Inventory Management: EOQ, Safety Stock & Cost Trade-offs

TAKEAWAYS:

• EOQ formula $EOQ=\sqrt{\frac{2DS}{H}}$ minimizes total inventory costs by balancing ordering and holding costs.
• Safety stock acts as a buffer against demand uncertainty, calculated as $\text{Safety Stock}=z\times {\sigma }_d\times \sqrt{L}$.
• Total inventory cost = Ordering cost + Carrying cost + Stockout cost, where each component must be quantified.
• Reorder point (ROP) = Average daily demand × Lead time + Safety stock ensures timely replenishment.
• ABC analysis classifies inventory by value (A: high-value, low-volume; C: low-value, high-volume) to prioritize management.
• Just-in-Time (JIT) eliminates safety stock but requires perfect supply chain coordination (used by Toyota and Nepali auto parts suppliers).

1. Introduction to Inventory Management

Inventory is the current asset held by a business for production or resale. It includes:

• Raw materials (e.g., steel for a Kathmandu bicycle manufacturer).
• Work-in-progress (WIP) (e.g., partially assembled scooters at Ncell’s assembly plant).
• Finished goods (e.g., Daraz’s unsold smartphones in its warehouse).

Why manage inventory?

• Cost savings: Avoid overstocking (wasted capital) or stockouts (lost sales).
• Customer satisfaction: Ensure product availability (e.g., NTC must always stock spare parts for its towers).
• Operational efficiency: Reduce lead times (e.g., Pathao’s delivery drivers need quick access to spare bikes).

2. Inventory Costs: The Trade-off Triangle

Inventory management balances three critical costs:

pie
    title Inventory Cost Components
    "Ordering Cost (Setup Cost)" : 20
    "Carrying Cost (Holding Cost)" : 50
    "Stockout Cost (Shortage Cost)" : 30

• Ordering cost (S): Cost per purchase order (e.g., Rs 1,000 for placing an order with a Kathmandu wholesaler).
• Carrying cost (H): Annual cost to hold one unit in inventory (e.g., Rs 2/unit/year for storage, insurance, and obsolescence).
• Stockout cost: Lost sales, goodwill, or emergency procurement costs (e.g., Rs 500/unit for a Daraz seller when a product runs out).

Goal: Find the optimal order quantity that minimizes total inventory cost (TIC): $$TIC=\left(\frac{D}{Q}\right)S+\left(\frac{Q}{2}\right)H+\text{Stockout Cost}$$ where:

• $D$ = Annual demand (units)
• $Q$ = Order quantity

3. Economic Order Quantity (EOQ): The Goldilocks Principle

The EOQ model determines the optimal order quantity that minimizes total inventory costs, assuming:

• Demand is constant and known.
• Lead time is fixed.
• No quantity discounts.
• Instant replenishment (no partial deliveries).

EOQ Formula

$$EOQ=\sqrt{\frac{2DS}{H}}$$ Example: Siddhartha Tools (from past exams)

• Annual demand ($D$) = 100,000 units
• Ordering cost ($S$) = Rs 1,000/order
• Carrying cost ($H$) = Rs 2/unit/year

$$EOQ=\sqrt{\frac{2\times 100,000\times 1,000}{2}}=\sqrt{100,000,000}=10,000\text{ units}$$ Interpretation: Order 10,000 units every 10 days (since $100,000/10,000=10$ orders/year).

EOQ Assumptions vs. Reality

4. Safety Stock: The Buffer Against Uncertainty

Safety stock prevents stockouts when:

• Demand exceeds forecasts (e.g., Khalti’s digital wallet balances before Dashain).
• Lead times increase (e.g., global chip shortage delaying Pathao’s new bike models).
• Suppliers delay deliveries (e.g., Chinese imports held at Nepal’s customs).

Calculating Safety Stock

$$\text{Safety Stock}=z\times {\sigma }_d\times \sqrt{L}$$ where:

• $z$ = Number of standard deviations (e.g., 1.65 for 95% service level).
• ${\sigma }_d$ = Standard deviation of daily demand.
• $L$ = Lead time (days).

