Question

Retailers Warehouse (RW) is an independent supplier of household items to department stores. RW attempts to stock enough items for a 90 percent service probability.

A stainless steel knife set is one item it stocks. Demand (1,800 sets per year) is relatively stable over the entire year. Whenever new stock is ordered, a buyer must assure that numbers are correct for stock on hand and then phone in a new order. The total cost involved to place an order is about $5. RW figures that holding inventory in stock and paying for interest on borrowed capital, insurance, and so on, add up to about $3 holding cost per unit per year.

Analysis of the past data shows that the standard deviation of demand from retailers is about four units per day for a 365-day year. Lead time to get the order is seven days.

a. What is the economic order quantity? (Round your answer to the nearest whole number.)

Economic order quantity

sets

b. What is the reorder point? (Use Excel's NORMSINV() function to find the correct critical value for the given ?-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Reorder point

sets

Answer 1

To be calculated:

(a) Economic Order Quantity (EOQ)

(b) Reorder Point

Given values:

Service level = 90%

Annual demand = 1,800 sets per year

Cost of ordering, Co = $5

Holding cost, H = $3 per unit per year

Standard deviation, SD = 4 units per day

Lead time, LT = 7 days

Solution:

(a) Economic Order Quantity (EOQ) is calculated as;

EOQ = SQRT (2*D*Co) / H

where,

D = Annual demand

Co = Cost of ordering

H = Holding cost

EOQ = SQRT (2 x 1800 x 5) / 3

EOQ = SQRT (6000)

EOQ = 77.46 or 77 sets

EOQ = 77 sets

(b) Reorder point is calculated as;

R = dL + [z x (d) x SQRT (L)]

where, d = daily demand

z = z-value

(d) = Standard deviation in demand

L = Lead time

Using Excel’s NORMSINV() function, z-value for 90% service level is computed as;

NORMSINV (0.90) = 1.28

z = 1.28

Daily demand, d = (1800/365) = 4.93151

Putting the given values in the above formula, we get;

R = dL + [z x (d) x SQRT (L)]

R = (4.93151 x 7) + [1.28 x 4 x SQRT (7)]

R = 34.52057 + 13.54625

R = 48.06682

Reorder point = 48 sets