Inventory Management: Costs, ABC Analysis, Models & Systems

TAKEAWAYS:

• Inventory costs (ordering, holding, shortage) directly impact profit—visualize their trade-offs using cost-volume graphs for optimal ordering decisions.
• ABC analysis prioritizes items by value (A=15% items, 70% value) to optimize stock control—pie chart shows the 80/20 rule in action.
• The EOQ model balances ordering and holding costs to minimize total cost—cost curve reveals the optimal order quantity (Q*).
• Real-world systems: Khalti’s perpetual inventory tracks digital payments in real-time; Daraz’s periodic reorder uses bulk discounts for high-demand items.
• Queuing theory’s M/M/1 model applies to inventory shortages—waiting-time graph shows how service levels affect costs.
• Compare fixed-order quantity vs. fixed-time period systems using a decision flowchart for when to use each.

Core Concepts: Inventory Costs and Trade-offs

Inventory management is about balancing costs to maximize efficiency. Three primary costs shape decisions:

1. Ordering Cost (Setup Cost)

   • Fixed cost per order (e.g., placing an order with Daraz, processing paperwork).
   • Formula: $C_o=\text{Ordering cost per order}\times \left(\frac{D}{Q}\right)$ Where:
     • $D$ = Annual demand (units/year)
     • $Q$ = Order quantity (units/order)

2. Holding (Carrying) Cost

   • Variable cost to store inventory (rent, insurance, spoilage, opportunity cost of capital).
   • Formula: $C_h=\text{Holding cost per unit per year}\times \left(\frac{Q}{2}\right)$ (Average inventory = $Q/2$ for steady demand.)

3. Shortage Cost

   • Cost of stockouts (lost sales, rush orders, customer dissatisfaction).
   • Formula: $C_s=\text{Shortage cost per unit}\times \text{Expected shortage quantity}$.

Worked Example: NTC’s Spare Parts Inventory NTC buys 18,000 spark plugs/year at Rs 25/unit. Ordering cost = Rs 250/order, holding cost = 10% of item value/year.

1. Calculate EOQ (Q)*: $$Q^{\ast }=\sqrt{\frac{2\times D\times C_o}{C_h}}=\sqrt{\frac{2\times 18000\times 250}{25\times 0.10}}=\sqrt{3,600,000}=1,897\text{ units}$$
2. Total Cost at Q*: $$\text{Total Cost}=\left(\frac{D}{Q^{\ast }}\right)C_o+\left(\frac{Q^{\ast }}{2}\right)C_h=\left(\frac{18000}{1897}\right)\times 250+\left(\frac{1897}{2}\right)\times 2.5=2,360+2,371=\text{Rs 4,731/year}$$
3. Reorder Point (ROP) (assuming lead time = 2 weeks, weekly demand = 346 units): $$ROP=\text{Demand during lead time}=346\times 2=692\text{ units}$$ NTC should order 1,897 units when stock drops to 692 units.

ABC Analysis: Prioritizing Inventory

ABC analysis classifies items by annual consumption value to focus resources on high-impact items.

• A Items: 15% of items, 70% of value (e.g., smartphone chips for Ncell).
• B Items: 30% of items, 20% of value (e.g., Daraz’s mid-range electronics).
• C Items: 55% of items, 10% of value (e.g., stationery for a school).

Worked Example: Pathao’s Bike Parts Inventory Pathao uses ABC analysis for bike parts:

Key Insight:

• A items (tires) get tight control (frequent reviews, higher safety stock).
• C items (chains) use minimal oversight (bulk orders, no stockouts tolerated).

Inventory Models: EOQ vs. Reorder Point

Two dominant models balance costs and service levels:

flowchart TD
    A["Start"] --> B["Demand Steady?"]
    B -->|"Yes"| C["Use EOQ Model"]
    B -->|"No"| D["Lead Time Known?"]
    D -->|"Yes"| E["Use ROP: ROP = d×L + SS"]
    D -->|"No"| F["Use Safety Stock + ROP"]
    C --> G["Calculate Q* = √(2DC₀/Cₕ)"]
    E --> H["Monitor stock; order when ≤ ROP"]
    F --> I["Increase SS for uncertainty"]
    G --> H

Worked Example: NEPSE’s Stock Trading Terminals NEPSE maintains 100 trading terminals/year at Rs 50,000/unit. Ordering cost = Rs 2,000/order, holding cost = 20% of value/year.

1. EOQ Calculation: $$Q^{\ast }=\sqrt{\frac{2\times 100\times 2000}{50000\times 0.20}}=\sqrt{40}=6.32\approx 6\text{ terminals}$$
2. Total Cost: $$\text{Ordering}=\frac{100}{6}\times 2000=\text{Rs 33,333/year}$$ $$\text{Holding}=\frac{6}{2}\times 50000\times 0.20=\text{Rs 30,000/year}$$ $$\text{Total Cost}=33,333+30,000=\text{Rs 63,333/year}$$
3. Reorder Point (lead time = 1 month, monthly demand = 8.33 units): $$ROP=8.33\times 1+2=10.33\approx 10\text{ terminals}$$ NEPSE should order 6 terminals when stock drops to 10.