Example: Nepal Pharmaceuticals

• Daily demand (${\mu }_d$) = 500 units, ${\sigma }_d=50$ units.
• Lead time ($L$) = 7 days.
• Desired service level = 95% ($z=1.65$).

$$\text{Safety Stock}=1.65\times 50\times \sqrt{7}=1.65\times 50\times 2.65\approx 220\text{ units}$$

Safety Stock Strategies

5. Reorder Point (ROP): When to Place an Order

The reorder point triggers a new order when inventory drops to a predefined level: $$ROP=\text{Average daily demand}\times \text{Lead time}+\text{Safety Stock}$$

Example: Kathmandu Retail Shop

• Daily demand = 20 units.
• Lead time = 5 days.
• Safety stock = 30 units (from above).

$$ROP=20\times 5+30=130\text{ units}$$ Action: Order when inventory reaches 130 units.

6. Inventory Management Techniques

A. ABC Analysis: The 80-20 Rule

Classify inventory by annual consumption value to prioritize management:

pie
    title ABC Inventory Classification
    "A Items (10% of items, 70% of value)" : 70
    "B Items (20% of items, 20% of value)" : 20
    "C Items (70% of items, 10% of value)" : 10

B. Just-in-Time (JIT) Inventory

• Goal: Eliminate waste by receiving goods only as needed.
• Requirements:
  • Reliable suppliers (e.g., Toyota’s Nepali vendors).
  • Short lead times.
  • Flexible production (e.g., Pathao’s bike assembly line).

Advantages:

• Reduces carrying costs.
• Improves cash flow (e.g., NTC doesn’t tie up capital in excess inventory).

Disadvantages:

• Vulnerable to supply chain disruptions (e.g., COVID-19 lockdowns).
• Requires perfect demand forecasting.

7. The Inventory Cycle: From Order to Sale

flowchart LR
    A["Place Order"] --> B["Lead Time: Supplier to Warehouse"]
    B --> C["Receive Inventory"]
    C --> D["Inventory Held: Carrying Costs"]
    D --> E["Issue to Production/Sales"]
    E --> F["Stockout Risk if Demand > Supply"]
    F --> G["Reorder if Inventory ≤ ROP"]
    G --> A

Key Metrics:

1. Inventory Turnover Ratio: $$\text{Turnover}=\frac{\text{Cost of Goods Sold (COGS)}}{\text{Average Inventory}}$$

   • High turnover (e.g., 12x/year) = Efficient inventory management (e.g., Khalti’s digital transactions).
   • Low turnover (e.g., 2x/year) = Overstocking (e.g., unsold festival decorations after Dashain).

2. Days Inventory Outstanding (DIO): $$DIO=\frac{365}{\text{Inventory Turnover}}$$

   • Example: If turnover = 8, $DIO=365/8=45.6$ days (NTC holds inventory for ~46 days).

8. Numerical Example: Daraz Nepal’s Inventory Optimization

Scenario: Daraz sells 50,000 units/year of a popular smartphone. Costs:

• Ordering cost ($S$) = Rs 5,000/order.
• Carrying cost ($H$) = Rs 1,000/unit/year (storage, insurance, obsolescence).
• Lead time = 10 days.
• Daily demand = 137 units ($50,000/365$).
• Safety stock = 200 units (based on demand variability).

Step 1: Calculate EOQ

$$EOQ=\sqrt{\frac{2\times 50,000\times 5,000}{1,000}}=\sqrt{500,000}\approx 707\text{ units}$$ Order frequency: $50,000/707\approx 71$ orders/year.

Step 2: Determine Reorder Point (ROP)

$$ROP=\text{Daily demand}\times \text{Lead time}+\text{Safety Stock}=137\times 10+200=1,570\text{ units}$$

Step 3: Calculate Total Inventory Cost (TIC)

• Ordering cost: $(50,000/707)\times 5,000=Rs353,600$.
• Carrying cost: $(707/2)\times 1,000=Rs353,500$.
• Total: $353,600+353,500=Rs707,100$.

