Q2] After a profitable Fall semester you decided to change your operations to th
ID: 3361773 • Letter: Q
Question
Q2] After a profitable Fall semester you decided to change your operations to the New-Age Pizza shop.
So, every weekend (consisting of three days: Friday, Saturday and Sunday) you run a pizza special event. You bake all the pizza for the weekend on Thursday and then sell them during the three days of the weekend. Each pizza costs you $1.50 in labor and materials and you sell each on for $2.50. However, pizza left after the weekend has be donated to hungry students (for free).
The daily demand during the weekend is distributed normally with a mean of 50 pizzas a day and standard deviation of 25 pizza (again for each day).
How many pizzas should you back on Thursday?
Later you found out that the sales during the weekend followed this specific discrete distribution (and not the one mentioned above):
Demand
Probability
35
0.2
40
0.25
45
0.15
50
0.15
55
0.10
60
0.10
65
0.05
If you decide to bake 55 pizzas for that demand find:
What is your service level Type I?
What is your service level type II?
Demand
Probability
35
0.2
40
0.25
45
0.15
50
0.15
55
0.10
60
0.10
65
0.05
Explanation / Answer
CP = $1.5 SP = $2.5 Salvage value = $0 (Given free)
Underage = SP - CP = $2.5 - $1.5 = $1
Overage = CP - Salvage = $1.5 - $0 = $1.5
p -> Underage/(Underage+Overage) = 1/(1+1.5) = 0.4
z* = -0.25335 [using NORMSINV formula in excel for the above probability of 0.4]
Mean = 50 SD = 25
Q = Mean + (Z* x SD)
= 43.66 ~ 44
Therefore, we should stock 44 pizzas on Thursday
Now, for the discrete distribution and a supply of 55 pizzas
Service level Type 1 is where the Demand <= Supply, i.e. there was a stock out.
From the given table, we can see that the demand is <=55 for 5 instances out of 7
Therefore, service level Type 1 = 71.4%
In the given table, we can see that Demand <= Supply probability is 0.85 for maintaining a supply of 55 pizzas.
Service Level type 2 = 0.85 or 85%
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