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MS3121 Fundamentals of Business Logistics
Management
Every management mistake ends up in
inventory.
Michael C. Bergerac
Former Chief Executive

Revlon, Inc.
Topic 5 Inventory Policy Decisions Part II
Advanced
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Inventory Decisions in Strategy
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Pull Methods (Contd)
Periodic review control with demand uncertainty
The inventory is reviewed at the time interval
(T) to determine the quantity on hand. The
replenishment quantity (Q) to be ordered is the
difference between a target level called MAX and
the quantity on hand. We need to find MAX and
T.

• Good method for products
• Of low value
• That are purchased from the same vendor
• Having economies of scale in production,
  purchasing, and transportation

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Periodic Control for a Single Item
M
Q2
Q1
Quantity on hand

q
Stock level reviewed
Order received
0
Time
LT
LT
T
T
T review interval q quantity on hand Qi
order quantity
M maximum level M - q replenishment
quantity LT lead time
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Periodic Review (Contd)
Estimate Q from the EOQ formula as if under
demand certainty conditions. Recall that this is
Q 11008 units. Now, T Q/d
11008/11107 0.991 month Construct the
demand-during-lead-time-plus-order-cycle-time
distribution.
T is order review time
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Periodic Review (Contd)
DD(T LT)
P
Z(s')
s'
X d(T LT)
MAX
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Periodic Review (Contd)
Given sd 3099, LT1.5 months, d11107 per
month, p0.75
Find MAX MAX d(T LT) z(sd)
27667.5370.674891 30945 units
Rule Review the inventory every 0.991 month and
place an order for (30945 units - quantity on
hand - quantity on order backorders).
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Periodic Review (Contd)
The total relevant cost for this design is
Note Compare this cost with that of the reorder
point method to see that periodic review control
carries a slight premium in cost due to more
safety stock.
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Periodic Review (Contd)
The service level for this design is
Note the service level is lower because demand
is variable during the lead time AND the review
period T
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Product items can be grouped according to 80-20
curve, each with different stocking policies
100
90
80
70
Aggregate Inventory Control
60
Total sales ()
50
40
30
A items
B items
C items
20
10
0
0
20
40
60
80
100
Total items ()
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Inventory Consolidation (Risk Pooling)
Illustration of risk pooling
Suppose there is a product stocked in two
warehouses. The replenishment quantities are
determined by the economic order quantity
formula. The replenishment lead-time is 0.5
months, the cost for a replenishment order is
50, the inventory carrying cost is 2 per month,
and the item value is 75 per unit. The
probability of an out of stock during the
lead-time period is 5. The demand is normally
distributed with typical demand over six months
as follows.
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Risk Pooling (Contd)
Combined
Demand
Demand
Demand in a
in
Whse
in
Whse
Central
Month
A
B
Whse
1
35
67
102
2
62
83
145
3
46
71
117
4
25
62
87
5
37
55
92
6
43
66
109
Avg. (
D
)
41.33
67.33
108.66
Std.
Dev. (
s
)
11.38
8.58
19.07
d
6
Estimate the average inventory levels for
two-warehouse and one-warehouse supply channels.
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Risk Pooling (Contd)
Regular stock
Regular stock in system is
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Risk Pooling (Contd)
Regular stock if item is entirely in one warehouse
Safety stock
System safety stock in 2 warehouses
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Risk Pooling (Contd)
Safety stock in 1 warehouse
Total inventory AIL Regular stock Safety
stock AIL 59.75 27.66 87.41 units In a
one-warehouse channel AIL 42.56 26.43
68.99 units
Two warehouses
Conclusion There is a reduction in the average
inventory level of an item as the number of
stocking points in the supply channel is
decreased. In this example, both regular stock
and safety stock decline.
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Square Root Law of Inventory Consolidation

• The amount of inventory (regular stock) at
  multiple stocking points can be estimated by the
  square root law when
• Inventory control at each point is based on EOQ
  principles
• There is an equal amount on inventory at each
  point
• The square root law is

where IT amount of inventory at one
location Ii amount of inventory at each of n
locations n number of stocking points
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Square Root Law (Contd)
Example Suppose that there is 1,000,000 of
inventory at 3 stocking points for a total of
3,000,000. If it were all consolidated into 1
location, we can expect
If we wish to consolidate from 3 to 2 warehouses,
the level of inventory in each warehouse would be
For a total system inventory of n x I 2 x
1,224,745 2,449,490.
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Square Root Law (Contd)
More simply
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Turnover Ratio
A fruit grower stocks its dried fruit products in
12 warehouses around the country. What is the
turnover ratio for the distribution system?
Ware-
Annual
Average
Ware-
Annual
Average
house
warehouse
inventory
house
warehouse
inventory
no.
throughput,
level,
no.
throughput,
level,
1
21,136,032
2,217,790
7
43,105,917
6,542,079
2
16,174,988
2,196,364
8
47,136,632
5,722,640
3
78,559,012
9,510,027
9
24,745,328
2,641,138
4
17,102,486
2,085,246
10
57,789,509
6,403,076
5
88,228,672
11,443,489
11
16,483,970
1,991,016
6
40,884,400
5,293,539
12
26,368,290

2,719,330

Totals
425,295,236
43,701,344
236
,
295
,
425

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