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 $13.5. The holding cost is based on an 14% annual rate, and production setup costs are $155 per setup. The equipment on which the book is produced has an annual production volume of 20500 copies. Wilson has 250 working days per year, and the lead time for a production run is 17 days. Use the production lot size model to compute the following values:

1. Minimum cost production lot size. Do not round intermediate values and round your final answer to two decimal places.
   
   Q^* =
   
2. 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 =
   
3. Cycle time. Do not round intermediate values and round your final answer to two decimal places.
   
   T =  days
   
4. Length of a production run. Do not round intermediate values and round your final answer to two decimal places.
   
   Production run length =  days
   
5. Maximum inventory. Do not round intermediate values and round your final answer to two decimal places.
   
   Maximum inventory =
   
6. Total annual cost. Do not round intermediate values and round your final answer to two decimal places.
   
   Total cost = $  
   
7. Reorder point. Do not round intermediate values and round your final answer to two decimal places.
   
   r =

Answer 1

Annual demand, D= 7400 copies

Cost of one copy= $13.5

Holding cost per unit per year, H= 14% of 13.5= $1.89

Setup cost, S= $155

Annual production volume, P= 20500 copies

Number of working days per year= 250

Lead time= 17 days

Daily demand, d= 7400/250 = 29.6 copies

Daily production, p= P/250= 20500/250= 82 copies

a. Minimum cost production lot size
Q* = √[2DS/H(1-(D/P))]

       = √[2*7400*155/1.89(1-(7400/20500))]

        = 1378.18 copies

b. Number of production runs per year, N= D/Q

                                      = 7400/1378.18

= 5.37
c. Cycle time= Q/d

                      = 1378.18/29.6 = 46.56
T =  46.56 days

d. Length of a production run= Q/p

                                   = 1378.18/82= 16.81 days

e. Maximum inventory= Q[1-(D/P) ]

                                         = 1378.18[1-(7400/20500)
                                         =880.69 copies

f. Total annual cost= ½ Q[1-(D/P)]H+ (D/Q)S

                                           = (880.69*1.89)/2+ (7400/1378.18)*155

                                          = 1664.51
Total cost = $1664.51  

g. Reorder point= daily demand*lead time in days

                            = 29.6*17= 503.2 copies