Question

Problem 14-13 (Algorithmic)

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 6900 copies. The cost of one copy of the book is $14.50. The holding cost is based on an 15% annual rate, and production setup costs are $160 per setup. The equipment on which the book is produced has an annual production volume of 21500 copies. Wilson has 250 working days per year, and the lead time for a production run is 14 days. Use the production lot size model to compute the following values:

a) Minimum cost production lot size. Do not round intermediate values and round your final answer to two decimal places.

Q* =

b) Number of production runs per year. Do not round intermediate values and round your final answer to two decimal places.

Number of production runs per year =

c) Cycle time. Do not round intermediate values and round your final answer to two decimal places.

T = ___ days

d) Length of a production run. Do not round intermediate values and round your final answer to two decimal places.

Production run length = ___ days

e) Maximum inventory. Do not round intermediate values and round your final answer to two decimal places.

Maximum inventory =

f) Total annual cost. Do not round intermediate values and round your final answer to two decimal places.

Total cost = $

g) Reorder point. Do not round intermediate values and round your final answer to two decimal places.

r =

Answer 1

a) Optimum Lot Size =

here, A= annual demand, S = setup cost, H = holding cost @ of 15% of production cost.

optimum lot size= = 1007.56 copies.

b) no. of production runs = annual demand/ optimal lot size = 6900/1007.56 = 6.85 runs

c) cycle time :

no. of units in 1 production run that can be produced= 21500/6.85 = 3138.69 units

lead time for 3138.69 units = 14 days

lead time for 1007.56 units = 14*1007.56/3138.69 = 4.49 days.

f) total cost = optimal production size*cost of production*no of runs + set up cost*no of runs + holding cost * no of order = 1007.56*14.5*6.85 + 160*6.85 + 2.175*6.85 = $101186.80