Safety Stock Model: when demand during lead time and its standard deviation are known

Problem Statement

A company has a SKU $($stock keeping unit, tracks a product with a bar code$)$ that is normally distributed during the lead time, with a mean of $350$ units and a standard deviation of $10.$ The company follows a policy that results in stockouts occurring only $5\%$ of the time on any order. How much safety stock should be maintained? And, what is the reorder point?

Data Table Symbol $/$ Equation Inputs Notes

Average demand during lead time u $350$

Standard deviation of lead time, $\backslash$sigma LT $\backslash$sigma LT $10$

Service level $(\%$ of demand met$)$ SL $5\mathrm{.}00\%$

Results Table

Z$-$value Z $=$NORM.S$.$INV$($SL$)-1\mathrm{.}64$ when the distribution has a mean of $0$ and standard deviation of $1$

Safety stock SS $=$ Z$*\backslash$sigma LT $-16\mathrm{.}45$

Reorder point ROP $=$ SS $+$ u $333\mathrm{.}55$

Safety Stock Model: when either daily demand, lead time or both are known

Problem Statement

A company has a SKU $($stock keeping unit, tracks a product with a bar code$)$ that is normally distributed during the lead time, with a constant demand of $25$ units, a standard deviation of $3,$ and an average lead time of $6.$ The company follows a service level policy of $98\%.$ How much safety stock should be maintained? And, what is the reorder point?

Data Table Symbol $/$ Equation Inputs Notes

Average daily demand davg $25$

Standard deviation of daily demand, $\backslash$sigma d $\backslash$sigma d $3$ Enter $0$ if demand is constant

Average lead time $($in days$)$ LT $6$

Standard deviation of lead time, $\backslash$sigma LT $\backslash$sigma LT $0$ Enter $0$ if lead time is constant

Service level $(\%$ of demand met$)$ SL $98\mathrm{.}00\%$

Results Table

Z$-$value Z $=$NORM.S$.$INV$($SL$)2\mathrm{.}05$ when the distribution has a mean of $0$ and standard deviation of $1$

Average demand during lead time LTavg $=$ davg$*$LT $150$

Standard deviation of demand during lead time, $\backslash$sigma dLT $\backslash$sigma dLT $=($LT$*\backslash$sigma d$^2+$ davg$*\backslash$sigma LT$^2)7\mathrm{.}348469228$

Safety stock SS $=$ Z$*\backslash$sigma dLT $15\mathrm{.}09$

Reorder point ROP $=$ SS $+$ LTavg $165\mathrm{.}09$

Safety Stock Model: when daily demand and its standard deviation are known

Problem Statement

A company has a SKU $($stock keeping unit, tracks a product with a bar code$)$ that is normally distributed during the lead time, with a mean of $15$ units and a standard deviation of $3.$ The lead time is exactly $4$ days. The company follows a service level policy of $97\%.$ How much safety stock should be maintained? And, what is the reorder point?

Data Table Symbol $/$ Equation Inputs Notes

Average daily demand davg $15$

Standard deviation of daily demand, $\backslash$sigma d $\backslash$sigma d $3$ Enter $0$ if demand is constant

Lead time $($in days$)$ LT $4$

Service level $(\%$ of demand met$)$ SL $97\mathrm{.}00\%$

Results Table

Z$-$value Z $=$NORM.S$.$INV$($SL$)1\mathrm{.}88$ when the distribution has a mean of $0$ and standard deviation of $1$

Average demand during lead time LTavg $=$ davg$*$LT $60$

Standard deviation of demand during lead time, $\backslash$sigma dLT $\backslash$sigma dLT $=\backslash$sigma d $*($LT$)6\mathrm{.}00$

Safety stock SS $=$ Z$*\backslash$sigma dLT $11\mathrm{.}28$

Reorder point ROP $=$ SS $+$ LTavg $17\mathrm{.}28$

Result Statements

Note: Write result statements that concisely presents all of the information in a recommendation format.

$1.$ Safety Stock Model: when demand during lead time and its standard deviation are known

$2.$ Safety Stock Model: when either daily demand, lead time or both are known

$3.$ Safety Stock Model: when daily demand and its standard deviation are known