NATIONAL MANUFACTURING COMPANY1
The National Manufacturing Company (NMC) assembles electronic equipment. The
demand for the equipment is seasonal and its trend is increasing. The demand for the
equipment in the past four years is given in Table 1.
The demand is captive i.e., whenever a month’s demand is not met, the unsatisfied
demand is required to be met from the production of the subsequent month. For every
unit that cannot be shipped because of insufficient inventory, NMC pays a penalty of Rs.
100.
A decision to change the production level for the following month should be made by the
end of the month. For example, if the production in May is 2,000 units and if a decision
is taken to increase the production level by 200 units at the end of May, then the
production for June is 2,200 units and the cost of increasing is Rs. 2,400/-. If, on the
other hand, no change in the production level has been decided, then the production for
June is 2,000 units. The maximum production capacity is 4,000 units per month.
The cost of changing the production level is given below:
--------------------------------------Decreasing Production Level
Between Any Two Consecutive
Months by
--------------------------------------100 or less
101 - 200
201 - 300
301 - 400
401 - 500
--(a- 99) - a
---------------------------------------------------------------------------Increasing Production Level
Between any Two Consecutive
Months by
-------------------------------------100 or less
101 - 200
201 - 300
301 - 400
(b - 99) - b
--------------------------------------
1
------------------------------------Cost of Changing
Production Level
------------------------------------Rs. 500
1200
2100
3200
4500
--Rs. 4a + a2/100
------------------------------------------------------------------------Cost of Changing
Production Level
-------------------------------------Rs. 1000
2400
4200
6400
Rs. 8b + b2/50
--------------------------------------
Prepared by Professor. M.A. Vanjour and Prof. M V Madan
1
There will be shut down in the months of March and September. If the production level
in April is different from the production level in February, then only the company will
incur a cost in April for change in production level. Similarly in the months of August
and October.
The cost of holding equipment in inventory is Rs. 1 per month. The opening inventory at
the beginning of January 1980 is 1500 units. The inventory level at the end of December
1980 should be 2500 units. This is due to a government regulation which stipulates a
stock of one month demand at the end of each calendar year: Government auditors verify
the stock in the first week of January. If there is a shortfall, then NMC will be compelled
to place orders with contractors and pays Rs. 100 more than their factory cost (i.e., the
penalty for falling short of 2500 units at the end of the year is Rs. 100 per unit). Because
of this regulation NMC paid a heavy penalty in 1979.
The company has decided to maintain a production of 2000 units in January 1981.
Hence, when the game ends in December 1980, the cost of changing the production level
in January will also be taken into account.
Table - 1
Demand for the Equipment in the Past Four Years
Month
JANUARY
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
OCTOBER
NOVEMBER
DECEMBER
TOTAL
1976
1401
898
404
967
1081
1601
1332
1047
692
1121
1321
1729
13594
1977
1328
954
648
1101
1381
1621
1556
1162
941
1360
1809
1905
15766
1978
1696
1510
972
1192
1681
1696
1780
1578
1128
1780
1916
2521
19450
1979
2005
1607
1056
1524
1780
2305
1985
1695
1357
1981
2285
2836
22476
2