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...