Inventory Management Formulas

Inventory Management

• Balances ordering cost, holding cost, and item cost
• Minimizes total inventory cost while meeting customer demand

EOQ (Economic Order Quantity)

• Optimal order quantity minimizes total inventory costs
• Formula: EOQ=√2DS/H
  • D = Annual demand
  • S = Setup/ordering cost
  • H = Holding cost per unit/year
  • Philly Fries orders 4000 bags/year, order costs $50, holding cost $5, resulting in an EOQ of 283 bags

TAC (Total Annual Cost)

• Formula: TAC=DC + (D/Q)S + (Q/2)H
  • C = Unit variable cost (4/unit)
  • Q = Order Quantity (units)
  • S = Setup (replenishment) costs
  • H = Holding (carrying) costs

ROP (Reorder Point)

• Inventory level at which a new order is placed
• Formula (no uncertainty): ROP=dxL
  • d = Average daily demand
  • L = Lead time
• Formula (with uncertainty): ROP=dL+ Z σ L

Service Levels

• 90% = 1.28
• 95% = 1.645
• 99% = 2.33

Inventory Systems

• Continuous Review: Fixed quantity is ordered when ROP is reached, used for high-value items
• Periodic Review: Order top-up amount at regular intervals, used for small-value items
• Fast “Usage” Recording: Button is pressed each time an item is taken, tied to software systems for constant tracking, low admin
• “Backflushing”: Product completion is recorded in software, automatically reducing all necessary components based on the bill-of-material

ABC Classification

• A: 10% of items = 70% of value
• B: 20% of items = 20% of value
• C: 70% of items = 10% of value

Safety Stock

• Buffer for demand or supply variability
• Formula: Safety Stock=Zx σ L

Examples

• Philly Fries uses EOQ and ROP
• Automated systems avoid year-end inventory
• Mattel’s inventory: 45% of items generate <5% of sales, categorized as C items

Supply Chain Components

• Procurement gets materials/services from suppliers
• Production makes products from raw materials
• Logistics moves and stores materials and goods
• Distribution gets finished products to customers/retailers
• The Customer is the person or business that buys and uses the product

Key Concepts/Terms

• Vertical Integration: doing in-house (ex. Tesla, Arc'Teryx), owning production stages
• Types of Purchasing:
  • Centralized purchasing: purchasing requests to a central procurement office
  • Stockless purchasing: supplier delivers material directly to the production area instead of a stockroom
  • Blanket purchase orders (POs): long-term commitment to a supplier for items delivered upon receipt of a shipping requisition
• Procurement and Contracts:
  • Vendor selection covers quality, price, and delivery
  • Buy-back: retailer returns unsold goods (Indigo)
  • Revenue sharing: share sales % instead of fixed purchase
  • VMI: vendor manages retailer's inventory (e.g., Coke coolers)
• Logistics Strategies:
  • Cross-docking: no storage, immediate shipping (Walmart)
  • Drop shipping: supplier ships directly to the customer
  • Intermodal shipping: same container on multiple modes
  • Postponement:
    • Delay customization (HP printers)
    • Reduce holding costs and increase flexibility
  • 3PL:
    • Third-party logistics (warehousing, fulfillment)
  • Humanitarian Supply Chains:
    • Fast response > cost
    • High inventory, perishable goods, multi-party coordination
  • Reverse Supply Chains:
    • Handle returns/recycling (Xerox manufacturing, Calgary recycling plant)
  • Product Design:
    • Design for manufacturability
    • Labeling and packaging postponement
    • Modular design flexibility: creation of products (goods and services) from some combination of basic, pre-existing subsystems (or modules)

Tesla's Lithium-Ion Battery Sourcing

• Tesla vertically integrates by partnering with and owning part of its battery suppliers (e.g., Panasonic) and building Gigafactories

Cost of Air Shipping vs. Rail or Cargo Ship

• Air freight can be cheaper overall due to fast delivery, lower inventory holding costs, and fewer damages/losses

Walmart's Distribution Center Efficiency

• Walmart uses cross-docking, where products are immediately transferred from inbound to outbound trucks without being stored

Improving Supply Chain Performance

• Slowing down (e.g., shipping in smaller batches or reducing rush orders) can reduce errors, variability, excess inventory, and costs

Printer and Laptop Power Supply Design

• The power supply is on the cord to postpone customization, allowing the same base product to be shipped globally

Humanitarian Supply Chain

• Supply chain is designed to quickly and efficiently deliver aid in emergencies, often prioritizing speed over cost operating under uncertain conditions

Reverse Supply Chain

• Flow of goods from customers back to suppliers for returns, recycling, or remanufacturing

