Answer:
The answer is "116 doorknobs".
Explanation:
The standard deviation of the demand before the (four weeks) protection intervals = [tex]\sigma-d \times (\sqrt{L}) = 100 \ units\\[/tex]
The desired cycle service level is [tex]99\%[/tex].Therefore, [tex]z = 2.33[/tex]
The safety stocks for the four-weeks protecting interval are:
Safety stock [tex]= z\times [ \sigma-d \times (\sqrt{L})][/tex]
[tex]= 2.33 \times 100 \\\\= 233\ door\ knobs[/tex]
The safety stocks require for the one-week protection interval are: [tex]\sigma-dLT = \sigma-dt \times (\sqrt{L}) = \sigma-dt \times (\sqrt{4}) = 100\ door\ knobs\\\\\sigma-d = \frac{100}{(\sqrt{4})} = \frac{100}{2} = 50 \ door\ knobs\\\\[/tex]
Safety stock [tex]= z\times \sigma-dt = 2.33 \times 50 = 116.5 \ or\ 117 \ door\ knobs\\\\[/tex]
Safety stock reduction[tex]= 233 -117 = 116 \ door\ knobs[/tex]
