Social Science
Business
Operations and Supply Chain Management (14th Edition)
Exercise 26
Chapter 20, Page 547
Operations and Supply Chain Management
ISBN: 9789339204105
Table of contents
Solution
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Answered 8 months ago
Step 1
1 of 8
In this task, we are required to calculate the number of capsules of an antibiotic
that the pharmaceutical company needs to order.
Step 2
2 of 8
By the text of the problem, we are given the following data:
Parameter
Value
Average daily demand
2,000 capsules/day
Standard deviation of daily demand
800 capsules
Review period
14 days
Lead time
5 days
Inventory level
25,000 capsules
Service probability
99%
Step 3
3 of 8
Let's introduce the main concepts:
Fixed-time period model (P-model) is a model where inventory is ordered at the
end of the specific time period. Because of that, the order size varies depending
on how much is needed.
Step 4
4 of 8
Since the review period is fixed, to determine the quantity to order, usually
denoted by q, we will use the fixed-time period model within which it is given by
the following formula:
q = d(T+L) + zσT+L − I
​
where:
q = Order quantity
d = Average daily demand
T = Review period in days
L = Lead time in days
z = Number of standard deviations depending on a service probability
σT+L = Standard deviation of demand during the period T+L
​
I = Inventory level
Step 5
5 of 8
Now, we will assign the information given in our problem to the notation of the
model and obtain the following expression for q:
q = 2, 000 × (14 + 5) + zσT+L − 25, 000
​
To complete the solution, we have to calculate z and σT+L .
​
Step 6
6 of 8
We can find the number z from the specified service probability using the Excel
or Calc =NORMSINV(0.99) function.
Thus, in our case,
z = 2.33
Step 7
7 of 8
The standard deviation during the period T+L is given by the formula
(T + L)σd2
σT+L =
​
​ ​
where σd is daily standard deviation.
​
Thus, in our case,
σT+L =
​
​
(14 + 5) × 8002
= 3, 487
​
​
capsules.
Step 8
8 of 8
Finally, the required quantity to order is
q = 2, 000 × 19 + 2.33 × 3, 487 − 25, 000
​
= 21, 125
​
Therefore, the order quantity is 21,125 capsules.
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