Comprehensive Study Guide and Formula Repository for EBC1029

Exam Structure and Study Recommendations

• The EBC1029 exam consistently tests knowledge across ten major blocks:
  • Strategy
  • Innovation
  • Processes
  • Structures and line balancing
  • Quality
  • Inventory
  • Sourcing
  • Logistics
  • Demand planning
  • Master Production Scheduling (MPS) and Material Requirements Planning (MRP)
• Effective study methods include:
  • Memorizing core terminology.
  • Memorizing frequently appearing formulas.
  • Learning the specific logic behind rounding rules.
  • Practicing the identification of which formula applies to specific question types.

Rounding Rules and Conventions

• Adhering to rounding rules is critical as exam answers are often dependent on precise logic.

Standard Rounding

• Rules: If the first omitted digit is $5$ or greater, round up. If it is less than $5$, leave the digit as is.
• Examples:
  • $2.44 \rightarrow 2.4$
  • $2.45 \rightarrow 2.5$
• Requirement: Round only at the final step. Unless specified, do not round intermediate calculations.

Rounding to Whole Numbers

• Use standard rounding to the nearest integer for counts and specific quantities:
  • Economic Order Quantity (EOQ)
  • Units of product
  • Counts of items
• Example: $EOQ = 136.6 \rightarrow 137$

Always Round Up

• Use this logic when a minimum level or capacity must be guaranteed. Even a small decimal remainder requires moving to the next whole number.
• Applicable to:
  • Target order quantity
  • Required production capacity
  • Theoretical number of workstations
  • Service-level-based order quantities
• Examples:
  • $4.06 \text{ workstations} \rightarrow 5$
  • $42.26 \text{ magazines needed} \rightarrow 43$

Supply Chain Strategy

Key Financial Metrics

• Return on Assets (ROA): Measures profit earned relative to total assets.
  • $\text{ROA} = \frac{\text{Net Profit}}{\text{Total Assets}}$
• Net Profit Margin (NPM): Shows profit earned per euro of sales.
  • $\text{NPM} = \frac{\text{Net Profit}}{\text{Sales}}$
• Asset Turnover (AT): Indicates efficiency in using assets to generate sales.
  • $\text{AT} = \frac{\text{Sales}}{\text{Total Assets}}$

The Strategic Profit Model

• The relationship between the key metrics is expressed as:
  • $\text{ROA} = \text{Net Profit Margin} \times \text{Asset Turnover}$

Components of the Model

• Net Profit Calculations:
  • $\text{Net Profit} = \text{Sales} - \text{COGS} - \text{Variable Expenses} - \text{Fixed Expenses}$
  • Sales: Total revenue.
  • COGS: Cost of Goods Sold.
  • Variable Expenses: Costs that vary with activity levels.
  • Fixed Expenses: Costs that remain constant in the short term.
• Total Assets Components:
  • Inventory
  • Accounts Receivable (A/R)
  • Fixed Assets
  • Other current assets (if specified)
• Exam Note: If the question states "all other factors are zero," include only the categories explicitly listed.

ROA Calculation Example

• Data:
  • Sales = $7,000,000$
  • COGS = $4,500,000$
  • Variable expenses = $850,000$
  • Fixed expenses = $1,400,000$
  • Inventory = $800,000$
  • A/R = $200,000$
  • Fixed assets = $600,000$
• Steps:
  1. Net Profit: $7,000,000 - 4,500,000 - 850,000 - 1,400,000 = 250,000$
  2. Total Assets: $800,000 + 200,000 + 600,000 = 1,600,000$
  3. ROA: $\frac{250,000}{1,600,000} = 0.15625 = 15.63\%$

Innovation and Design Analysis

Failure Modes and Effects Analysis (FEMA)

• Used to identify potential failures early in the design phase.
• Risk Priority Number (RPN): Calculated to rank risks.
  • $\text{RPN} = \text{Occurrence} \times \text{Severity} \times \text{Undetectability}$
• Important Distinction: Exam questions may include an "Importance" table, but "Importance" is typically not included in the RPN product; use only Occurrence, Severity, and Undetectability.

