Question

Winona Knit (WK), a wholesaler of wool sweaters, sources the sweaters from an Iowa company, Chilwool Inc. (CI), for $15 per sweater when ordered 3 months ahead of the selling season. WK’s wholesale price is $30. At the end of the selling season discount outlets buy the sweaters from WK at $13 each. WK’s demand forecast for the sweater is normally distributed with a mean of 2,500 sweaters and standard deviation of 1,200 sweaters.

The mismatch cost between supply and demand is defined as the cost of over ordering times the expected leftover inventory plus the cost of under ordering times the expected lost sales. If the cost of underage $12, cost of overage is $3 and WK orders 3,520 sweaters, what is WK’s approximate mismatch cost?

a. 1584

b. 1980

c. 3456

d. 3520

e. 5040

Answer 1

Mismatch Cost = C_o*Expected left over inventory+ C_u*Expected lost sales

where C_{o =} $3 and C_u= $12

Expected Lost sales: ? * L(z) where ? = standard deviation, lets calculate z value

z= (Q-µ)/? =(3520-2500)/1200=0.85 where µ = mean

Now looking the value of z in loss function table: L(0.85)= 0.10997

Expected Lost sales=  ? * L(z) = 1200 * 0.10997 = 131.96

Expected leftover inventory=Q-Expected sales =Q-(µ-Lost sales)= 3520 -(2500-131.96) = 1151.96

Expected mismatch costs= C_o*Expected left over inventory+ C_u*Expected lost sales

= (3*1151.96)+(12*131.96)= 5039.4

hence option e. 5040 is correct