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 copies. The cost of one copy of the book is $13.5. The holding cost is based on an 20% annual rate, and production setup costs are $135 per setup. The equipment on which the book is produced has an annual production volume of 24,500 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

a.

Economic production quantity(EPQ) = Square root (((2*D*Cs)/Ch)*(p/(p-d))
where p = production rate = 24500/250 = 98, d = daily demand = 7600/250 = 30.4,D = annual demand = 7600
,Cs = setup cost = 135, Ch = holding cost = 13.5*20% = 2.7

Economic production quantity = Optimal production lot size = SQRT(((2*7600*135)/2.7)*(98/(98-30.4))) = 1049.654776 = 1050 (Rounded to nearest whole number)

b.

Number of production runs per year = 7600/1049.654776 = 7.240475796 = 7.24 (Rounded to 2 decimal places)

c.

Cycle time = Economic production quantity(EPQ)/demand rate = 1049.654776/30.4 = 34.52811763 = 34.53 days (Rounded to 2 decimal places)

d.

Production run length = Economic production quantity(EPQ)/production rate = 1049.654776/98 = 10.71076302 = 10.71 days (Rounded to 2 decimal places)

e.

Maximum inventory = EPQ*(1-(demand rate/production rate)) = 1049.654776*(1-(30.4/98)) = 724.0475802 = 724 (Rounded to nearest whole number)

f.

Total annual cost = setup cost + holding cost + purchase cost

=(7600/1049.654776)*135+(1049.654776/2)*2.7+7600*13.5 = 104994.4982 =104994 (rounded to nearest dollar)

g.

reorder point = daily demand*lead time = 30.4*15 = 456