Question

Inventory Modeling

A company needs about 250,000 carton of butter per month. Each butter order costs $17. It costs $1 in storage. The order is supplied at the same day of the order. One butter takes 0.05m2 of space.
In addition, the company needs 1,500 bags of flour per month. Each flour order costs $30. Each flour bag costs $1 in storage. The order is supplied at the same day of the order. One flour bag takes 2.5m2 of space. The company has a 5000m2 storage space.

1)The order quantity Y1(butter) ≅ *

2619 butter carton

$2916

2916 butter carton

$2619

2) The order quantity Y2(flour) = *

300 flour bags

$300

$303

303 flour bags

3) After applying the constraint ∑(?? ??)≤? we deduce that _______________ and _____________. *

the constraint is satisfied; Y(butter) & Y(flour bags) are not optimal.

the constraint is satisfied; Y(butter) & Y(flour bags) are optimal.

the constraint is violated & binding; must be accounted for

the constraint is violated; Y(butter) & Y(flour bags) are optimal.

4) TCU (Y(butter)) = *

K1/(D1/y1) + h1Y1/2 = $2915.47/month

K1/(y1/D1) + h1Y1/2 = $2915.47/year

K1/(y1/D1) + h1Y1/2 = $2915.47/month

K1/(D1/y1) + 2h1/Y1 = $2915.47/month

5) TCU (Y(flour)) = *

K2/(y2/D2) + h2Y2/2 = $300/month

K2/(D2/y2) + h2Y2/2 = $300/month

K2/(y2/D2) + h2Y2/2 = $300/year

K2/(D2/y2) + 2h2/Y2 = $300/month

Answer 1

Economic order quantity formula = √(2DO/C)

Where D = Requirement of the product

O = ordering cost per order

C = carrying cost per unit per year

(1) Given D = 250000 per month

O = 17$

C= 1$

Economic order quantity = √2*250000*17/1

= 2915.4759 or 2916 cartons of butter per day

Hence option 3 2916 butter cartons.

(2) Given D= 1500

O= 30$

C=1$

Economic order quantity =√2*1500*30/1 = 300 flour bags per day

Hence option 1 is the correct answer.

(3)The given constraint is satisfied and both products are optimal is the correct option.

Total cost = ordering cost + carrying cost

Ordering cost = number of orders*ordering cost per order

Number of orders = total quantity required/Economic order quantity

Carrying cost = carrying cost per unit * number of units per order/2

(4) Number of orders = 250000/2916 = 85.7389 orders

Ordering cost= 85.7389*17 = 1457.4760$

Carrying cost = 1*2916/2 =1458$

Total cost per month = 2915.4760

Hence option 3 is the correct answer where

K1 = ordering cost per order

D1 = total demand

Y1 = economic.order quantity

h1 = carrying cost per order

(5) Number of orders = 1500/300 = 5 orders

Ordering cost = 5*30 = 150$

Carrying cost = 1/2*300= 150$

Total cost = 150+150 = 300$

Hence option 1 is the correct answer

K2 = ordering cost of flour

D2 = demand of flour

Y2 = economic order quantity of flour

h2 = carrying cost of wheat flour