Without EOQ: If Daraz orders 1,000 units at a time:

• Ordering cost: $(50,000/1,000)\times 5,000=Rs250,000$.
• Carrying cost: $(1,000/2)\times 1,000=Rs500,000$.
• Total: $Rs750,000$ (higher than EOQ).

In the Real World

1. Daraz Nepal

   • EOQ in Action: Daraz uses EOQ to optimize orders from suppliers like Xiaomi and Samsung. For example, during the Diwali season, demand spikes by 300%, so Daraz increases safety stock by 50% and places larger, less frequent orders to avoid stockouts.
   • ABC Analysis: Daraz’s "A items" (e.g., iPhones, laptops) are tracked daily, while "C items" (e.g., phone chargers) are ordered in bulk every 3 months.

2. NTC (Nepal Telecommunications Corporation)

   • Safety Stock: NTC maintains a 30-day safety stock of network cables and batteries to handle power outages or sudden demand surges (e.g., during elections or festivals).
   • JIT for Spare Parts: Critical components (e.g., 5G tower chips) are ordered via JIT from global suppliers, reducing warehouse costs.

3. Pathao (Ride-Hailing App)

   • Inventory as Bikes: Pathao’s "inventory" is its fleet of bikes/scooters. The company uses dynamic EOQ to adjust orders based on:
     • Peak hours (e.g., 30% more bikes in Kathmandu’s Thamel at night).
     • Rider demand forecasts (using AI).
   • Stockout Cost: A missing bike in a high-demand zone costs Pathao Rs 20,000/hour in lost bookings.

Exam Tip

What Examiners Want to See

1. Formulas: Always show the EOQ, safety stock, and ROP formulas with substituted values. Partial credit is given for correct setup.
2. Units: Ensure all answers are in NPR and units (e.g., "units/year," not just numbers).
3. Assumptions: State any assumptions explicitly (e.g., "Assuming constant demand").
4. Real-World Tie-Ins: Link numerical examples to Nepali businesses (e.g., "Like Daraz’s Diwali sales").
5. Diagrams: Draw T-accounts for inventory costs or inventory level graphs to visualize stock fluctuations.

Common Pitfalls

• Ignoring safety stock: Many students calculate EOQ but forget to add safety stock to ROP.
• Miscounting ordering frequency: $D/Q$ gives the number of orders, not the order quantity.
• Unit mismatches: Carrying cost must be per unit per year, not per month or per order.

Past Exam Patterns

• Short Questions: Define terms like "EOQ," "safety stock," or "inventory turnover."
• Numerical Problems: Always provide step-by-step calculations (e.g., EOQ → ROP → TIC).
• Case Studies: Expect questions on Nepali firms (e.g., "How would NTC manage its inventory during a monsoon?").

Practice Question (Worked Solution)

Question: A Kathmandu electronics shop sells 18,000 LED bulbs/year. Ordering cost is Rs 200/order, and carrying cost is Rs 4/bulb/year. Lead time is 15 days, and daily demand is 50 bulbs. Calculate:

1. EOQ.
2. Reorder point (assume safety stock = 100 bulbs).
3. Total inventory cost at EOQ.

Solution:

1. EOQ: $$EOQ=\sqrt{\frac{2\times 18,000\times 200}{4}}=\sqrt{1,800,000}=1,341.6\approx 1,342\text{ bulbs}$$

2. Reorder Point (ROP): $$ROP=50\times 15+100=750+100=850\text{ bulbs}$$

3. Total Inventory Cost (TIC):

   • Ordering cost: $(18,000/1,342)\times 200=2,682$ orders/year × Rs 200 = Rs 536,400.
   • Carrying cost: $(1,342/2)\times 4=Rs2,684$.
   • Total: $536,400+2,684=Rs539,084$.

Note: The carrying cost seems low because the per-unit carrying cost is minimal (Rs 4/bulb). In reality, this shop should negotiate lower ordering costs or bulk discounts!