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 6,900 copies. The cost of one copy of the book is $12. The holding cost is based on an 18% annual rate, and production setup costs are $130 per setup. The equipment on which the book is produced has an annual production volume of 24,000 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:

1. Minimum cost production lot size. Round your answer to the nearest whole number. Do not round intermediate values.
   
   Q^* =
   
2. Number of production runs per year. Round your answer to two decimal places. Do not round intermediate values.
   
   Number of production runs per year =
   
3. Cycle time. Round your answer to two decimal places. Do not round intermediate values.
   
   T = _________ days
   
4. Length of a production run. Round your answer to two decimal places. Do not round intermediate values.
   
   Production run length = _________ days
   
5. Maximum inventory. Round your answer to the nearest whole number. Do not round intermediate values.
   
   Maximum inventory = _______
   
6. Total annual cost. Round your answer to the nearest dollar. Do not round intermediate values.
   
   Total annual cost =_________ $  
   
7. Reorder point. Round your answer to the nearest whole number. Do not round intermediate values.
   
   r = ___________

Answer 1

Demand for book – D = 6900 copies

Set up cost = C = $130

Annual unit holding cost = I = 18% of $12 = $2.16

Daily demand for books =d = 6900/250 days = 27.6

Daily production capacity = p = 24000/250 = 96

a) Minimum cost production lot size (EPQ)

= Square root ( 2 x 6900 x 130/2.16 x ( 96/96 -27.6))

= Square root ( 2 x 6900 x 130/2.16 x ( 96 /68.4)

= 1079.67 ( 1080 rounded to nearest whole number)

b) Number of production runs per year

= Annual demand/ EPQ

= 6900/1080

= 6.39

c) Cycle time =EPQ/Annual demand x 250 days = (1080/6900 ) x 250 =39.13 days

d) Length of production run = 1080/96 = 11.25 days

e) Maximum inventory = EPQ/p x ( p – d) =(1080/96) x ( 96 – 27.6) = 769.5

f) Annual set up cost = Set up cost x number of production runs= $130 x 6.39 = $830.7

Annual inventory holding cost = I x Maximum inventory/2 = $2.16 x 769.5/2 =$831

Annual cost of books = $12 / book x 6900 books annually= $82800

Total cost = $830.7 +$831 + $82800 = $84461.7

g) Reorder point = Daily demand xLead time = 27.6 x 15 = 414 books