Question

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7400 copies. The cost of one copy of the book is $13.50. The holding cost is based on an 18% annual rate, and production setup costs are $150 per setup. The equipment on which the book is produced has an annual production volume of 25,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 15 days. Use the production lot size model to compute the following values:

e. Maximum inventory

f. Total annual cost

g. Reorder point

Answer 1

Annual demand, D= 7400 copies

Number of working days per year= 250

Daily demand, d= 7400/250 = 29.6

Cost of one book= $13.50

Holding cost = 18 %( 13.50) = $2.43

Setup cost, S = $150

Annual production volume= 25,000

Hence daily production volume, p= 25000/250 = 100

Lead time for production run= 15 days

e. Economic production quantity, Q= √[2DS/H(1-(d/p))]

                                                     = √[2*7400*150/2.43(1-(29.6/100))

                                                      = 1139.17

maximum inventory= Q(1-d/p) = 1139.17(1-(29.6/100)) = 801.98

f. Total annual cost= Annual holding cost+ Annual setup cost

                              = Q/2[1-(d/p)]H+ (D/Q)S

                               = 1139.17/2[1-(29.6/100))2.43 + (7400/1139.17)150

                           = 974.4+974.4= $1948.8

g. When demand and lead time are constant,

reorder point= daily demand*lead time= 29.6*15 = 444 units