Inventory Management & EOQ: Models, Costs & Optimization

TAKEAWAYS:

• EOQ formula minimizes total inventory costs by balancing ordering and holding costs: $EOQ=\sqrt{\frac{2DS}{H}}$, where $D$ = annual demand, $S$ = ordering cost, $H$ = holding cost per unit.
• Inventory costs are categorized into ordering costs (fixed per order), holding costs (storage, insurance, obsolescence), and stockout costs (lost sales, emergency orders).
• Reorder point (ROP) = $\text{Average daily usage}\times \text{Lead time}+\text{Safety stock}$, ensuring no stockouts while avoiding excess inventory.
• Just-in-Time (JIT) and ABC analysis are two key strategies to classify and manage inventory efficiently, reducing waste and improving cash flow.
• Safety stock acts as a buffer against demand uncertainty, calculated using standard deviation of demand and desired service level.
• Technology integration (e.g., ERP systems like SAP or local tools like eSewa’s inventory module) automates EOQ calculations and real-time tracking for businesses.

1. Introduction to Inventory Management

Inventory management is the process of ordering, storing, and using a company’s inventory to meet customer demand while minimizing costs. Poor inventory management leads to:

• Overstocking: High holding costs, obsolescence, and tied-up capital.
• Understocking: Lost sales, emergency orders, and dissatisfied customers.

Why Hold Inventory?

mindmap
  root((Why Hold Inventory?))
    Production Smoothing
    Customer Demand Fluctuations
    Lead Time Coverage
    Bulk Purchase Discounts
    Speculation (Price/Supply Risks)
    Seasonal Demand

2. Types of Inventory

Inventory is classified based on its stage in production and usage:

3. Costs Associated with Inventory

Inventory costs are categorized into three main types:

A. Ordering Costs (Setup Costs)

• Fixed costs per order, regardless of order size.
• Includes: Purchase order processing, transportation, and receiving.
• Example: For a Kathmandu retail shop, ordering 100 shirts from a supplier costs Rs. 500 (fixed), whether they order 10 or 100 shirts.

B. Holding (Carrying) Costs

• Variable costs per unit per time period (e.g., per year).
• Includes: Storage, insurance, taxes, obsolescence, and capital costs.
• Example: A shop holds 100 units of a product worth Rs. 20/unit. If holding cost is 10% per year, the annual holding cost = 100 × Rs. 20 × 10% = Rs. 200.

C. Stockout Costs

• Costs incurred when demand exceeds supply.
• Includes: Lost sales, emergency orders, and customer dissatisfaction.
• Example: If Daraz runs out of a popular smartphone, they may lose Rs. 50,000 in potential sales and face customer complaints.

4. Economic Order Quantity (EOQ) Model

The EOQ model determines the optimal order quantity that minimizes total inventory costs (ordering + holding).

EOQ Formula

$$EOQ=\sqrt{\frac{2DS}{H}}$$ Where:

• $D$ = Annual demand (units)
• $S$ = Ordering cost per order (Rs.)
• $H$ = Holding cost per unit per year (Rs.)

Total Cost under EOQ

$$\text{Total Cost}=\left(\frac{D}{Q}\times S\right)+\left(\frac{Q}{2}\times H\right)$$ Where $Q=EOQ$.

5. Worked Example: EOQ for a Kathmandu Retail Shop

Scenario: Mr. Thapa’s Electronics Shop in Kathmandu sells 5,000 solar lamps annually.

• Ordering cost (S) = Rs. 200 per order.
• Holding cost (H) = 20% of the lamp’s cost per year.
• Cost per lamp = Rs. 500.

Step 1: Calculate Holding Cost per Unit per Year

$$H=20\%\times \text{Cost per unit}=0.20\times 500=\text{Rs. 100 per lamp per year}$$

Step 2: Apply EOQ Formula

$$EOQ=\sqrt{\frac{2\times 5,000\times 200}{100}}=\sqrt{\frac{2,000,000}{100}}=\sqrt{20,000}=141.42\approx 141\text{ units}$$

Step 3: Calculate Total Cost at EOQ

$$\text{Number of orders}=\frac{D}{Q}=\frac{5,000}{141}\approx 35.46\approx 36\text{ orders/year}$$ $$\text{Ordering Cost}=36\times 200=\text{Rs. 7,200}$$ $$\text{Average Inventory}=\frac{Q}{2}=\frac{141}{2}=70.5\text{ units}$$ $$\text{Holding Cost}=70.5\times 100=\text{Rs. 7,050}$$ $$\text{Total Cost}=7,200+7,050=\text{Rs. 14,250}$$

6. Reorder Point (ROP) and Safety Stock

Reorder Point (ROP)

$$ROP=(\text{Average Daily Usage}\times \text{Lead Time})+\text{Safety Stock}$$

• Lead Time: Time between placing an order and receiving it.
• Safety Stock: Extra inventory to prevent stockouts.

Example: Reorder Point for a Daraz Warehouse

• Annual demand = 20,000 units.
• Lead time = 10 days.
• Safety stock = 500 units (to cover demand uncertainty).
• Working days/year = 300.

$$\text{Average Daily Usage}=\frac{20,000}{300}\approx 66.67\text{ units/day}$$ $$ROP=(66.67\times 10)+500=666.7+500=1,167\text{ units}$$

When to Order? When inventory drops to 1,167 units, place an order for EOQ (e.g., 1,000 units).

