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 7,600 coples. The cost of one copy of the book is $11.50. The holding cost is based on an 18% annual rate, and production setup costs are $150 per setup. The equipment with 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. (Round your answers to two decimal places.) (a) Minimum cost production lot size (b) Number of production runs per year (c) Cycle time (d) Length of a production run (in days) (e) Maximum inventory (f)Total annual cost in $ (g) Reorder point

Answer 1

Answer:

Given data,

Annual demand (D) = 7600 copies

Cost of the book (C) = $11.50

Holding cost (H) = 18% of cost of book = 18% of $11.50

Holding cost (H) = $2.07

Setup costs (S) = $150

Annual production volume = 25,000 copies

Number of working days = 250

Lead time (L) = 15 days

Daily demand (d) = Annual demand / Number of working days = 7600 / 250 = 30.4 copies

Daily production (p) = Annual production / Number of working days = 25000 / 250 = 100 copies

(a) Minimum cost production lot size (Q):

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

Q = SQRT [(2 x 7600 x $150) / $2.07 x (1 – 30.4/100)] = 1258

Minimum cost production lot size (Q) = 1258 copies

(b) Number of production runs:

Number of production runs = Annual demand (D) / Production quantity (Q)

Number of production runs = (7,600 / 1258) = 6.041 runs per year

(c) Cycle time:

Cycle time = Production quantity (Q) / Daily demand (d)

Cycle time = 1258 / 30.4 = 41.38 days

(d) Length of a production run:

Length of production run = Production quantity (Q) / Daily production (p)

Length of production run = 1258/ 100 = 12.58 days

(e) Maximum inventory (Imax):

Imax = Q x (1 - d/p)

Imax = 1258x (1 – 30.4/100) = 875.56

Maximum inventory = 875.56copies

(f) Total annual cost:

Total annual cost = Annual holding cost + Annual setup cost

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

Total annual cost = [(1258/ 2) x $2.07 x (1 – 30.4/100)] +  [(7,600 / 1258) x $150]

Total annual cost = $906.21 + $ 906.2

Total annual cost = $ 1812.4

(g) Reorder point:

Reorder point = Daily demand x Lead time

Reorder point = 30.4 x 15

Reorder point = 456 copies