Question

Anna owns and operates a small bagel shop in Montreal, Canada. She is constantly baking bagels which are sold fresh out of the oven and customers line up to purchase them. She manages the inventory of the bread flour used to make the bagels very carefully. The quantity of bread flour she uses is exactly equal to 21 kilos per day (which makes exactly 210 bagels). The selling price of a bagel is $1. The bread flour is purchased from a supplier at a cost of $2 per kilo, plus a fixed delivery fee of $60 per order (no matter what the order size is). Orders for flour are always received exactly 2 days after they are placed. On a day when a flour delivery is scheduled to arrive, Anna hires her friend Gilbert to help with the receiving and storing of the bread flour. She always pays him $40 for the job, no matter what the quantity delivered is and how long it takes him to do the work. The bread flour is stored in a dry storage room which is kept at a constant temperature at all times of the day and night. The electricity cost associated with the storage room is estimated at $10 per week (this amount does not vary with the quantity of flour stored in the storage room). Anna currently gets a 1.5% interest rate on her savings’ account annually. She plans to invest any cash the bagel business generates into an exciting business opportunity (mass market gluten‐free bagels) promising an amazing return on investment of 3% per week. Assume 50 weeks per year and 7 days per week.

(a) How much should Anna order every time she orders from the bread flour supplier in order to minimize her cost per week?

(b) Assume she follows your suggestion from

.i. How many orders does she place per year?

ii. What is her total cost per week?

(c) Suppose the setup cost (ordering cost) gets multiplied by 4, how much should she order now in order to minimize her cost per week?(

d) Assume she follows your suggestion when the setup cost gets multiplied by 4.

i. How many orders does she place per year?

ii. What is her total cost per week?

Note:

Demand per week: D = 21 kilos of flour day = 147 kilos bags per week.

Cost of flour per kilo: C = $2 per kilo.

Ordering cost per order: K = $60 + 40 = $100.

Holding cost per kilo per week: h = 0.03 x 2 = $0.06 per kilo per week

The $1 selling price, the 1.5% interest rate and $10 electricity cost are not relevant numbers for the EOQ analysis.

Answer 1

ANSWER

Ordering cost for Anna = 60+40 =100

Annual quantity in Kgs. = 21x50x7 = 7350

Inventory holding cost = 2x1.5/100 =0.03 per unit per annum

EOQ = [ 2 x demand xordering cost / holding cost of a unit per year]^1/2

EOQ = [ 2 x 7350 x100/0.03]^1/2 = 7000 kgs

(b)

Number of orders per annum = 7350/7000 =1.05

Total cost per week = Ordering cost + holding cost

= 100x 1.05/50 +7000/2 x 0.03/50 + 10 =2.1+105/50+10 = 14.2

(c)

If set up cost increases by 4 fold, the EOQ which is directly proportional to the square root of the quantity will be dloubled. The quantity now will be 14000 units.

(d)

Number of orders = 7350/14000 =0.525 per year
Weekly cost = 0.525 x100 /50 + 14000/2 x0.03/50 +10 =15.25

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