House of Quality (HoQ)

• A matrix used in Quality Function Deployment (QFD).
• Customer Requirements: What the customer desires.
• Technical Requirements: Engineering and design characteristics.
• Roof of the House: Displays relationships between technical requirements.
  • Positive Relationship: One requirement supports another.
  • Negative Relationship: One requirement compromises another.
• Matrix Cells: Identify the strength of the linkage between customer and technical requirements.
• Common questions involve reading matrices to find:
  • Count of negative relationships between technical requirements.
  • Strong technical-to-customer requirement linkages.
  • Comparative performance against competitors.

Process Management and Capacity

Key Definitions

• Capacity: Maximum output a process can produce.
• Bottleneck: The specific step with the lowest capacity; it limits the entire system.
• Throughput: The rate at which units flow through the system.
• Cycle Time: The time between the completion of consecutive units or runs.

Capacity and Utilization Formulas

• Utilization of Maximum Capacity:
  • $\text{Utilization} = \frac{\text{Actual Output}}{\text{Maximum Capacity}} \times 100\%$
• Utilization of Effective Capacity:
  • $\text{Utilization} = \frac{\text{Actual Output}}{\text{Effective Capacity}} \times 100\%$
• Capacity Types:
  • Maximum Capacity: The ideal, best possible output.
  • Effective Capacity: Realistic output under normal, sustainable conditions.
  • Actual Output: The volume produced in reality.

Event and Ride Throughput Logic

1. Calculate required throughput:
   • $\text{Required Throughput} = \frac{\text{Total People}}{\text{Available Time}}$
2. Calculate required runs per hour:
   • $\text{Runs per Hour} = \frac{\text{Required Throughput}}{\text{People per Run}}$
3. Convert to cycle time:
   • $\text{Cycle Time} = \frac{60}{\text{Runs per Hour}}$

• Note: If multiple cabins/teams operate simultaneously, multiply the capacity per run by the number of units.

Parallel Processes

• If activities occur in parallel and perform the same task, their capacities are summed.
• To find process capacity, identify the capacity of every stage and select the lowest (the bottleneck stage).

Production Structures and Line Balancing

Metrics and Formulas

• Takt Time: The maximum time allowed per unit to meet demand.
  • $\text{Takt Time} = \frac{\text{Available Production Time}}{\text{Required Output}}$
• Theoretical Number of Workstations ($N_t$):
  • $N_t = \frac{\sum \text{Task Times}}{\text{Takt Time}}$
  • Rounding Rule: Always round up to the nearest whole integer.
• Idle Time: Calculated per workstation.
  • $\text{Idle Time} = \text{Takt Time} - \text{Workstation Time}$
• Efficiency of a Balanced Line:
  • $\text{Efficiency} = \frac{\sum \text{Task Times}}{\text{Number of Workstations} \times \text{Takt Time}} \times 100\%$

Assignment Rules and Terminology

• Longest Operating Time Rule:
  1. Respect precedence relationships (tasks that must be done first).
  2. From available tasks, assign the task with the longest duration first.
  3. Ensure total workstation time does not exceed takt time.
• Predecessor: A task that must be completed before another starts.
• Workstation Time: Sum of all task times assigned to a specific station.

Quality Management

Six Sigma Standards

• Represents a very low-defect quality goal.
• Standard Exam Rule: The total specification (tolerance) width is equal to $12$ standard deviations ($6\sigma$ on each side of the mean).
• Standard Deviation ($\sigma$) Calculation:
  • $\sigma = \frac{\text{Tolerance Width}}{12}$
  • If given a plus/minus tolerance: $\sigma = \frac{USL - LSL}{12}$
  • Alternatively: $\sigma = \frac{\text{Allowed deviation on one side}}{6}$

Categories of the Cost of Quality (CoQ)

1. Prevention Costs: Costs incurred to avoid defects (e.g., training, quality planning, design improvements).
2. Appraisal Costs: Costs for inspection, testing, and audits.
3. Internal Failure Costs: Defects found before delivery (e.g., scrap, rework, downtime).
4. External Failure Costs: Defects found after delivery (e.g., complaints, warranty, returns).

