Mathilda’s Bakery & Cakes is a local chain offering breads, rolls, and cakes in
ID: 391396 • Letter: M
Question
Mathilda’s Bakery & Cakes is a local chain offering breads, rolls, and cakes in Germany. The owner, Mathilda, is working on her expansion plans. Marie, is the second in command at Mathilda’s Bakery & Cakes and she is in charge of all operations related activities.
Mathilda’s Bakery & Cakes follows a traditional production concept. They bake breads and rolls early in the morning to fill the daily demand at a store. If they make too few breads or rolls they run the risk of not satisfying all customers that come in and loose the margin. If they make too many breads or rolls they may have left over products which they have to throw away. Discarding left over products incurs an additional disposal fee. (So if too many products are made, not only the materials and labor is wasted, but also, an additional disposal fee has to be paid to throw away excess products.)
Mathilda and Marie are evaluating two products.
King Rolls Whole Wheat Bread
Selling price (Euro per unit) 0.2 4.28
Production cost (Euro per unit) 0.02 0.856
Disposal cost (Euro per unit) 0.01 0.03
Calculate the optimal cycle service level for King Rolls and Whole Wheat Bread.
Optimal cycle service level for king rolls:
Round your answer to four decimal digits.
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Optimal cycle service level for whole wheat bread:
Round your answer to four decimal digits.
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Question 2
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Mathilda and Marie analyze past daily demand for King Rolls and Whole Wheat Bread. According to their analysis daily demand for both products follows a Normal distribution. The parameters of the Normal Distribution are shown in the following table.
King Rolls Whole Wheat Bread
Mean 683 59
Standard Deviation 166 36
Identify an appropriate model from our course considering the information provided above and the results from Question 1 to calculate the optimal number of King Rolls and Whole Wheat Bread to be baked every morning.
Optimal quantity for King Rolls:
Round your answer to the nearest integer.
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Optimal quantity for Whole Wheat Bread:
Round your answer to the nearest integer.
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Question 3
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The optimal quantity you calculated in Question 2 increases...
Select all correct answers
...if the service level decreases.
...if the shortage costs increase or the excess costs decrease.
...if the product's margin decreases.
...if mean or standard deviation of the demand distribution increase.
None of the above
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Question 4
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Calculate the expected units short and the expected profit for both products using the information provided in Question 1 and Question 2.
Expected units short for King Rolls:
Round your answer to two decimal digits.
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Expected profit for King Rolls:
Round your answer to two decimal digits.
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Expected units short for Whole Wheat Bread:
Round your answer to two decimal digits.
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Expected profit for Whole Wheat Bread:
Round your answer to two decimal digits.
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Question 5
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Mathilda wants to expand her business. She is planning on offering large supermarkets to run a bakery in the supermarket as a shop-in-shop concept. Unfortunately, supermarkets demand from their shop-in-shops to have product on the shelfs until the end of the day. That is, stockouts must be avoided.
To implement this strategy Mathilda and Marie decide to set a cycle service level of 99% for the products.
Calculate for both products the optimal quantity and the additional shortage cost that are implied when Mathilda and Marie use a 99% cycle service level. Use all the provided in Question 1 and Question 2.
Optimal quantity for King Rolls if cycle service level is 99%:
Round your answer to the next integer.
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Additional shortage costs for King Rolls if cycle service level is 99%:
Round your answer to two decimal digits.
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Optimal quantity for Whole Wheat Bread if cycle service level is 99%:
Round your answer to the next integer.
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Additional shortage costs for Whole Wheat Bread if cycle service level is 99%:
Round your answer to two decimal digits.
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Explanation / Answer
The problem is solved by applying newsvendor problem method:
Product
Kings Roll
Whole wheat Bread
Selling Price (p)
0.2
4.28
Production cost (c)
0.02
0.856
Disposal Cost (s)
0.01
0.03
Cu = under-stocking cost = cost of shortage (underestimate demand) = Sales price/unit – Cost/unit
Cu = 0.2 – 0.02
Cu = 0.18
Cu = 4.28 – 0.856
Cu = 3.424
Co = Over-stocking cost = Cost of overage (overestimate demand) = Cost/unit – Salvage value/unit
Co = c – s = 0.02 – 0.01
Co = 0.01
Co = c – s = 0.856 – 0.03
Co = 0.826
The service level or optimal probability of not stocking out, is set at,
Service Level = critical ratio = Cu/( Cu + Co)
SL = 0.18/(0.18 + 0.01)
SL = 0.9473
SL = 94.73%
SL = 3.424/(3.424 + 0.826)
SL = 0.8056
SL = 80.56%
Mean Demand (µ)
µ = 683
µ = 59
Standard Deviation ()
= 166
= 36
Optimal Order Quantity = [=Norminv(service level,µ, )]
**from excel
Q* =Norminv(0.9473,683, 166)
Q* = 951.79
Q* =Norminv(0.8056,59, 36)
Q* = 90.02
Q 1:
Optimal cycle service level for king rolls = 0.9473 or 94.73%
Optimal cycle service level for Wheat bread = 0.8056 or 80.56%
Q2.
Optimal quantity for King Rolls = 951.79 or 952
Optimal quantity for Wheat bread = 90.02 or 90
Product
Kings Roll
Whole wheat Bread
Selling Price (p)
0.2
4.28
Production cost (c)
0.02
0.856
Disposal Cost (s)
0.01
0.03
Cu = under-stocking cost = cost of shortage (underestimate demand) = Sales price/unit – Cost/unit
Cu = 0.2 – 0.02
Cu = 0.18
Cu = 4.28 – 0.856
Cu = 3.424
Co = Over-stocking cost = Cost of overage (overestimate demand) = Cost/unit – Salvage value/unit
Co = c – s = 0.02 – 0.01
Co = 0.01
Co = c – s = 0.856 – 0.03
Co = 0.826
The service level or optimal probability of not stocking out, is set at,
Service Level = critical ratio = Cu/( Cu + Co)
SL = 0.18/(0.18 + 0.01)
SL = 0.9473
SL = 94.73%
SL = 3.424/(3.424 + 0.826)
SL = 0.8056
SL = 80.56%
Mean Demand (µ)
µ = 683
µ = 59
Standard Deviation ()
= 166
= 36
Optimal Order Quantity = [=Norminv(service level,µ, )]
**from excel
Q* =Norminv(0.9473,683, 166)
Q* = 951.79
Q* =Norminv(0.8056,59, 36)
Q* = 90.02