Marie, is the second in command at Mathilda’s Bakery & Cakes and she is in charg

Question

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.

Mathilda and Marie are evaluating two products.

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. (The original CSL for king roll is 0.861, order quantity is 708, and the original CSL for whole wheat bread 0.795, order quantity is 91.

King roll normal mean distribution is 575, Standard deviation is 123

Whole Wheat bread normal mean distribution is 56, Standard deviation is 43

King Rolls Whole Wheat Bread Selling price (Euro per unit) 0.22 4.75 Production cost (Euro per unit) 0.022 0.95 Disposal cost (Euro per unit) 0.01 0.03

Explanation / Answer

The unit cost of king rolls(c)=0.022

Selling price (p) = 0.22

Salvage value(s)= disposal cost = -0.01

Here negative sign is taken as it is another cost that has to be incurred to dispose of the extra unit

Cost of underage(Cu) = p-c= 0.22-0.022= 0.198

Cost of overage(Co) = c-s= 0.022-(-0.01)=0.032

Critical ratio = Cu/Cu+Co=0.198/(0.198+0.032)=0.8608=0.861

This is the optimal service level

With the required service level the optimal order quantity would be

Mean demand+z*standard deviation of demand= 575+z*123

For 99% service level z= norm.s.inv(0.99)=2.33

Putting z value

Q*= 575+2.33*123= 861.59=862

With original service level=0.861

z= norm.s.inv(0.861)=1.085

Order quantity = 575+1.085*123=708 quantity

next we need to determine the optma order quantity for whole wheat bread

selling price(p)=4.75

Production cost (c)= 0.95

Salvage value(s)=-0.03

Cu= p-c= 3.8

Co= c-s=0.98

Critical ratio= Cu/Cu+Co= 3.8/3.8+0.98=0.795

Order quantity with this service level= 56+norm.s.inv(0,795)*43=56+0.824*43=91 units

Order quantity with 99% service level = 56+norm.s.inv(0.99)*43= 156.62=157 units

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