Question

Problem 2: Clark Equipment manufactures and then sells the Model 10 bread slicer. It costs Clark $57 to produce a unit, and the estimated annual demand for slicers is 4500 units. The company used to hold 100 units safety stock to prevent occasional shortages. Clark uses 15% rate of holding cost a year, and setting up its production line each time a production run is planned costs $900. Production capacity for the bread slicers is 6000 units.

1. Clark tries to reduce its total costs by shifting to the optimal production and inventory policy. Answer questions 2-3, 2-4, and 2-5.
   
   3. What is the annual holding cost of the optimal production policy?
      a. 57*4500    b. 57*1946.66/2   c. 261515.98 – 4160.98     d. None of the above
      
   4. How many months of demand does one optimal lot size cover?
      a. 0.4326            b. 12/2.3117              c. 1946.66*0.4326     
      
   5. The slicers are stored in a storage space large enough to store 487 slicers. Is this space large enough to hold the amount of inventory at the end of the optimal production run? Show your work.

Answer 1

demand / production ration (d/p) = 4500/6000 = 0.75

EPQ = [ 2 x demand x set up cost / cost of holding one unit for a year x ( 1-d/p)]1/2

= [ 2 x 4500x900 / 0.15x57x(1-0.75)]1/2 =1947 units

annual holding cost = 1947/2* ( 1-0.75)*57*0.15+ 100*57*0.15

= 2935

None of the oprions is correct.

Months' demand covered = 1947 / (4500/12) =5.19

Option b is right

Max inventory = EPQ x ( 1-d/p) = 1946.66 x(0.25 ) =486.66

The space of 487 unitsis good enough to hold the maximum inventory as it is more than max inventory.