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 6,800 copies. The cost of one copy of the book is $14. The holding cost is based on an 21% annual rate, and production setup costs are $155 per setup. The equipment on which the book is produced has an annual production volume of 22,500 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. 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

a.

Economic production quantity(EPQ) = Square root (((2*D*Cs)/Ch)*(p/(p-d)) where p = production rate = 22500/250 = 90, d = daily demand = 6800/250 = 27.2
,D = annual demand = 6800
,Cs = setup cost = 155, Ch = holding cost = 21%*14 =2.94

Economic production quantity = Optimal production lot size = SQRT(((2*6800*155)/2.94)*(90/(90-27.2))) = 1013.6851186 1014 (Rounded to nearest whole number)

b.

Number of production runs = Annual demand/EPQ = 6800/1013.6851186 = 6.708197484 = 6.71 (rounded to 2 decimal places)

c.

Cycle time = EPQ/d = 1013.6851186 / 27.2 = 37.2678352426 = 37.27 days (rounded to 2 decimal places)

d.

length of production run = EPQ/p = 1013.6851186 / 90 = 11.2631679843 = 11.26 days (rounded to 2 decimal places)

e. Maximum inventory = EPQ*((p-d)/p) = 1013.6851186*((90-27.2)/90) = 707.326949401 = 707 (Rounded to nearest whole number)

f.

Total annual cost =(1/2)(EPQ/p)(p-d)Ch+(D/EPQ)Cs = (1/2)(1013.6851186 / 90)*(90-27.2)*2.94+(6800/1013.6851186)*155 = 2079.5412316 = 2080 (rounded to nearest whole number)

g.

Reorder point = lead time deman = (6800/250)*17 = 462.4