Inventory Control – Part 2
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
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