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 7,800 copies. The cost of one copy of the book is $13.5. The holding cost is based on an 21% annual rate, and production setup costs are $135 per setup. The equipment on which the book is produced has an annual production volume of 27,000 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:

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

Given,

Demand = 7800 copies

Price = $ 13.5

Holding cost = H = 13.5 x 0.21 = $ 2.835

Setup cost (S) = $ 135

Annual Production Capacity = 27000 units

Number of days = 250

Lead time = 14 days

(a)

Usage rate:

Consumption(u) = Demand / Working days = 7800/250 = 31.2 units / day

Production(P) = Annual Production rate / Number of Working days = 27000/250 = 108 units per day

Cost Production Lot Size:

EOQ =

EOQ = EOQ = 1022.078 = 1022 units

(b)

Number of Production runs per year = D/Q = 7800 / 1022 = 7.63 times per year

(c)

Cycle time = Q/u = 1022 / 31.2 = 32.75 days

(d)

Length of Production run = Q/P = 1022 / 108 = 9.46 days

(e)

Maximum Inventory = (Q/P) x (P-u) = (1022/108) x (108-31.2) = 726.528 = 727 units

(f)

Total Annual cost = Total Holding cost + Total Setup cost = (D/2)xH + Number of production runs in a year x Setup cost = (7800/2) x 2.835 + 7.63 x 135 = 11056.5 + 1030.05 = $12086.55

(g)

Reorder Point = Production / Lead Time = 108/14 = 7.714 = 8 units