Respuesta :
Solution :
The optimal order quantity, EOQ = [tex]$\sqrt{\frac{2 \times \text{demand}\times \text{ordering cost}}{\text{holding cost}}}$[/tex]
EOQ = [tex]$\sqrt{\frac{2 \times 2000 \times 12}{3.6}}$[/tex]
= 115.47
The expected number of orders = [tex]$\frac{\text{demand}}{EOQ}$[/tex]
[tex]$=\frac{2000}{115.47}$[/tex]
= 17.32
The daily demand = demand / number of working days
[tex]$=\frac{2000}{240}$[/tex]
= 8.33
The time between the orders = EOQ / daily demand
[tex]$=\frac{115.47}{8.33}$[/tex]
= 13.86 days
ROP = ( Daily demand x lead time ) + safety stock
[tex]$=(8.33 \times 8)+10$[/tex]
= 76.64
The annual holding cost = [tex]$\frac{EOQ}{2} \times \text{holding cost}$[/tex]
[tex]$=\frac{115.47}{2} \times 3.6$[/tex]
= 207.85
The annual ordering cost = [tex]$\frac{\text{demand}}{EOQ} \times \text{ordering cost}$[/tex]
[tex]$=\frac{2000}{115.47} \times 12$[/tex]
= 207.85
So the total inventory cost = annual holding cost + annual ordering cost
= 207.85 + 207.85
= 415.7
