Question

 An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $1.50 each. It is estimated that the cost of order processing and receipt is $100 per order. The company uses an inventory carrying charge based on a 25 percent annual interest rate. The monthly demand for the filter follows a normal distribution with mean 280 and standard deviation 70. Order lead time is assumed to be five months. Assume that if a filter is demanded when the warehouse is out of stock, then the demand is back-ordered, and the cost assessed for each back-ordered demand is $12.80. Determine the optimal values of the order quantity and the reorder level. Q= R=

Answer 1

Answer:

Given data,

Monthly average demand, d = 280
Std. dev of monthly demand, s = 70
Annual demand, D = 280*12 = 3360
Ordering cost, K = $100
Cost per item = $1.5
Average lead time, L = 5 months
Carrying cost, h = 25%*1.5 = $0.375
Backordering cost, b = $12.80

Optimal order quantity,

Q = √ (2.D.K.(h+b) / h.b) = √ (2*3360*100*(0.375+12.8)/(0.375*12.8))

Q = 1,358

If type-I service level = 95%

Z = NORMSINV (0.95) = 1.645

Safety stock, SS = Z * s * √L = 1.645*70*√5 = 257

Reorder point, R = d.L + SS = 280*5 + 257 = 1,657