Question

TchotchkesRUs must determine the size of production runs for a certain type of product.

The demand has been fairly steady at 5 million per year, and currently it is being produced in batch sizes of 100,000.

The cost of setting up for each production run is $800.

Assume that the material cost for each product is $0.85, labor cost is $0.45 and the distribution cost is $0.15 and the interest rate of the opportunity cost of alternative investment and storage cost is at 25% value of each item.

a) What is the optimal value of the EOQ for this product?

b) What is the additional cost resulting from using the wrong production size that they are currently using: 50,000?

Answer 1

A.

EOQ = Root (2DO/C)

D = Annual demand

O = Ordering Cost

C = carrying cost

= Root {[(2*5000000*800)]/[(0.85+0.15+0.45)*25%]}

= 148556 units

Total cost at EOQ level of production = Cost of Units + Ordering Cost + Carrying Cost

= 5000000*1.45 + (5000000/148556)*800 + (148556/2)*1.45*25%

= 7250000 + 26926 + 26926

= $ 7303852

B.

If current production is 50000 units

Total costs = Cost of Units + Ordering Cost + Carrying Cost

= 5000000*1.45 + (5000000/50000)*800 + (50000/2)*1.45*25%

= 7250000 + 80000 + 9063

= $ 7339063

If Current production is 100000 units

Total costs = Cost of Units + Ordering Cost + Carrying Cost

= 5000000*1.45 + (5000000/100000)*800 + (100000/2)*1.45*25%

= 7250000 + 40000 + 18125

= $ 7308125

If 50000 units are produced, Costs from current production i.e 100000 increases by 30938 and from EOQ by 35211.

Cost of current production are up by EOQ by 4273.