Inventory Management: Models, Costs & Optimization

TAKEAWAYS:

• Inventory is classified into raw materials, WIP, finished goods, MRO, and buffer stocks, each serving distinct operational needs.
• The EOQ model minimizes total inventory costs by optimizing order quantity, order frequency, and reorder points.
• ABC analysis prioritizes inventory items by value (A=high, B=medium, C=low) to focus resources on critical stock.
• Lead time, safety stock, and reorder point formulas prevent stockouts while reducing excess holding costs.
• Real-world tools: eSewa uses EOQ for digital payment service stock (servers/bandwidth), Daraz applies ABC analysis to high-demand products, and Nabil Bank manages loan documentation inventory with periodic review.
• Exam focus: Solve EOQ problems with/without discounts, interpret inventory cost trade-offs, and justify inventory policies (e.g., "just-in-time" vs. "safety stock").

1. What is Inventory? Types and Their Roles

Inventory is the stock of goods a business holds to support production, sales, or operations. Poor inventory management leads to stockouts (lost sales) or excess holding costs (storage, obsolescence, insurance). Classify inventory into five types based on function:

2. Inventory Costs: The Trade-Off Triangle

Three costs drive inventory decisions:

1. Ordering Cost (Setup Cost): Fixed cost per order (e.g., Rs 75 to place an order with a supplier).
2. Holding Cost (Carrying Cost): Variable cost to store inventory (25% of item value/year in the exam example).
3. Stockout Cost: Intangible cost of lost sales or customer dissatisfaction (hard to quantify but critical).

Trade-off:

• Order frequently → Low holding cost, high ordering cost.
• Order infrequently → High holding cost, low ordering cost.

Example: Nepal’s traffic police use "buffer stock" of cones and barriers (MRO inventory) to manage roadblocks. Ordering too often wastes time; ordering too late causes delays.

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

The EOQ model finds the optimal order quantity (Q)* that minimizes total inventory cost. Derived from: $$\text{Total Cost (TC)}=\text{Ordering Cost}+\text{Holding Cost}+\text{Purchase Cost}$$ $$TC=\frac{D}{Q}\times S+\frac{Q}{2}\times H+P\times D$$ Where:

• $D$ = Annual demand (units/year)
• $S$ = Ordering cost per order (Rs)
• $H$ = Holding cost per unit per year (% of unit cost)
• $P$ = Unit cost (Rs)
• $Q$ = Order quantity (units)

EOQ Formula: $$Q^{\ast }=\sqrt{\frac{2DS}{H}}$$ Reorder Point (ROP): $$ROP=\text{Lead Time}\times \text{Daily Demand}+\text{Safety Stock}$$

Worked Example: EOQ with Discount

Problem: A company buys 5,000 units/year at Rs 25/unit. Ordering cost = Rs 75/order. Holding cost = 25% of unit cost/year. Supplier offers a 5% discount if ordering ≥ 1,000 units.

1. Calculate EOQ without discount.
2. Check if the discount makes sense.

Solution:

1. EOQ Calculation:

   • $D=5000$, $S=75$, $H=25\%\times 25=\text{Rs }6.25/\text{unit/year}$ $$Q^{\ast }=\sqrt{\frac{2\times 5000\times 75}{6.25}}=\sqrt{120,000}=346.41\approx 346\text{ units}$$
   • Optimal orders/year: $D/Q^{\ast }=5000/346\approx 14.45$ (order every 25 days).

2. With Discount:

   • New unit cost = Rs 25 × 0.95 = Rs 23.75.
   • New holding cost $H=25\%\times 23.75=\text{Rs }5.94/\text{unit/year}$.
   • New EOQ: $$Q^{\ast }=\sqrt{\frac{2\times 5000\times 75}{5.94}}=\sqrt{126,262}\approx 355\text{ units}$$
   • Decision: Order 1,000 units (discount threshold) only if total cost savings > Rs 1,250/year (5% of 5,000 × Rs 25).

4. Inventory Control Systems: When to Order?

Two primary methods:

5. Safety Stock and Lead Time: The Buffer Against Uncertainty

Lead Time (LT): Time between placing an order and receiving it (e.g., 10 days for Daraz suppliers). Safety Stock (SS): Extra inventory to prevent stockouts due to:

• Demand fluctuations (e.g., Pathao’s scooter demand spikes on weekends).
• Supply delays (e.g., NTC’s fiber optic cable shortages during monsoon).

Formula: $$SS=Z\times {\sigma }_d\times \sqrt{LT}$$ Where:

• $Z$ = Safety factor (from Z-table, e.g., 1.65 for 95% service level).
• ${\sigma }_d$ = Standard deviation of daily demand.

Example: Nepal’s traffic police maintain 3 extra traffic cones (SS) in each district to handle unexpected road closures (LT = 2 days, ${\sigma }_d=1$ cone/day).

6. Real-World Applications in Nepal

Case 1: eSewa’s Digital Inventory

• Problem: eSewa’s servers must handle 10,000 transactions/hour during festivals (e.g., Dashain).
• Solution:
  • EOQ for server capacity: Order extra cloud bandwidth (holding cost = Rs 500/GB/month; ordering cost = Rs 2,000/setup).
  • Safety stock: 20% extra capacity during peak hours.
• Outcome: Avoids crashes but minimizes idle capacity costs.

