Question

A company produces plastic powder in lots of 2000 pounds at the beginning of each week. The company uses the powder in an injection moulding process at the steady rate of 50 pounds per hour for an eight-hour day, five days a week. The manager has indicated that the cost of placing an order is $100, but “we really have not determined what the holding cost is”. (1) What weekly holding cost rate does the lot size imply, assuming the lot size 2000 is optimal? (2) Suppose the figure you compute for weekly holding cost rate has been shown to the manager, and the manager says that it is not that high. Would that mean the lot size 2000 is too large or too small? Explain in at most two sentences

Answer 1

Weekly demand of powder to be used in an injection moulding process

= 50 Pounds / hour x 8 hours/ day x 5 days/ week

= 2000 pounds per week

Therefore , Annual demand of powder= D = 2000 Pounds/ week x 52 weeks = 104000 Pounds

Order Cost = Co = $100

Let, annual unit holding cost = $ Ch

Therefore Optimal lot size ( EOQ )

= square root ( 2 x Co x D/ Ch )

= Square root ( 2 x 100 x 104000/Ch)

= Square root ( 20800000/Ch)

Given, Optimal lot size = 2000

Therefore ,

Square root ( 20800000/Ch) = 2000

Or, 20800000/Ch = 4000000

Or, Ch = 20800000/4000000

Or, Ch = $5.2

Annual unit holding rate = $5.2

Therefore , weekly unit holding rate = $5.2 / 52 = $0.1

WEEKLY UNIT HOLDING RATE = $0.10

Annual unit holding rate = Ch

In that case , total annual holding cost = Ch x Optimal lot size / 2

If the manager means that total annual holding cost is not too high when he utters “ that it is not that high”, we can assume that Optimum lot size is not too high since annual holding cost is proportional to optimum lot size