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VirtualUniversity
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OperationsResearch
(MTH601)
66
Itemcost
=
18000×
2
=
Rs.
36000
Orderingcost
=
500× 180004470
=
Rs.
2013.5
holdingcost
=
0.15× 12 × 2235× 1800036000
=
Rs.
2011.5
Totalannual
cost
=
36000+ 2013.5+ 2011.5
=
Rs.
40025.0
Model
4. Manufacturing model
withshortages
Theassumptions
in this modelare the
same as in model 3 except
that the shortagesare
also considered.
Thismodel
is
illustrated in the figure in
power point presentation of
the lecture, given on
thenext page.
Thereare
four components of inventory
costs in thismodel. They
are
(1)
Itemcost.
(2)
Set
up or order cost.
(3)
Itemsholding
cost.
(4)
Shortagecost.
Theitems
t1, t2,
t3 andt4 are as
represented in figure on
thenext page. The
totalcost per period
t
is
C′
= C
Q +
C
+
C
(t +
t
)
Im 2
+
C
(t +
t
)
S
2
(46)
1
2
3
1
2
4
3
4
Thevalues
of t1, t2,
t3 andt4 are to be
determined in terms of Q
andS, so
thatthe cost is
expressed
as
a function of only
twovariable Q
andS.
Finalresults
are given belowwithout
proof.
C3 +C4
2C2D
Q*
=
So
(47)
C3 (1-D
R)
C4
and
2C2D
C3
S*
=
1-D
R
C3 +C4
C4
66
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VirtualUniversity
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OperationsResearch
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67
Q
Im
t
t
t
t
67