IKEA Mug Redesign

• Redesigning mugs to be stackable and flat-packed increased pallet efficiency by four times

Blockchain's Impact on Supply Chains

• Blockchain can increase transparency, traceability, and trust by recording tamper-proof transactions

Walmart's Use of AI in Negotiations

• Walmart uses AI to automatically negotiate contracts to save time and improve consistency

SCM eBeer Simulation: Key Learnings

• Bullwhip Effect: amplification of demand as it moves upstream
  • Caused by lack of communication, long lead times, panic ordering
  • 3-week lead time
  • stockouts, overstock, backlogs

Fixes

• Share actual consumer demand (POS)
• Reduce batch size
• CPFR: Collaborative Planning, Forecasting, Replenishment
• IT Tools: ERP systems, VMI

Cost of Quality

• Prevention (checklists, failsafe)
• Appraisal (inspections)
• Internal Failure (rework, scrap)
• External Failure (returns, lawsuits)
• Quality is “free” (Crosby) if costs shift from failure to prevention

Quality Philosophies

• Six Sigma: 3.4 defects per million (DMSIC)
• PDCA (Plan, Do, Check, Act)

Tools

• Checklists (WHO surgical)
• Failsafe (5 cent syringe, crib recall, envelope windows)
• Pareto Chart (80/20 rule)
• Fishbone Diagram (Man, Material, Method, Machine, Measurement)
• Scatterplots

Control Charts

• p-Chart (proportion defective) determines the average proportion defective from a number of samples

Control Limits

• Upper and lower control limits for p-charts are calculated

UCL and LCL

• UCL (upper control limit) = p + z s p
• LCL (lower control limit) = p - z s p
  • The LCL is equal to zero if it is calculated as a negative number

Charts Used in Tandem

• Chart for central tendency (x̄ – chart)(average)
  • UC Lx = x́ + 3 s x = X́ + A2 R
  • LC Lx = x́ - 3 s x = X́ - A2 R
• Chart used for variability (R-chart)(range)
  • UC LR =R+3 s R=D 4 R
  • LC LR =R-3 s R= D3 R
• The most common case is z=3

Examples

• MGM cleaning p-chart
• Battery life example: use x and R charts to test if the process is in control

Certification

• ISO 9000: Quality processes
• ISO 14000: Environmental
• ISO 26000: Social responsibility (non-certifiable)

How Quality Costs Money

• Quality costs money (prevention, testing), but avoids bigger costs like rework and lawsuits

Process be “idiot-proofed”

• By using failsafes or poka-yoke devices that make mistakes impossible

“Self-Destructing” Syringe

• Prevents reuse, helping stop the spread of diseases like HIV

Black Belts

• Six Sigma experts trained to lead process improvement projects

ISO9000 and ISO14000 Banners

• Show that a company meets international standards

FAQs

• Built by tracking common issues over time and preventing repeat mistakes

Fishbone Diagram (Ishikawa)

• Visually maps the root causes of problems (e.g., Man, Machine, Material, Method)

Process “in control”

• Use control charts – if data points are within UCL and LCL and show no weird patterns, the process is statistically stable

Process capability analysis

• Shows if a process consistently produces within spec limits

Flowcharts

• Map process steps and identify bottlenecks

Symbols

• tasks, decisions, queues

Benchmarking

• Internal: within the same firm
• Competitive: hard to get data
• Functional: Compared to industry leaders

Process Improvement

• BPR (tear-down): radical redesign
• CPI (tinker): incremental changes
• Disruptive Tech Examples: cell phones, digital music/cameras

“Expose the Rocks”

• Inventory hides inefficiencies
• Culture Requirements:
  • Cross-functional teams
  • Creativity Time
  • Willingness to change

Formal Process Flow Diagram

• Map each step in a process using standard symbols

Benchmarking

• Comparing processes to top performers for improvement

Process Improvement Approaches

• Tinker = CPI (Continuous Process Involvement), small, steady changes
• Tear-Down = BPR (Business Process Reengineering), radical redesign for major improvement

Technologies Revolutionized Industries

• Disruptive tech like smartphones changed entire industries

“Push” vs. “Pull” Production System

• Push = produce based on forecasts then try to sell
• Pull = produce based on actual demand to minimize waste

“Expose the Rocks”

• Reduce inventory to reveal hidden problems

Case Studies

• HP Printers: postponed customization for better global inventory use
• Canadian Tire: CPFR reduced lead times dramatically
• Mattel: 45% of products = 5% of sales
• Canadian Blood Services: flow redesign reduced donor frustration
• Walmart: cross-docking