Demand for an item is Normally distributed with a mean of 40

Demand for an item is Normally distributed with a mean of 400 units a week and a standard deviation of 60 units. Ordering and delivery cost $300, holding cost is $12 a unit a year and lead time is constant at 3 weeks. Describe an ordering policy that gives a 95 per cent cycle-service level. What is the cost of holding the safety stock in this case? How much would costs rise if the service level is raised to 98 per cent?

Solution

It is given that ,

Standard deviation of weekly demand = 60 units

Lead time = 3 weeks

Therefore,

Standard deviation of demand during lead time

= Standard deviation of weekly demand x Square root ( Lead time) = 60 x Square root ( 3 ) = 60 x 1.732 = 103.92

95 percent service level means in stock probability of 0.95

Corresponding Z value for in stock probability of 0.95 = NORMSINV ( 0.95) = 1.6448

Therefore, Required safety stock = Z value x Standard deviation of demand during lead time = 1.6448 x 103.92 = 170.92 ( 171 rounded to nearest whole number)

Reorder point = Average weekly demand x Lead time + Safety stock = 400 x 3 + 171 = 1200 + 171 = 1371

THE ORDERING POLICY WILL BE TO HAVE A REORDER POINT OF 1371

Cost of holding safety stock = Holding cost per unit per year x Safety stock = $12 x 171 = $2052

COST OF HOLDING SAFETY STOCK = $2052 A YEAR

Service level of 98 percent means in stock probability of 0.98

Corresponding Z value for in stock probability of 0.98 = NORMSINV ( 0.98 ) = 2.0537

Corresponding safety stock = Z value x Standard deviation of demand during lead time = 2.0537 x 103.92 = 213.42 ( 214 rounded to next higher whole number )

Cost of holding safety stock = Holding cost per unit per year x Safety stock = $12 x 214 = $2568

COST OF SAFETY STOCK AT SERVICE LEVEL OF 98 PERCENT WILL BE $2568 PER YEAR

THE ORDERING POLICY WILL BE TO HAVE A REORDER POINT OF 1371