6. The Italian eatery at the Student Union orders pre-made, frozen calzones from

Question

6. The Italian eatery at the Student Union orders pre-made, frozen calzones from a gourmet food
distributor. They cost $2.50 apiece and can be sold to students for $4 apiece. Fixed Order costs
are $10 per order, and orders always take 4 days to arrive. The demand over a term (for which
the eatery is open 100 days) averages 80 calzones a day, with a standard deviation of 20 calzones
per day. Holding costs are 10% of the Eatery’s purchase price.
a) What is the economic order quantity for calzones, and how often do we expect to place
this order? (800, 10)
b) What is the re-order point (ROP) for calzones if the management has specified that the
chance of a stock out during a cycle is 15.87%? (360)
c) Assume that we placed an order 3 days ago, and our inventory of calzones is at 85. What
is the chance we run out of calzones before the next order comes in? (40.13%)
d) What do we expect our holding costs of cycle stock and our fixed order costs to be per
term if we use the EOQ? (100, 100)
e) Bonus: The Eatery has decided to make calzones themselves. These are made
periodically in large batches, and everything not used that day is frozen. The daily
production rate, p, is 160 calzones. Assume that the holding cost, H, is now $.40/calzone
per term and S, the setup cost, is $16 per run. All other parameters remain unchanged.
What is the EPQ, and how often do we start a production cycle? How many days do we
run production? (1131, 14.14, 7.07)

**please provide example on how its done**

Explanation / Answer

Assuming,

C, Cost of each Calzone=$2.5
P is the price of each calzone=$4
D is the total demand of calzones=80 mean , std dev SD=20
H is the holding cost per unit=10% of purchase=2.5*0.10=.25$
Q is the quantity ordered each time an order is placed
S is the fixed cost of each order=$10

P production =160 calzones/day

Lead time L=4 days

For Economic order quantity (EOQ), Holding cost of inventory=cost of ordering

Holding cost of Inventory, HOI=holding cost*quantity/2, considering continuous depletion of quantity ordered=HQ/2

Cost of Ordering=Fixed cost per order*Avg Demand /Quantity ordered=SD/Q

For EOQ, HQ/2=SD/Q

a. Or Q=(2SD/H)^1/2=(2*10*80/.25)^1/2=800

. order frequency= order/demand=800/80=10day

b. Re order Point-15.87% chances of stock out implies 100-15.87=84.13% all demands fullfilled.

using normal distribution table, with 84.13 probability, z=1

demand during lead time=DXL=80*4=320

Std dev during lead time= SD*L1/2=20*2=40

Therefore, z=(x-320)/40

which implies that x=360 ie at 360 calzones in inventory, one should order

c. As order is placed 3 days ago, order will arrive in 1 day. Avg demand in 1 day=80

inventory=85 calzones

value of z=(85-80)/20=.25

using normal distribution curve probability with value of z is .0987 ie (50+9.87)=59.87% chances are that stock will not run out

therefore stock running out chances=100-58.97=41.13%

d. no: of orders=no of days/frequency of order=100/10=10 orders

Fixed ordering cost=10*10=100$

Holding cost=holding cost*Q/2=.25*400=100

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