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11-1 Inventory Management
Chapter 11
InventoryManagement
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11-2 Inventory Management
CORE MRP II
MANUFACTURING RESOURCE PLANNING
Aggregate ForecastAggregate Production
Plan
Detailed ForecastMaster Production
Schedule
Rough-Cut Capacity
Planning
Material
Requirements
Planning
Capacity
Requirements
Planning
DispatchingPurchasing
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11-3 Inventory Management
Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain.
Dependent demand is certain.
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11-4 Inventory Management
Why Have Inventory?
Anticipation of demand surge
Cycle stock to minimize setups/orders
Buffering against uncertainty
Pipeline inventory of goods in transit
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11-5 Inventory Management
Lot-Sizing
Cycle stock inventories are determined by two
interrelated decisions
When to order/produce
How much to order/produce
Lot-sizing models attempt to provide answers which
minimize the total cost over some period of time
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11-6 Inventory Management
Reactive vs. Proactive
Systems Two basic types of inventory systems
Reactive systems Require little detailed knowledge of future
demand
Never look beyond the next purchase/production order
Proactive systems Require detailed knowledge of demand
Plan purchase/production orders far into the future
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11-7 Inventory Management
Reactive InventorySystems Order Q more units when inventory
drops
below ROP Q -- Order quantity (lot size)
ROP Reorder point
LT -- Lead time (1 Period)
T -- Reorder interval
TIME
Q
ROP
LTT
INVENTORY
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11-8 Inventory Management
How should Q and ROP be determined?
ROP = expected demand during lead time + safety stock
TIME
Q
ROP
LTT
INVENTORY
Reactive InventorySystems
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11-9 Inventory Management
D -- Average demand per period (40)
If safety stock is zero, then:
ROP = (D)(LT) = ____________________
TIME
Q
ROP
LTT
INVENTORY
Finding ROP
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11-10 Inventory Management
Finding Q
EOQ -- The best or most "economic" orderquantity that minimizes
the total cost per period
Need to determine how Q affects holding and setup
costs per period
TIME
Q
ROP
LTT
INVENTORY
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11-11 Inventory Management
Economic Order Quantity
The total cost per period function TC[Q] can be written as
a function of Q:
TC[Q] = total holding cost + total setup cost
TC[Q] = (avg. inventory)Ch+ (setups/period)C
s
TC[Q] = ( ) Ch+ ( ) C
s
2Q
QD
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11-12 Inventory Management
Economic Order Quantity
Sh CQ
DC
2
Q]Q[TC
+
=
40
Q
4050.0
2
Q]Q[TC
+
=
41162540100
4050.0
2
100]100[TC =
+
=
5.44325.124050
4050.0
2
50]50[TC =
+
=
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11-13 Inventory Management
Cost Minimization Goal
Order Quantity
(Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
Annua
lCost
(optimal order quantity)
TCQH
D
QS= +
2
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11-14 Inventory Management
Deriving the EOQUsing calculus, we take the derivative of the
total cost
function and set the derivative (slope) equal to zero
and solve for Q.
The total cost curve reaches its minimum where thecarrying and
ordering costs are equal.
Q = 2DSH
= 2(Annual Demand )(Order or Setup Cost )Annual Holding Cost
OPT
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11-15 Inventory Management
Economic Order Quantity
Solution:
COST
Q
TOTAL
HOLDINGSETUP
EOQ
h
S
C
DC2EOQ =
8050.0
)40)(40(2Q:Example =
11 16
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11-16 Inventory Management
Economic Order Quantity
COST
Q
TOTAL
HOLDINGSETUP
EOQ
4020204080
4050.0
2
80]80[TC =
+
=
11 17 I M
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11-17 Inventory Management
Proactive Inventory Systems
If we have a detailed forecast for the part or product . .
A lot-sizing decisions can be planned in advance
A proactive, rather than reactive approach
11 18 I M
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11-18 Inventory Management
Lot For Lot
Simplest lot-sizing rule
Make as much as you need each period
Maximizes total setup cost
Minimizes total holding cost
Period 1 2 3 4 5 6 Total
Demand 50 10 30 80 50 20
Lot Size
Projected Available Balance 0Net Requirements
Setup Cost
Holding Cost
Total Cost
11 19 I t M t
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11-19 Inventory Management
Economic Order Quantity
EOQ can also be modified for use in aproactive system Some EOQ
assumptions are violated
Use average demand for EOQ formula
8050.0
)40)(40(2EOQ =
Period 1 2 3 4 5 6 Total
Demand 50 10 30 80 50 20
Lot Size
Projected Available Balance 0
Net Requirements 50
Setup Cost
Holding Cost
Total Cost
11 20 I t M t
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11-20 Inventory Management
Periodic Order Quantity
POQ modifies the EOQ for discrete demand
Assumes a single best reorder interval (number of periods
covered by a single lot)
DEOQPOQ = 24080 =
Period 1 2 3 4 5 6 Total
Demand 50 10 30 80 50 20
Lot Size
Projected Available Balance 0Net Requirements 50
Setup Cost
Holding Cost
Total Cost
11 21 I t M t
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11-21 Inventory Management
Too much inventoryTends to hide problems
Easier to live with problems than to eliminatethem
Costly to maintain Wise strategy
Reduce lot sizes
Reduce safety stock
Operations Strategy
