Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

Key Equations

Equations 6-1 through 6-8 are associated with the economic order quantity (EOQ).

(6-1)

Average inventory level = \frac{Q}{2}

$Average inventory level = \frac{Q}{2}$

(6-2)

Annual ordering cost = \frac{D}{Q} C_{o}

$Annual ordering cost = \frac{D}{Q} C_{o}$

(6-3)

Annual holding cost = \frac{Q}{2} C_{h}

$Annual holding cost = \frac{Q}{2} C_{h}$

(6-4)

EOQ = Q^{*} = \sqrt{\frac{2 D C_{o}}{C_{h}}}

$EOQ = Q^{*} = \sqrt{\frac{2 D C_{o}}{C_{h}}}$

(6-5)

T C = \frac{D}{Q} C_{o} + \frac{Q}{2} C_{h}

$T C = \frac{D}{Q} C_{o} + \frac{Q}{2} C_{h}$

Total relevant inventory cost.

(6-6)

Average dollar level = \frac{(C Q)}{2}

$Average dollar level = \frac{(C Q)}{2}$

(6-7)

Q^{*} = \sqrt{\frac{2 D C_{o}}{I C}}

$Q^{*} = \sqrt{\frac{2 D C_{o}}{I C}}$

EOQ with $C_{h}$ $C_{h}$ expressed as percentage of unit cost.

(6-8)

ROP = d \times L

$ROP = d \times L$

Reorder point: d is the daily demand and L is the lead time in days.

Equations 6-9 through 6-13 are associated with the production run model.

(6-9)

Average inventory = \frac{Q}{2} (1 - \frac{d}{p})

$Average inventory = \frac{Q}{2} (1 - \frac{d}{p})$

(6-10)

Annual holding cost = \frac{Q}{2} (1 - \frac{d}{p}) C_{h}

$Annual holding cost = \frac{Q}{2} (1 - \frac{d}{p}) C_{h}$

(6-11)

Annual setup cost = \frac{D}{Q} C_{s}

$Annual setup cost = \frac{D}{Q} C_{s}$

(6-12)

Annual ordering cost = \frac{D}{Q} C_{o}

$Annual ordering cost = \frac{D}{Q} C_{o}$

(6-13)

Q^{*} = \sqrt{\frac{2 D C_{s}}{C_{h} (1 - \frac{d}{p})}}

$Q^{*} = \sqrt{\frac{2 D C_{s}}{C_{h} (1 - \frac{d}{p})}}$

Optimal production quantity.

Equation 6-14 is used for the quantity discount model.

(6-14)

Total cost = D C + \frac{D}{Q} C_{o} + \frac{Q}{2} C_{h}

$Total cost = D C + \frac{D}{Q} C_{o} + \frac{Q}{2} C_{h}$

Total inventory cost (including purchase cost).

Equations 6-15 to 6-20 are used when safety stock is required.

(6-15)

ROP = (Average demand during lead time) + SS

$ROP = (Average demand during lead time) + SS$

General formula for determining the reorder point when safety stock (SS) is carried.

(6-16)

ROP = (Average demand during lead time) + Z σ_{d LT}

$ROP = (Average demand during lead time) + Z σ_{d LT}$

Reorder point formula when demand during lead time is normally distributed with a standard deviation of $σ_{d LT} .$ $σ_{d LT} .$

(6-17)

ROP = \bar{d} L + Z (σ_{d} \sqrt{L})

$ROP = \bar{d} L + Z (σ_{d} \sqrt{L})$

Formula for determining the reorder point when daily demand is normally distributed but lead time is constant, where $\bar{d}$ $\bar{d}$ is the average daily demand, L is the constant lead time in days, and $σ_{d}$ $σ_{d}$ is the standard deviation of daily demand.

(6-18)

ROP = d \bar{L} + Z (d σ_{L})

$ROP = d \bar{L} + Z (d σ_{L})$

Formula for determining the reorder point when daily demand is constant but lead time is normally distributed, where $\bar{L}$ $\bar{L}$ is the average lead time in days, d is the constant daily demand, and $σ_{L}$ $σ_{L}$ is the standard deviation of lead time.

(6-19)

ROP = \bar{d} \bar{L} + Z (\sqrt{\bar{L} σ_{d}^{2} + {\bar{d}}^{2} σ_{L}^{2}})

$ROP = \bar{d} \bar{L} + Z (\sqrt{\bar{L} σ_{d}^{2} + {\bar{d}}^{2} σ_{L}^{2}})$

Formula for determining the reorder point when both daily demand and lead time are normally distributed, where $\bar{d}$ $\bar{d}$ is the average daily demand, $\bar{L}$ $\bar{L}$ is the average lead time in days, $σ_{L}$ $σ_{L}$ is the standard deviation of lead time, and $σ_{d}$ $σ_{d}$ is the standard deviation of daily demand.

(6-20)

THC = \frac{Q}{2} C_{h} + (SS) C_{h}

$THC = \frac{Q}{2} C_{h} + (SS) C_{h}$

Total annual holding cost formula when safety stock is carried.

Equation 6-21 is used for marginal analysis.

(6-21)

P \geq \frac{ML}{ML + MP}

$P \geq \frac{ML}{ML + MP}$

Decision rule in marginal analysis for stocking additional units.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for Key Equations

Create new playlist

Sign In

Sign Up

Table of Contents for
Key Equations