Operations Management: Processes and Supply Chains, 12th Edition

Key Equations

Types of Inventory

1. 1. Average cycle inventory: $\frac{Q}{2}$

2. 2. Pipeline inventory: ${\overline{D}}_L=\overline{d}L$

Economic Order Quantity

1. 3. $\text{Total annual cycle}\text{-}\text{inventory cost}=\text{Annual holding cost}+\text{Annual ordering or setup cost}:$

   $$C=\frac{Q}{2}\left(H\right)+\frac{D}{Q}\left(S\right)$$

2. 4. Economic order quantity:

   $$\text{EOQ}=\sqrt{\frac{2DS}{H}}$$

3. 5. Time between orders, expressed in weeks:

   $${\text{TBO}}_{\text{EOQ}}=\frac{\text{EOQ}}{D}\left(52\text{ weeks}/\text{year}\right)$$

Continuous Review System

1. 6. $\text{Inventory position}=\text{On}\text{-}\text{hand inventory}+\text{Scheduled receipts}-\text{Backorders}:$

   $$\text{IP}=\text{OH}+\text{SR}-\text{BO}$$

2. 7. Continuous review system:

   • $\text{Protection interval}=\text{Lead time }\left(L\right)$

   • $\text{Standard deviation of demand during the lead time }\left(\text{constant }L\right)={\sigma }_{dLT}={\sigma }_d\sqrt{L}$

   • $\text{Standard deviation of demand during the lead time }(\text{variable ...}$