Weekly demand for private label washing machines at Karstadt, a German departmen

Question

Weekly demand for private label washing machines at Karstadt, a German department store chain, is normally distributed with a mean of 500 and a standard deviation of 300. Karstadt currently has a supply source in China that delivers machines at a cost of 200 euro. The lead time required by the supplier is normally distributed with a mean of nine weeks and a standard deviation of six weeks. A European supplier has offered to deliver washing machines with a guaranteed lead time of one week at a cost of 210 euro. Karstadt has a holding cost of 25 percent and targets a cycle service level of 99 percent. Should Karstadt accept the local supplier’s offer?

Explanation / Answer

Standard deviation of demand at store during lead time for the Chinese supplier

= Square root ( Standard deviation of weekly demand^2x Lead time + Weekly demand^2 x Standard deviation of lead time^2)

= Square root ( 300^2x9 + 500^2 x 6^2)

= Square root ( 810000 + 250000 x 36)

= Square root ( 810000 + 9000000)

= Square root ( 9810000)

= 3132 ( rounded to nearest whole number )

Standard deviation of demand during lead time of 1 week for the store for the local supplier ( with ZERO standard deviation of lead time )

= Square root ( 300^2 x 1)

= 300

Z value for service level of 99 percent = NORMSINV ( 0.99) = 2.326

Therefore,

Safety stock to be maintained for Chinese supplier

= Z x Standard deviation of demand during lead time for Chinese supplier

= 2.326 x 3132

= 7285.032

Safety stock to be maintained for local supplier

= Z value x Standard deviation of demand during lead time of 1 week

= 2.326 x 300

= 697.8

Thus annual locked upmoney in terms of safety stock

= 25 percent of unit value of washing machine x safety stock

Therefore locked up money in safety stock to be maintained for Chinese supplier

= 25 percent of Euro 200 x 7285.032

= Euro 364251.6

Locked up money in terms of safety stock to be maintained for local supplier

= 25 percent of Euro 210 x 697.8

= Euro 36634.50

Therefore additional annual locked up money due to excess safety stock to be maintained for Chinese supplier

= Euro 364251.6 – Euro 36634.50

= Euro 327617.1

Average weekly demand for the store = 500

Therefore , annual demand = 500 x 52 = 26000

Savings in sourcing from Chinese supplier due to cheaper price

= ( Euro 210 – Euro 200 ) x 26000

= Euro 260000

However savings of Euro 260,000 in sourcing from Chinese supplier gets much nullified by additional annual locked up money of Euro 327617.10, making a net annual disadvantage for Chinese supplier = Euro 327617.10 – Euro 260000 = Euro 67610.10

Thus overall offer from local supplier is cheaper.

KARSTADT SHALL ACCEPT LOCAL SUPPLIER’S OFFER

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