# Solve and Economic Order Quantity (EOQ) Problem

## Case Study: Economic Order Quantity

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 Input: Carrying cost, Cc = $2.00 Setup or Ordering cost, Co =$10 Annual Demand, D = 36,000 Annual days, months or weeks = 240 Demand rate, d = 150.00 Production rate, p = 300

${{Q}^{*}}=\sqrt{\frac{2DS}{H\left( 1-\frac{d}{p} \right)}}=\sqrt{\frac{2\times 36,000\times 10}{2\left( 1-\frac{150}{300} \right)}}=849$

 Output: Qopt = 849 Total Cost, TC = \$848.53 Production run length = 2.83 Number of runs = 42.43 Maximum inventory = 424.26 Cycle Time = 5.66

$Q*\left( 1-\frac{d}{p} \right)=849\left( 1-\frac{150}{300} \right)=425$

$IC=\frac{HQ*}{2}\left( 1-\frac{d}{p} \right)=\frac{2\times 849}{2}\left( 1-\frac{150}{300} \right)=\424.26$

$ROP = d\times L = 150\times 2 = 300$

$TC=\frac{DS}{Q}+\frac{HQ}{2}+PD = 2\times \frac{D\times 25}{285}+450.50\times D$

$AC=\frac{TC}{D}=\frac{50}{285}+450.50=450.6754$

$OC=HC=\frac{HQ}{2}=\frac{0.20\times 450.50\times 285}{2}=\12,839.25$

$OC=\12,839.25$