Question

Weekly demand for electric motors at a Japanese motor manufacturer is normally distributed, with a mean of 1,000 and a standard deviation of 1,000. Motors are currently assembled in China and delivered at a cost of 20,000 yen/motor. The supplier takes eight weeks to supply an order. A local Japanese manufacturer has offered to deliver motors with a lead time of one week at a cost of 20,400 yen per motor. The motor manufacturer monitors its inventory continuously. The manufacturer incurs an annual holding cost of 25 percent. Develop a chart showing total annual cost vs. desired CSL for each of the two alternatives. At what CSL value, the motor manufacturer would be indifferent between the two alternatives?

Answer 1

Average weekly demand, = 1000

Average annual demand, D = 52*1000 = 52,000 (considering 52 weeks per year)

Standard deviation of weekly demand, = 1000

Annual holding charge, i = 25%

Chinese supplier

Unit cost, c = 20000 yen

Lead time, L = 8 weeks

Annual holding cost, H = i*c = 20000*25% = 5000

Japanese supplier

Unit cost, c = 20400 yen

Lead time, L = 1 week

Annual holding cost, H = i*c = 20400*25% = 5100

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Transit inventory = *L

Safety stock = z**L

Total annual cost = Carrying cost of transit inventory + Carrying Cost of safety stock

= D*c + H**L + H*z**L

Chart showing annual cost vs desired CSL is as follows:

EXCEL FORMULA:

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In the above chart, we see that for Desired CSL of 6%, Total annual cost are approximately same for both alternatives. Therefore,

At CSL of 6%, the motor manufacturer would be indifferent between the two alternatives.