Cost of Quality Savings Calculation

1. Sum current costs for all four categories.
2. Adjust specific categories based on the proposal.
3. Calculate the new total cost.
4. $\text{Savings} = \text{Old Total} - \text{New Total}$

Inventory Management

Economic Order Quantity (EOQ)

• Designed to minimize the sum of ordering and holding costs.
• Formula 1: $EOQ = \sqrt{\frac{2DS}{H}}$
• Formula 2 (Course Notation): $EOQ = \sqrt{\frac{2D C_o}{C_i U}}$
• Variables:
  • $D$ = Annual demand (if monthly/quarterly, multiply to reach annual).
  • $S$ or $C_o$ = Ordering cost per order.
  • $H$ = Annual holding cost per unit ($H = C_i \times U$).
  • $C_i$ = Annual inventory carrying cost rate (percentage).
  • $U$ = Unit purchase cost.

Total Acquisition Cost (TAC) with Quantity Discounts

• $\text{TAC} = C_o \times \frac{D}{Q} + U \times C_i \times \frac{Q}{2} + U \times D$
• Components:
  • Term 1: Total Ordering Cost.
  • Term 2: Total Holding Cost.
  • Term 3: Total Purchase Cost (Product Cost).
• Problem-Solving Steps:
  1. Calculate EOQ using the discounted price.
  2. Determine if this EOQ qualifies for the discount (meets the threshold).
  3. If unqualified, test the minimum quantity required for the discount.
  4. Compare TAC at EOQ vs. TAC at the discount threshold; choose the lower cost.

Newsvendor Model / Target Service Level

• Target Service Level (TSL):
  • $\text{TSL} = \frac{C_{shortage}}{C_{shortage} + C_{excess}}$
• Cost Definitions:
  • Shortage Cost ($C_{shortage}$ or Underage): $\text{Selling Price} - \text{Purchase Cost}$.
  • Excess Cost ($C_{excess}$ or Overage): $\text{Purchase Cost} + \text{Disposal Cost} - \text{Salvage Value}$.

Normal Distribution and Target Order Quantity

• When demand follows a normal distribution:
  • $Q = \mu + z\sigma$
  • Variables: $Q$ = quantity to order, $\mu$ = expected demand, $z$ = z-value for service level, $\sigma$ = standard deviation.
• Common z-values:
  • $80\% \rightarrow 0.84$
  • $90\% \rightarrow 1.28$
  • $95\% \rightarrow 1.65$
  • $99\% \rightarrow 2.33$
  • $99.9\% \rightarrow 3.08$

Periodic Review Model

• Order quantity ($Q$):
  • $Q = d(T + L) + z\sigma_{T+L} - I$
• Variables:
  • $T$ = Review interval.
  • $L$ = Lead time.
  • $T + L$ = Uncertainty period.
  • $d$ = Average demand per period.
  • $\sigma_{T+L}$ = Standard deviation during uncertainty.
  • $I$ = Inventory on hand at review.

Sourcing and Supplier Evaluation

Insourcing vs. Outsourcing

• Insource Cost: $\text{Fixed Cost} + (\text{Variable Cost per Unit} \times \text{Demand})$
• Outsource Cost: $\text{Supplier Price per Unit} \times \text{Demand}$
• Decision: Select the option with the lower total annual cost.

Weighted-Point Model

• $\text{Supplier Score} = \sum (\text{Weight} \times \text{Rating})$
• Decision: Select the highest score.

Sourcing Portfolio and Strategy

• Item Categories: Leverage items, Routine items, Bottleneck items, Critical items.
• Purchasing Strategies: Simplify acquisition, ensure continuity of supply, maximize commercial advantage, build partnerships.

