Question

Please show all the work

Question 1

A manufacturer produces umbrellas with the following parameters:

The monthly demand for umbrellas is 3000

Daily usage is 100 (assume 1 month = 30 days and demand is uniform throughout the month)

The production rate is 400 per day

Setup cost is $200 for a run

Holding cost is $1 per umbrella per month

What is the economic production quantity?

Question 2

Suppose a gas station has expected sales of 6000 gallons during lead time. Sales are normally distributed with a standard deviation of 400 gallons.

To avoid stockouts with probability P(z < +3.00), what should be the reorder point?

Question 3

Suppose a gas station has daily sales of 1500. Expected lead time is four days, normally distributed with a standard deviation of one day.

To avoid stockouts with probability P(z < +3.00), what should be the reorder point?

Question 4

Suppose a gas station has expected daily sales of 1500 gallons, normally distributed with a standard deviation of 400 gallons. Expected lead time is four days, normally distributed with a standard deviation of one day.

To avoid stockouts with probability P(z < +3.00), what should be the reorder point?

Question 5

Suppose a gas station has daily sales of 1500. Lead time is four days and orders are placed every Monday to arrive on Fridays.

What should the order quantities be if:

Safety stock and on-hand inventory at the time of ordering are zero?

Safety stock is 1000 gallons and on-hand inventory at the time of ordering is 3000 gallons?

Safety stock is 3000 gallons and on-hand inventory at the time of ordering is also 3000 gallons?

Question 6

A grocery store sells fresh cookies, which are only sold for one day. Any unsold cookies are donated to charity for a tax deduction:

Unit revenue is $1.00

Unit cost is $0.50

Unit salvage value is $0.20

What is the optimal service level?

Assume demand is normally distributed with mean = 200 and standard deviation = 25, and the z-score for the optimal service level was approximated as 0.3, what is the optimal stocking level?

Answer 1

Ans. 1) Annual demand (D)= 3000*12= 36000

Setup cost (S)= $200

Holding cost per unit per year (H)= $1*12= $12

Demand rate (d)= 100/day

Production rate (p)= 400/day

Optimal production quantity (Q_opt) =

=

= 1265 units

Ans.2) Re-order point(ROP) = average demand during lead time + Safety stock

ROP = d*L + ss

ROP = d*L + z

where, d= daily demand

L = lead time

z= number of standard deviations for a specified service probability =1.65 for 95% confidence level

   = standard deviation of usage during lead time

ROP = 6000 + 1.65*400 = 6000+ 660 = 6660 units

Ans. 3) d= 1500 ; L= 4 days, z=1.65, = 1 day,  = = =2

ROP= d*L + z = 1500*4 + 1.65*2 = 6003.3 6003 units

Ans. 4) d= 1500 gallons, L= 4 days, = 400 gallons,   = = = 894 gallons

ROP = 1500*4 + 1.65*894 = 7475 gallons

Ans. 5)a) d = 1500, L=4 days

ROP= d*L = 1500*4 = 6000 units

b)  Re-order point(ROP) = average demand during lead time + Safety stock - Inventory(I)

d =1500, L= 4 days, Safety stock= 1000, Inventory = 3000

ROP = d*L+ss-I = 1500*4 +1000 - 3000 = 6000+1000-3000 = 4000 gallons

c) Re-order point(ROP) = average demand during lead time + Safety stock - Inventory(I)

d = 1500, L =4 days, ss=3000, I= 3000

ROP = 1500*4 +3000 - 3000 = 6000+3000-3000 = 6000 gallons