Case 2: Daraz’s Warehouse Strategy

• ABC Analysis:
  • A-items: Electronics (70% value, 10% SKUs) → Daily stock checks.
  • B-items: Clothing (20% value, 20% SKUs) → Weekly reviews.
  • C-items: Toys (5% value, 70% SKUs) → Monthly bulk orders.
• Result: Reduces holding costs by 30%.

Case 3: Nabil Bank’s Loan Documentation

• Issue: Loan processing requires physical files (high storage cost).
• Solution:
  • Periodic Review (FTP): Check files every 3 months.
  • Digital backup: Reduces physical SS by 50%.

7. Inventory Models: Beyond EOQ

8. Inventory Management Pitfalls (and How to Avoid Them)

flowchart TD
  A["Poor Inventory Management"] --> B["Stockouts"]
  A --> C["Excess Inventory"]
  A --> D["Cash Flow Problems"]
  B --> E["Lost Sales\n(e.g., Daraz out of stock during Dashain)"]
  C --> F["High Storage Costs\n(e.g., Nabil Bank’s unused files)"]
  D --> G["Opportunity Cost\n(e.g., eSewa’s idle server capacity)"]
  H["Solutions"] --> I["Use EOQ & ABC Analysis"]
  H --> J["Implement JIT for lean ops"]
  H --> K["Train staff on demand forecasting"]

In the Real World

1. eSewa’s Server Inventory:

   • Idea: EOQ + Safety Stock.
   • How: eSewa treats server capacity like physical inventory. During Dashain, they calculate EOQ for transaction-processing units (TPUs) and add a 30% safety buffer to handle peak loads. If they order too little, users face timeouts; if too much, they pay for unused cloud resources.

2. Daraz’s "Same-Day Delivery":

   • Idea: Fixed-Order Quantity (FOQ) + ABC Analysis.
   • How: Daraz’s Kathmandu warehouse uses FOQ for high-demand items (e.g., mobile phones) with a 2-hour reorder cycle. For low-value items (e.g., batteries), they use monthly bulk orders (FTP). The ABC analysis helps prioritize which items to stock closer to delivery hubs.

3. NTC’s Network Equipment:

   • Idea: Safety Stock for Critical Spare Parts.
   • How: NTC stores backup routers and fiber optic cables in multiple depots across Nepal. The safety stock formula accounts for monsoon-related lead time delays (LT increases by 50% during rains). For example, in Pokhara, NTC keeps 3 extra routers (SS) to ensure minimal downtime during cloudbursts.

Exam Tip

What Examiners Want to See

1. EOQ Problems:

   • Always show all steps: Calculate $Q^{\ast }$, reorder point, and compare with/without discounts.
   • Unit consistency: Ensure $D$ is in units/year, $S$ in Rs/order, $H$ in Rs/unit/year.
   • Interpretation: State whether the discount is cost-effective (e.g., "Order 1,000 units to save Rs X/year").

2. ABC Analysis:

   • Classify items by value (not quantity). Example:

     Item	Annual Usage	Unit Cost (Rs)	Annual Cost (Rs)	Classification
     Printer Ink	500	500	250,000	A
     Staplers	20	1,000	20,000	B
     Notepads	5,000	5	25,000	C

3. Safety Stock:

   • Always justify the service level (e.g., "95% service level → Z = 1.65").
   • Link to real scenarios: "NTC uses SS to handle 20% demand spikes during exams."

4. Short-Answer Questions:

   • "Inventory is a necessary evil":
     • Justification:
       • Necessary: Enables production/sales (e.g., Daraz can’t sell without stock).
       • Evil: Ties up cash, risks obsolescence (e.g., NTC’s outdated SIM cards).
     • Solution: Optimize with EOQ/JIT to minimize the "evil."

5. Case Studies:

   • Structure:
     1. Identify the inventory type (e.g., "Pathao’s scooters = finished goods").
     2. Apply a model (e.g., "Use EOQ to reduce ordering costs").
     3. Quantify benefits (e.g., "Saves Rs 50,000/year in holding costs").

Common Mistakes to Avoid

• Ignoring units: Mixing annual demand with monthly holding costs.
• Forgetting safety stock: EOQ alone doesn’t account for uncertainty.
• Overlooking discounts: Always check if bulk discounts outweigh holding costs.
• Vague answers: Instead of "ABC analysis is important," say:

  "ABC analysis helps Nabil Bank focus 80% of its inventory control efforts on 20% of high-value loan documents (e.g., property deeds), reducing stockouts by 40%."

Practice Questions (Exam-Style)

1. Calculate EOQ: A company needs 10,000 units/year. Ordering cost = Rs 100/order. Holding cost = 30% of Rs 50/unit.

   • Find $Q^{\ast }$.
   • If supplier offers 10% discount for orders ≥ 2,000 units, should they accept?

2. ABC Analysis: Classify the following items for a stationery shop:

   Item	Annual Usage	Unit Cost (Rs)
   Pens	5,000	10
   Notebooks	2,000	50
   Erasers	10,000	2

3. Safety Stock: Demand for a product follows a normal distribution with $\mu =100$ units/day, $\sigma =10$ units/day. Lead time = 5 days. Calculate SS for a 90% service level.

Final Checklist Before the Exam

• Can you derive the EOQ formula from total cost?
• Do you know when to use FOQ vs. FTP?
• Can you justify ABC analysis with a real example?
• Are you comfortable calculating safety stock with Z-values?
• Can you explain the trade-offs in inventory costs?