Answer:
730 items
Explanation:
The objective of the given information is to determine the number of hamburgers UAHH should order for the following conditions:
Average daily demand 600
Standard deviation of demand 100
Desired service probability 99%
Hamburger inventory 800
The formula for a given order quantity in a fixed period of time can be expressed as :
[tex]q = \overline d(L+T)+ z \sigma_{L+T}-I[/tex]
where;
[tex]q[/tex] = order quantity = ???
[tex]\overline d[/tex] = daily demand average = 600
L = lead time in days = 1
T = time taken = 1
z = no of standard deviation = ???
[tex]\sigma_{L+T}[/tex] = standard deviation of usage in lead time and time taken = ???
I = present inventory level = 800
[tex]\sigma_{L+T}[/tex] = [tex]\sqrt 2[/tex] × standard deviation of daily demand
[tex]\sigma_{L+T}[/tex] = [tex]\sqrt{2} *100[/tex]
[tex]\sigma_{L+T}[/tex] = 1.4142 * 100
[tex]\sigma_{L+T}[/tex] = 141.42 items
From the Desired service probability 99% = 0.99; we can deduce the no of standard deviation by using the excel function (=NORMSINV (0.99))
z = 2.33
From [tex]q = \overline d(L+T)+ z \sigma_{L+T}-I[/tex]
[tex]q =600(1+1)+ 2.33*(141.42)-800[/tex]
[tex]q =600(2)+ 2.33*(141.42)-800[/tex]
[tex]q =1200+329.5086-800[/tex]
q = 729.5086 items
q ≅ 730 items
Therefore; the number of hamburgers UAHH should order from the following given conditions = 730 items