Inventory Systems: Periodic vs. Perpetual

Real-World Tie-In: eSewa’s Digital Inventory eSewa uses a perpetual system for:

• Transaction logs (inventory = "completed transactions").
• Reorder point: When daily transactions drop below a threshold (e.g., 50,000), they scale servers.
• Costs:
  • Ordering: Rs 50,000 per server upgrade.
  • Holding: Rs 10,000/month per server (electricity, maintenance).
  • Shortage: Rs 200/transaction lost (customer churn).

Queuing Theory in Inventory: Shortage Costs

When demand exceeds supply, queuing theory models waiting costs. For inventory:

• M/M/1 Model: Single "server" (inventory), arrivals (demand) follow Poisson distribution.
• Key Metrics:
  • $L_q$: Average number of units waiting (shortage).
  • $W_q$: Average waiting time per unit.

Worked Example: Daraz’s Out-of-Stock Scenario Daraz sells 500 TVs/month. Supplier delivers 400 TVs/month (shortage = 100 units).

• Shortage Cost: Rs 5,000 per TV (lost sale + customer refund).
• Waiting Cost: Customers wait 2 weeks for backorder.
• Total Cost: $$C_s=100\times 5000=\text{Rs 500,000/year}$$ $$C_w=100\times 7\text{ days}\times \text{Rs 100/day}=\text{Rs 70,000/year}$$ Total shortage-related cost = Rs 570,000/year.

Solution: Increase order quantity to 450 TVs/month to reduce shortages.

## In the Real World

1. eSewa’s Transaction Processing

   • Idea Used: Perpetual Inventory System
   • How: eSewa tracks "inventory" of completed transactions in real-time. When daily transactions drop below a threshold (e.g., 50,000), they trigger server scaling (equivalent to reordering). The EOQ model helps decide how many servers to keep idle vs. ordering new capacity.
   • Cost Breakdown:
     • Ordering: Rs 50,000 per server upgrade.
     • Holding: Rs 10,000/month per server (electricity, maintenance).
     • Shortage: Rs 200 per lost transaction (customer churn).

2. Khalti’s Digital Payment Gateway

   • Idea Used: Fixed-Time Period Inventory System
   • How: Khalti processes payments in batches. They review inventory (server capacity) monthly and order upgrades if demand exceeds 80% capacity. This avoids over-provisioning but risks stockouts during peak periods (e.g., Dashain).
   • Real Example: During Dashain 2023, Khalti’s monthly review missed a 30% demand spike, causing Rs 2 million in lost transactions due to downtime.

3. Pathao’s Bike Maintenance Inventory

   • Idea Used: ABC Analysis + Safety Stock
   • How: Pathao classifies bike parts into A/B/C categories:
     • A (Tires): Weekly stock checks, 2-week safety stock (cost: Rs 240/unit).
     • B (Brakes): Monthly checks, 1-week safety stock (cost: Rs 24/unit).
     • C (Chains): Quarterly checks, no safety stock (cost: Rs 3/unit).
   • Impact: Reduced holding costs by 40% while maintaining 99% uptime.

## Exam Tip

1. Costs Are Everything

   • Always label costs in diagrams (ordering, holding, shortage).
   • For EOQ, show the parabola and mark $Q^{\ast }$. Examiners love this.

2. ABC Analysis = Pie Charts

   • Draw a pie chart with A/B/C labels. Example:
     • A: 70%, B: 20%, C: 10%.
     • Policies: "A items = weekly review, B = monthly, C = quarterly."

3. Real-World Scenarios

   • Tie examples to Nepali businesses:
     • NTC: Spare parts (EOQ + ROP).
     • Daraz: Bulk electronics (ABC + EOQ).
     • eSewa: Digital inventory (perpetual system).

4. Queuing Theory Shortcut

   • If demand > supply, use: $$\text{Shortage Cost}=(\text{Demand}-\text{Supply})\times \text{Cost per unit}$$
   • Example: Daraz’s TV shortage = (500 - 400) × Rs 5,000 = Rs 500,000/year.

5. Common Pitfalls

   • Forgetting lead time in ROP: $ROP=d\times L+SS$.
   • Mixing periodic/perpetual: Periodic = time-based; perpetual = stock-level.
   • Units mismatch: Ensure $D$ is in units/year, $Q$ in units/order.

Final Visual Summary:

mindmap
  root((Inventory Management))
    Costs
      Ordering Cost: Co × (D/Q)
      Holding Cost: Ch × (Q/2)
      Shortage Cost: Cs × (Demand - Supply)
    Models
      EOQ: Q* = √(2DC₀/Cₕ)
      ROP: d×L + SS
    Systems
      Periodic: Time-based (Khalti)
      Perpetual: Stock-level (eSewa)
    ABC Analysis
      A: 70% value, 15% items
      B: 20% value, 30% items
      C: 10% value, 55% items
    Real-World
      Daraz: ABC + EOQ
      NTC: ROP for spares
      eSewa: Perpetual system