Q1] Given the following demand for your pizza and your capacity for the next 5 m
ID: 365421 • Letter: Q
Question
Q1] Given the following demand for your pizza and your capacity for the next 5 months:
Month
1
2
3
4
5
Demand
45
75
15
55
60
Capacity
60
65
60
50
50
1-Is this plan feasible at all?
2-If it is - perform a Lot-Shifting so you get a strictly feasible production vector?
3- Each setup costs you $50 and the holding costs are $1 per item per period. How much will you pay to extend your capacity in Period 5 from 50 to 60 parts?
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?
Month
1
2
3
4
5
Demand
45
75
15
55
60
Capacity
60
65
60
50
50
Explanation / Answer
Doing the Lot shifting will give you the answer to qn 1.1. So let us do the Lot shifting which is the answer for Qn 1.2
The lot shifting method repeatedly does the following: We have to find the first period with less capacity than demand. If possible, back-shift the excess demand to some prior periods. Continue. If it is not possible to back-shift the excess capacity to some prior periods, stop. Then there is no feasible solution.
Demand Capacity
Month 1 45 60
Month 2 75 65
Month 3 15 60
Month 4 55 50
Month 5 60 50
When we go month by month, we see that here in month 2, the demand exceeds capacity by 10. So the excess demand of 10 is moved to Month 1 which can take this demand. So Demand in Month 1 will be revised to 55 (45 + 10).
Same way, as we go down, we see that in Month 4, demand exceeds capacity by 5. So we can move this 5 to month 3 as demand is very low there. So Month 3 demand becomes 15 + 5 = 20.
Again in Month 5 we see that demand exceeds capacity by 10. This also can be moved to Month 3 and so the revised demand in Month 3 becomes 20 + 10 = 30.
So after Lot shifting the demand and capacity will look like this.
Demand Capacity
Month 1 55 60
Month 2 65 65
Month 3 30 60
Month 4 50 50
Month 5 50 50
So the answer to the first question is yes, the plan is feasible.
In Qn 1.3, if we extend capacity from 50 to 60, we do not need to make 10 units in advance by two months. So you can save $ 1 x 10 units x 2 months = $ 20. But your setup cost is $50 So final cost is $ 30.
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