# Operations Research

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VirtualUniversity of Pakistan
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
VirtualUniversity of Pakistan
OperationsResearch (MTH601)
67
Q
Im
t
t
t
t
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