Economic Order Quantity (EOQ) is a classic inventory management model that determines the optimal order quantity that minimizes the total cost of ordering and holding inventory. EOQ is widely used in purchasing and inventory control to strike a balance between the costs associated with ordering and holding inventory. The Economic Lot Quantity (ELQ) is an extension of the EOQ model that considers defective items in the received lot.

Economic Order Quantity (EOQ):

1. Basic EOQ Formula:
   • The basic EOQ formula is given by:
     
     $\mathrm{EOQ}=\sqrt{\frac{2\mathrm{DS}}{H}}$

      

     EOQ=H2DS​​ Where:

     • D = Demand rate (number of units per period).

     • S = Ordering cost per order.

     • H = Holding cost per unit per period.

2. Assumptions:
   • Demand is constant and known.
   • Ordering and holding costs are constant.
   • The entire order quantity is delivered at once.
   • No quantity discounts or stockouts.
3. Total Cost Calculation:
   • The total cost is the sum of ordering costs and holding costs: TotalCost=EOQD​×S+2EOQ​×H
4. Reorder Point (ROP):
   • The reorder point is the inventory level at which a new order should be placed to avoid stockouts.
     
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     ROP=D×LT Where:

     • 
       
       $��$

        

       LT = Lead time in periods.

Economic Lot Quantity (ELQ):

1. Extension to EOQ:
   • The ELQ model extends the EOQ model by considering the possibility of receiving defective items in the ordered lot.
2. ELQ Formula:
   • The ELQ formula is given by:
     
     $\mathrm{ELQ}=\sqrt{\frac{2\mathrm{DS}}{H(1-p)}}$

      

     ELQ=H(1−p)2DS​​ Where:

     • 
       
       $\mathrm{<br>}$

        

       p = Proportion of defective items in the received lot.

3. Total Cost Calculation for ELQ:
   • The total cost for ELQ includes ordering costs, holding costs for non-defective items, and holding costs for defective items.
4. Reorder Point (ROP) for ELQ:
   • The reorder point for ELQ accounts for both non-defective and defective items:
   • $ROP=(D\times LT)+(p\times D\times LT)$

Considerations for ELQ:

1. Quality Control:
   • ELQ assumes the presence of defective items, and effective quality control measures are essential to minimize the proportion of defects (
     
     $\mathrm{<br>}$

      

     p).

2. Cost Trade-offs:
   • ELQ considers the trade-offs between ordering costs, holding costs for non-defective items, and holding costs for defective items.
3. Practical Implementation:
   • ELQ may be more complex to implement in practice, and organizations need to carefully consider the implications of quality control and defect prevention.

Both EOQ and ELQ models are valuable tools for optimizing inventory management, and their application depends on the specific characteristics and requirements of the organization’s supply chain. They provide insights into the balance between ordering and holding costs, helping organizations make informed decisions to minimize total inventory-related expenses.