Logistics and Facility Location

Transportation and In-Transit Holding Costs

• $\text{Total Cost} = \text{Transport Cost} + \left(\frac{\text{Transit Days}}{365}\right) \times \text{Annual Carrying Rate} \times \text{Item Value} \times \text{Units}$
• Used to compare regular vs. express shipping.

Center-of-Gravity Method

• Calculates optimal coordinates for a facility based on weights (e.g., volume or shipments per year).
• X-coordinate: $X = \frac{\sum x_i w_i}{\sum w_i}$
• Y-coordinate: $Y = \frac{\sum y_i w_i}{\sum w_i}$

Demand Planning and Forecast Errors

Models

• Weighted Moving Average: $\text{Forecast} = \sum (\text{Weight} \times \text{Past Demand})$
• Exponential Smoothing: $F_{t+1} = \alpha D_t + (1 - \alpha)F_t$
  • $\alpha$ = smoothing constant.

Forecast Error Measures

• Error: $Actual - Forecast$
• Mean Forecast Error (MFE): $\frac{\sum (Actual - Forecast)}{n}$. Positive indicates underforecasting; negative indicates overforecasting.
• Mean Absolute Deviation (MAD): $\frac{\sum |Actual - Forecast|}{n}$. Average size of error regardless of sign.
• Mean Squared Error (MSE): $\frac{\sum (Actual - Forecast)^2}{n}$
• Root Mean Squared Error (RMSE): $\sqrt{MSE}$

Master Production Scheduling (MPS) and Material Requirements Planning (MRP)

Key Terms

• Bill of Materials (BOM): Shows relationships between parent items and children components.
• MPS: Production schedule for end items.
• MRP: Explosion of demand for components.
• Gross Requirements: Total needed in a period.
• Scheduled Receipts: Orders already in transit for arrival.
• Projected On-Hand: $On\,Hand_{t-1} + Scheduled\,Receipts_t + Planned\,Order\,Receipts_t - Gross\,Requirements_t$
• Net Requirements: $\text{Gross Requirements} - \text{Available Inventory}$.
• Planned Order Release: Started based on lead time.
• Fixed Order Quantity (FOQ): Rules for lot sizing (e.g., multiples of $60$).

Logic Applications

• BOM Explosion: Multiply requirements along the path (e.g., $1 \text{ product} \times 1 \text{ frame} \times 4 \text{ panels} = 4 \text{ total panels}$). Sum multiple paths to same item.
• Cumulative Lead Time: The longest summation of lead times from end item to the lowest component.
• Available to Promise (ATP):
  • First Period: $\text{Beginning Inventory} + \text{MPS} - \text{Sum of Booked Orders until next MPS}$.
  • Later Periods: $\text{MPS} - \text{Sum of Booked Orders until next MPS}$.

Miscellaneous Terms and Queuing Theory

• Root Cause Tools: Five Whys, Cause-and-Effect (Fishbone), Check Sheet, Scatterplot.
• Benchmarking: Competitive (against rivals) vs. Process (across industries).
• Alignment Stages: Internally neutral, Internally supportive, Externally neutral, Externally supportive.
• Project Management:
  • $EF = ES + \text{Duration}$
  • $\text{Slack} = LS - ES = LF - EF$. Critical path slack is zero.
• Queuing Theory:
  • Arrival Rate ($\lambda$), Service Rate ($\mu$). Only stable if $\lambda < \mu$.
  • Utilization: $\rho = \frac{\lambda}{\mu}$
  • Avg. number in system: $L = \frac{\lambda}{\mu - \lambda}$
  • Avg. time in system: $W = \frac{1}{\mu - \lambda}$
• Learning Curve: As output doubles, unit time falls by a constant rate. $T_n = T_1 n^b$.
• Layouts: Job shop, Batch, Assembly line, Fixed-position (e.g., airplanes).
• Push vs. Pull: Push relies on forecasts; Pull is triggered by actual demand.

Practice Exam Problems and Extended Solutions

1. Strategy: Sales $5,000,000$, COGS $3,000,000$, Var Exp $700,000$, Fixed Exp $900,000$. Inventory $400,000$, A/R $150,000$, Fixed Assets $450,000$.

