Page 192 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Unit 9: Inventory Model and Safety Stocks

=  2*5400*1200*0.40*40 Notes
= ` 14,400.00
The Total annual Cost under the present system = ` (1200*5400/150 + 0.40*40*150/2) =
` (43,800 + 1200) = ` 45,000.00
The loss to the company = ` 45,000 – ` 14,400 = `. 30,600.00
Reorder Level = Ro = L*D = (6/12)*1200 = 600 units
The company should place orders for economic lot sizes of 900 units in each order. It
should have a reorder level at 600 units.

9.4.3 EOQ Model with Demand and Delivery Uncertainty

If you have both demand and delivery (lead time) uncertainty, you must use a convolution
formula (Bowersox 2010) to calculate the safety stock level.
Standard Deviation of Combined Probabilities
c = Square Root of [(L * d^2) + (d^2 * l^2)], where
 L = Lead time (in days)
 d = the average daily demand
 d = the standard deviation of daily demand (demand variation)
 d = STDEV (daily demand times) when using Excel
 l = Standard Deviation of lead time = STDEV (lead times)
Reorder Point = R = (d * L) + (NORMSINV(p) * c)
Reorder Point = R = (d * L) + (NORMSINV(p) * Square Root of [(L * d^2) + (d^2 * l^2)]

Type I and Type II Error

A statistical hypothesis test is a method of making statistical decisions using experimental data.
There are two types of errors:
1. Hypothesis is rejected when it is true.
2. Hypothesis is not rejected when it is false.
(1) is called Type 1 error (a), (2) is called Type 2 error (b). When a = 0.10 it means that true
hypothesis will be accepted in 90 out of 100 occasions. Thus, there is a risk of rejecting a true
hypothesis in 10 out of every 100 occasions. To reduce the risk, use a = 0.01 which implies that we
are prepared to take a 1% risk i.e., the probability of rejecting a true hypothesis is 1%. It is also
possible that in hypothesis testing, we may commit Type 2 error (b) i.e., accepting a null
hypothesis which is false.

Did u know? The only way to reduce Type 1 and Type 2 error is by increasing the sample
size.

Example of Type 1 and Type 2 Error

Type 1 and Type 2 error is presented as follows. Suppose a marketing company has 2 distributors
(retailers) with varying capabilities. On the basis of capabilities, the company has grouped them

LOVELY PROFESSIONAL UNIVERSITY 187