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MRP
– Part II
technical issues in MRP system design
source: Vollmann, Berry, Whybark and Jacobs’ textbook – Chapters 7
lot – sizing
processing frequency in MRP
bucketless MRP systems
Pegging
Scheduled receipts vs planned order
releases
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Lecture Notes on MRP  Part II
2
Lotsizing in MRP
The problem of finding order quantities (planned
order releases) and their timing is the lot sizing
problem.
Checking the row of “net requirements” in the MRP
record, we observe:
Known,
Timevarying (dynamic),
Lumpy,
Dependent demand.
IE 324  April 20, 2010
Lecture Notes on MRP  Part II
3
Lotsizing in MRP
Costs involved in lot sizing:
Setup (fixed ordering) cost
Inventory holding cost
Backorder cost
Production cost.
What order quantities will minimize the total cost?
(usually the sum of setup and inventory holding
cost)
There are several popular heuristic lotsizing
methods. They provide “good” nearoptimal or
sometimes even optimal solutions.
Silver & Meal heuristic, partperiod balancing heuristic,
least unit cost heuristic, …
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Lecture Notes on MRP  Part II
4
Lotsizing in MRP
lot sizing
method.
generates a minimumcost solution
yielding optimum order quantities.
The optimization is based on Dynamic
Programming.
The objective is minimizing the inventory holding +
setup (ordering) cost over the planning horizon.
The lotsizing problem in the context of MRP is the
socalled “Uncapacitated Lot Sizing Problem” in
the literature.
IE 324  April 20, 2010
Lecture Notes on MRP  Part II
5
Lotsizing in MRP
“Uncapacitated Lot Sizing Problem” in the
literature.
Let
demand (net requirements): (r
1
, r
2
, r
3
,…, r
n
) known.
Inventory holding cost: h TL / unit /period, charged for the
ending inventory.
Setup cost: K TL / order.
No shortages.
We can formulate the problem as an IP as follows:
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Lecture Notes on MRP  Part II
6
Lotsizing in MRP
Uncapacitated Lot Sizing Model – IP:
( 29
{ }
n
1,.
..,
t
0
I
,
P
and
0,1
y
n
1,.
..,
t
y
M
P
n
1,.
..,
t
r
I
P
I
s.to.
P
c
I
h
y
K
min
t
t
t
t
t
t
t
t
1

t
n
1
t
t
t
t
=
≥
∈
=
≤
=
=

+
+
+
∑
=
given.
I
and
r
M
inventory
period

of

end
:
I
size;
order
:
P
where
0
n
1
t
t
t
t
∑
=
=
IE 324  April 20, 2010
Lecture Notes on MRP  Part II
7
Lotsizing in MRP
Uncapacitated Lot Sizing Model :
In an optimal policy
I
t1
. P
t
= 0.
There cannot be
both production and inventory carried to period t.
Proof
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This note was uploaded on 05/23/2010 for the course IE 324 taught by Professor T during the Spring '10 term at Middle East Technical University.
 Spring '10
 t

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