   • Net Profit: $5,000,000 - 3,000,000 - 700,000 - 900,000 = 400,000$
   • Assets: $400,000 + 150,000 + 450,000 = 1,000,000$
   • ROA: $\frac{400,000}{1,000,000} = 40.00\%$. (Correct Answer: C)

2. Innovation: RPN with Occurrence $4$, Severity $5$, Undetectability $3$.

   • RPN: $4 \times 5 \times 3 = 60$. (Correct Answer: C)

3. Processes: Ride capacity $8/run$. $240$ visitors in $4$ hours.

   • Throughput: $\frac{240}{4} = 60/hour$.
   • Runs: $\frac{60}{8} = 7.5/hour$.
   • Cycle Time: $\frac{60}{7.5} = 8.0 \text{ minutes}$. (Correct Answer: A)

4. Processes: Max capacity $20$, Actual $12$.

   • Utilization: $\frac{12}{20} = 60\%$. (Correct Answer: A)

5. Structures: $7 \text{ hour shift}$, $21 \text{ units}$.

   • Takt: $\frac{7 \times 60}{21} = 20 \text{ minutes}$. (Correct Answer: B)

6. Structures: Total task time $33$, Takt $8$.

   • Workstations: $\frac{33}{8} = 4.125 \rightarrow 5$. (Correct Answer: B)

7. Quality: Target $40g \pm 3g$.

   • $\sigma = \frac{6}{12} = 0.5$. (Correct Answer: B)

8. Quality: Prev $900$, Appr $1000$, Internal $2400$, External $3000$ (Total $7300$). Proposal: Prev $+10\%$, Internal $-5\%$.

   • New Prev: $990$. New Internal: $2280$.
   • New Total: $990 + 1000 + 2280 + 3000 = 7270$.
   • Savings: $7300 - 7270 = 30$. (Correct Answer: A)

9. Inventory: Demand $300/quarter$, $C_o = 20$, $U = 8$, $C_i = 25\%$.

   • $D = 1200$. $H = 0.25 \times 8 = 2$.
   • $EOQ = \sqrt{\frac{2 \times 1200 \times 20}{2}} = 154.91 \rightarrow 155$. (Note: Options were incorrect in original test; 155 is correct).

10. Inventory: Demand $50, \sigma = 10, z = 1.28$.

    • $50 + 1.28(10) = 62.8 \rightarrow 63$ (Round up). (Correct Answer: A)

11. Sourcing: Demand $700$. Insource: $F=1500, V=9$. Outsource: $P=11$.

    • Insource: $700(9) + 1500 = 7800$.
    • Outsource: $700(11) = 7700$. (Correct Answer: B)

12. Sourcing: Ratings Price $4 (0.3)$, Quality $5 (0.5)$, Delivery $2 (0.2)$.

    • Score: $0.3(4) + 0.5(5) + 0.2(2) = 1.2 + 2.5 + 0.4 = 4.1$. (Correct Answer: A)

13. Logistics: A ($x=2, y=3, w=100$), B ($x=6, y=5, w=200$).

    • $X = \frac{2(100) + 6(200)}{300} = \frac{1400}{300} = 4.67$. (Correct Answer: A)

14. Demand: Demand $100, 120, 110, 150$. Weights $0.1, 0.2, 0.3, 0.4$.

    • Forecast: $10 + 24 + 33 + 60 = 127$. (Correct Answer: B)

15. Demand: Actuals ($40, 50, 45, 55$), Forecasts ($42, 49, 43, 50$).

    • Squared Errors: $4, 1, 4, 25$. Sum: $34$.
    • MSE: $34/4 = 8.5$. (Correct Answer: A)

16. MRP: $1 \text{ End product} = 2A, 3B$. $1A = 4C, 1B = 2C$.

    • Path 1: $1 \times 2 \times 4 = 8C$. Path 2: $1 \times 3 \times 2 = 6C$.
    • Total C: $14 \text{ per end product}$. For $100 \text{ products} = 1400$. (Correct Answer: A)