7. Inventory Management Strategies

A. Just-in-Time (JIT) Inventory

• Goal: Minimize inventory by receiving goods only as they are needed.
• Advantages:
  • Reduces holding costs.
  • Improves cash flow.
• Disadvantages:
  • Vulnerable to supply chain disruptions.
  • Requires high supplier reliability.
• Example: Toyota’s production system (used by Nepali auto parts suppliers).

B. ABC Analysis

Classifies inventory into three categories based on annual consumption value:

8. Technology in Inventory Management

Modern businesses use software and automation to optimize inventory:

• ERP Systems (SAP, Oracle): Used by Nepal’s largest banks (Nabil, Global IME) for real-time inventory tracking.
• Barcode/RFID: Daraz and eSewa use scanners to track inventory levels.
• AI/Predictive Analytics: Khalti’s logistics arm uses demand forecasting to optimize orders.

In the Real World

1. eSewa’s Inventory Module

   • Uses EOQ and ROP to manage mobile recharge cards and utility bills.
   • How? Calculates optimal order quantities for high-demand months (Dashain, Tihar) to avoid stockouts.

2. Daraz’s Warehouse Optimization

   • Applies ABC analysis to prioritize high-value electronics (A items) over low-cost household goods (C items).
   • Result: Reduces holding costs by 15% while ensuring 99% order fulfillment.

3. Nepal Food Corporation’s Safety Stock

   • Maintains 3 months of safety stock for rice and wheat to handle monsoon disruptions in supply chains.
   • Calculation: Uses historical demand variability to set safety stock levels.

4. Pathao’s Delivery Fleet Inventory

   • Tracks fuel, spare parts, and delivery bags using JIT principles.
   • Example: Orders new delivery bags only when stock falls below 50 units (ROP).

9. Limitations of EOQ Model

While EOQ is powerful, it has assumptions that may not hold in real life:

• Demand is constant (but real demand fluctuates seasonally).
• Lead time is fixed (delays happen due to traffic, strikes).
• No quantity discounts (but suppliers often offer bulk discounts).
• Instant replenishment (but suppliers may take weeks).

Solution: Use modified EOQ models or simulation tools for complex scenarios.

Exam Tip

How to Score Full Marks in TU/PU Exams

1. Understand the Formula

   • Memorize $EOQ=\sqrt{\frac{2DS}{H}}$ and total cost formula.
   • Exam trick: Always show all steps in calculations (even if partial marks are given).

2. Practical Application

   • Always relate to Nepali businesses (e.g., Kathmandu shops, Daraz, NTC).
   • Example: If asked about EOQ, use Mr. Thapa’s Electronics Shop (as above).

3. Diagrams and Tables

   • Draw EOQ cost curves (total cost vs. order quantity).
   • Use tables for inventory types (raw materials, WIP, finished goods).

4. Common Exam Questions

   • "Calculate EOQ" → Always verify units (e.g., Rs., units).
   • "What is safety stock?" → Define + give a Nepali example (e.g., Nepal Food Corporation).
   • "Advantages of JIT" → List 3 pros and 2 cons with real-world examples.

5. Avoid These Mistakes

   • ❌ Forgetting to convert annual demand to daily usage for ROP.
   • ❌ Ignoring holding cost as a percentage of unit cost.
   • ❌ Not labeling axes in graphs (e.g., "Order Quantity vs. Total Cost").

Quick Revision Checklist

Final Worked Example: NTC’s Spare Parts Inventory

Scenario: Nepal Telecommunications Company (NTC) needs to manage transformer oil for its power stations.

• Annual demand (D) = 5,000 liters.
• Ordering cost (S) = Rs. 1,000 per order.
• Holding cost (H) = 15% of Rs. 200/liter = Rs. 30/liter/year.
• Lead time = 7 days.
• Safety stock = 200 liters (to cover sudden power outages).

Step 1: Calculate EOQ

$$EOQ=\sqrt{\frac{2\times 5,000\times 1,000}{30}}=\sqrt{\frac{10,000,000}{30}}=\sqrt{333,333.33}\approx 577.35\approx 577\text{ liters}$$

Step 2: Calculate ROP

$$\text{Daily Usage}=\frac{5,000}{300}\approx 16.67\text{ liters/day}$$ $$ROP=(16.67\times 7)+200=116.69+200=316.69\approx 317\text{ liters}$$

Conclusion for NTC:

• Order 577 liters every time stock reaches 317 liters.
• This minimizes costs while ensuring no stockouts during emergencies.

Summary Flowchart: Inventory Management Process

Key Takeaways for Exam

1. EOQ is about balancing costs – never order too much or too little.
2. ROP ensures you never run out – but don’t overstock unnecessarily.
3. Real-world adjustments – use safety stock for uncertainty.
4. Technology helps – ERP, barcodes, and AI make inventory smarter.
5. Nepali examples score marks – Daraz, eSewa, NTC, Kathmandu shops are gold in exams!

Final Note: Inventory management is not just about storing goods—it’s about optimizing cash flow, reducing waste, and ensuring customer satisfaction. Master EOQ, ROP, and ABC analysis, and you’ll ace this unit! 🚀