Question

Annual demand for an item is 1,250,000 units. The holding cost rate is 20% of the item cost. Ordering costs are $4 per order. Quantity discounts are available according to the schedule below: Quantity Price per Unit ($)

1-999 1.15

1,000-2,499 1.10

2,500-4,999 1.08

5,000+ 1.05

What is the total annual cost of your policy?

~$1,313,949

~$1,351,540

~$1,377,276

~$1,422,620

Assume 52 5-day weeks per year. If the lead-time is 1 weeks, what should the reorder point be? If necessary, round your final answer UP to the nearest whole number?

4,808

6,901

24,039

33,654

Answer 1

Annual demand(D) = 1250000 units

Ordering cost (S) =$4

Holding cost(H) = 20% of purchase price

Order size Price per unit Holding cost(20% of price per unit)

1-999 800 1.15 0.23

1000-2499 1.10 0.22

2500-4999 1.08 0.216

5000 or more 1.05 0.21

First find the minimum point for each price starting with the lowest price until feasible minimum point is located.This means until a minimum point falls in the quantity range for its price

Minimum point for price of 1.05 = √ (2DS/H)= √[(2X1250000X4)/0.21] = √( 10000000/0.21) = √47619047.619 = 6901 units.Because an order size of 6901 units will cost $1.05 , it is a minimum feasible point for $1.05 per unit.

Total cost for Q=6901 is (Q/2)H + (D/Q)S + (PriceXD)

= [(6901/2)0.21] + [(1250000/6901)4] + (1.05X1250000)

= 724.605 + 724.53 + 1312500

= $1313949.135 ~ 1313949

As $1.05 is the lowest unit price which has a minimum feasible point there is no need to calculate the total cost for other price ranges

So the total annual cost is $1313949

Number of weeks per year = 52

Average weekly demand (d) = D/number of weeks per year = 1250000/52 = 24039

Lead time(L) = 1 week

Reorder point = d × L = 24039 × 1 = 24039