 13,000 + Mu 19,500 + Mu 8,400 =
Mu 1992, 920
Thus option (a) is cheaper compared to option
(b) by Mu 1992,920 - Mu 1920, 440 = Mu 72, 480 (or by about
3,7 %) . |
|
