Inventory Control – Part 2

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Session - 12
Chapter 17

Inventory Control – Part 2
Dr. G. Anand
“QM & OM” Area
Indian Institute of Management Kozhikode (IIMK)
IIMK Campus, Kunnamangalam, Kozhikode,
Kerala - 673570

17-2

OBJECTIVES
• Multi-Period Inventory Models: Basic
Fixed-Time Period Model
• Miscellaneous Systems and Issues
– Optional Replenishment System
– 2 Bin System
– ABC Analysis

Fixed-Time Period Model with Safety
Stock Formula

17-3

q = Average demand + Safety stock – Inventory currently on hand q = Average demand + Safety stock – Inventory currently on hand q = d(T + L) + Z σ T + L - I
Where :
q = quantitiy to be ordered
T = the number of days between reviews
L = lead time in days
d = forecast average daily demand
z = the number of standard deviations for a specified service probability σ T + L = standard deviation of demand over the review and lead time I = current inventory level (includes items on order)

17-4

Multi-Period Models: Fixed-Time Period Model:
Determining the Value of sT+L
σ T+ LL =
σ T+ =

T+ LL
T+

∑ ((σ ))
∑σ
i ==1
i1

22

dd
i
i

Since each day is independent and σ d is constant,
Since each day is independent and σ d is constant,

σ T+ LL = (T + L)σ dd22
σ T+ = (T + L)σ

• The standard deviation of a sequence
of random events equals the square
root of the sum of the variances

17-5

Example of the Fixed-Time Period Model
Given the information below, how many units
Given the information below, how many units
should be ordered?
should be ordered?
Average daily demand for a product is
20 units. The review period is 30 days,
and lead time is 10 days. Management
has set a policy of satisfying 96 percent
of demand from items in stock. At the
beginning of the review period there are
200 units in inventory. The daily
demand standard deviation is 4 units.

Example of the Fixed-Time Period
Model: Solution (Part 1)
σ T+ L =

(T + L)σ d 2 =

( 30 + 10 )( 4 ) 2 = 25.298

The value for “z” is found by using the Excel
The value for “z” is found by using the Excel
NORMSINV function, or as we will do here, using
NORMSINV function, or as we will do here, using
Appendix D. By adding 0.5 to all the values in
Appendix D. By adding 0.5 to all the values in
Appendix D and finding the value in the table that
Appendix D and finding the value in the table that
comes closest to the service probability, the “z”
comes closest to the service probability, the “z”
value can be read by adding the column heading
value can be read by adding the column heading
label to the row label.
label to the row label.
So, by adding 0.5 to the value from Appendix D of 0.4599,
So, by adding 0.5 to the value from Appendix D of 0.4599,
we have a probability of 0.9599, which is given by a zz= 1.75 we have a probability of 0.9599, which is given by a = 1.75

17-6

Example of the Fixed-Time Period
Model: Solution (Part 2)

17-7

q = d(T + L) + Z σ T + L - I
q = 20(30 + 10) + (1.75)(25.298) - 200
q = 800 + 44.272 - 200 = 644.272, or 645 units

So, to satisfy 96 percent of the demand,
So, to satisfy 96 percent of the demand,
you should place an order of 645 units at
you should place an order of 645 units at
this review period
this review period

Miscellaneous Systems:
Optional Replenishment System
Maximum Inventory Level, M

q=M-I
Actual Inventory Level, I

M
I
Reviews inventory at a fixed frequency (say weekly) and
order if the level has fallen below certain amount
Q = minimum acceptable order quantity

If q > Q, order q, otherwise do not order any.

17-8

Miscellaneous Systems:
Bin Systems

17-9

Two-Bin System

Full

Empty

Order One Bin of
Inventory
Q-Model

Miscellaneous Systems:
Bin Systems
One-Bin System

Periodic Check

Order enough to refill
bin fully irrespective of
consumption at fixed
intervals (p model)

17-10

ABC Inventory Planning
• It is also called as RRS system – Runner
Repeater and...
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