8. One item a computer store sells is supplied by a vendor who handles only that

Question

8.

One item a computer store sells is supplied by a vendor who handles only that item. Demand for that item recently changed, and the store manager must determine when to replenish it. The manager wants a probability of at least 96 percent of not having a stockout during lead time. The manager expects demand to average a dozen units a day and have a standard deviation of two units a day. Lead time is variable, averaging four days with a standard deviation of one day. Assume normality and that seasonality is not a factor. What is the reorder point to achieve the desired service level? (round to 2 decimal places) 

Select one:

a. 55.00

b. 70.26

c. 55.04

d. None of the listed 

e. 70.14

Explanation / Answer

At SL>=96%, Z = 1.76

d = 12 and LT = 4

standard deviation of demand = 2 units a day

ROP = d*LT+Z*[(LT*standard deviation of demand^2 + (d^2*standard deviation of lead time^2)]^0.5

= 12*4 + 1.76*[4*2^2 + (12^2 * 1^2)]^0.5

= 48+1.76*[4*4 + 144*1]^0.5

= 48+1.76*12.65

= 48+22.26

= 70.26

Hence the answer is option "b" i.e. 70.26

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