Question

Daily demand for neckties at a MegaMart store is normally distributed with a mean of 20 units and a standard deviation of 7. The supplier, Suits Galore, takes on average about 9 days to supply a MegaMart order. The standard deviation of lead time is 3 days. MegaMart is targeting a customer service level of 95 percent (z = 1.65) and monitors its inventory continuously. How much safety inventory of neckties should MegaMart carry? What should their reorder point (ROP) be?

Megamart should carry 105 units of safety stock and should order their optimal quantity at 285 units

Megamart should carry 117 units of safety stock and should order their optimal quantity at 305 units

Megamart should carry 93 units of safety stock and should order their optimal quantity at 354 units

Megamart should carry 98 units of safety stock and should order their optimal quantity at 272 units

Answer 1

Mean daily demand for neckties ()= 20

Standard deviation of demand (_d)= 7

Desired service level = 95 percent (Z = 1.65)

Mean of lead time () = 9 days

Standard deviation of lead time (_l) = 3 days

Re-order point = * + Z

where the 2nd term, i.e. Z represents the safety stock

= 20 * 9 + 1.65(

= 180 + 1.65(63.56)

= 180 + 104.88

= 180 + 105

= 285 units approximately

The safety stock is the second term , i.e. 105 units

Hence Megamart should carry 105 units of safety stock and should order their optimal quantity at 285 units