Production, Capacity And Material Planning Page 41
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60Material Requirements Planning
Decision variables:
x
i
t
deliverd quantity of item
in period
it
I
i
t
inventory level of item
at the end of period
it
O
m in
t
overtime hours required for machine
period
mt
y
i
t
binary variable indicating if item
is produced in period
(=1) or not (=0)
it
Equations:
P
T
T
M
+
+
∑ ∑
∑ ∑
s
y
h
I
oc
O
min
(
)
i
it
i
it
m
mt
= =
=
=
i
t
t
m
1 1
1
1
∑
∀
=
+
−
−
−
≤
∀
t i,
I
I
x
c
x
D
t i,
x
Gy
0
−
t i
t i
t i
ij
jt
it
,
,
1
,
it
it
∈
Γ
j
i
(
)
P
≥
∈
x
I
O
y
+
≤
+
∑
,
,
, 0
0 {
} 1 ,
∀
a
x
b
y
L
O
m,
t
(
)
it
it
mt
it
mi
it
mi
it
mt
mt
=
i
1
∀
i
m
t
,
,
Production Management
140
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