Question

Ye' Olde Barrel Shop sells oak barrels to a local winery. The Master Cooper would like to reduce her oak lumber inventory by determining the optimal number of oak boards to order. the annual demand averages 50,000 boards and the order cost is $15.00 per order. Holding cost is estimated to be 10%. the purchase cost of each board is $6.00. The standard deviation of daily demand is 4 boards. The standard deviation of lead time is 2.0 days. Assume 268 days in the year and an average lead time of 4 days. If a service level of 98% (Z = 2.06) is desired during the reorder interval, what is the reorder point? Remember you cannot order partial units, round to the nearest whole unit in the LAST step.

Group of answer choices:

~748

~771

~1,122

~1,519

Answer 1

Annual demand (D) = 50000 units

Number of days per year = 268 days

Average daily demand (d) = D/number of days per year = 50000/268 = 186.5671641 units

Lead time(L) = 4 days

Standard deviation of lead time ($\sigma$L) = 2 days

Standard deviation of daily demand ($\sigma$d) = 4 units

At 98% service level value of Z = 2.06

Standard deviation of demand during lead time ($\sigma$dL) = √[(L × square of $\sigma$d) + (square of d × square of $\sigma$​​​​​L)]

= √[(4 × square of 4) + (square of 186.5671641 × square of 2) ]

= √[(4 × 16) + (34807.30673 × 4) ]

= √(64+139229.2269)

= √139293.2269

= 373.2200784 units

Reorder point = d × L + (Z × $\sigma$dL)

= 186.5671641 × 4 + (2.06 × 373.2200784)

= 746.2686564 + 768.8333615

= 1515.102017

~1519