Operations Management

Operations Management:

The systematic design, direction, and control of business processes that convert organizational resources (inputs) into finished goods and services (outputs).

• Transformation Model: $\text{Inputs} \xrightarrow{\text{Transformation / Conversion Process}} \text{Outputs} \xrightarrow{\text{Feedback Loop}} \text{Continuous Control}$. Inputs include 5 Ms (Manpower, Material, Machine, Money, Methods).

Productivity Formulas:

• Single-Factor Labor Productivity:

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  $$\text{Labor Productivity} = \frac{\text{Total Output (Units or Value)}}{\text{Labor Hours (or Labor Cost)}}$$
• Multi-Factor Productivity:

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  $$\text{Multi-Factor Productivity} = \frac{\text{Total Output}}{\text{Labor} + \text{Materials} + \text{Energy} + \text{Capital} + \text{Overhead}}$$

Cycle Time ($C$):

The maximum time that a product is allowed to spend at each individual workstation on an assembly line to achieve the target daily production quota.

Formula:

Six Sigma Quality:

A statistical quality standard indicating that process performance operates at six standard deviations between the mean and nearest specification limit. It translates to no more than 3.4 Defects Per Million Opportunities (DPMO), representing $99.99966\%$ defect-free manufacturing accuracy.

Kanban:

A Japanese visual signaling card or electronic trigger utilized in Lean pull production systems. It authorizes the production or withdrawal of a standardized container of parts from upstream processes only when an immediate downstream process has consumed its existing inventory.

Step 1: Compute Inputs & Outputs

• Total Output in Units = 100,000 crates
• Total Output Value = $100,000 \times 100 = \text{NPR } 10,000,000$
• Total Labor Hours = $50 \times 160 = 8,000 \text{ hours}$
• Total Labor Cost = $8,000 \times 200 = \text{NPR } 1,600,000$
• Material Cost = NPR 3,000,000
• Energy Cost = NPR 500,000
• Total Multi-Factor Inputs = $1,600,000 + 3,000,000 + 500,000 = \text{NPR } 5,100,000$

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Step 2: Compute Productivity Metrics

(a) Labor Productivity (Physical Units):

(b) Labor Productivity (Value Ratio):

(Each rupee spent on labor generates NPR 6.25 in revenue).

(c) Multi-Factor Productivity:

(Every NPR 1.00 of combined operational input yields NPR 1.96 of revenue).

(a) Cycle Time ($C$):

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(b) Theoretical Minimum Workstations ($N_{min}$):

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(c) Line Efficiency & Balance Delay ($N_{actual} = 5$):

• Line Efficiency:

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  $$\text{Efficiency} = \frac{\sum t}{N_{actual} \times C} \times 100\% = \frac{8.0}{5 \times 2.0} \times 100\% = \frac{8.0}{10.0} \times 100\% = \mathbf{80.0\%}$$
• Balance Delay (Idle Time Percentage):

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  $$\text{Balance Delay} = 100\% - \text{Efficiency} = 100\% - 80\% = \mathbf{20.0\%}$$

(a) Economic Order Quantity (EOQ):

Given:

• Annual Demand ($D$) = 10,000 units
• Ordering Cost ($S$) = NPR 500
• Holding Cost ($H$) = NPR 4 per unit/year

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(b) Optimal Number of Orders per Year ($N$):

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(c) Total Annual Inventory Cost (TIC):

(Note: At EOQ, Annual Ordering Cost exactly equals Annual Holding Cost).

Center-of-Gravity Method:

Finds the location that minimizes total weighted transportation costs based on Euclidean coordinates $(x_i, y_i)$ and shipment volumes $(W_i)$:

Calculations:

The optimal location coordinate for the central warehouse is (48.0, 36.0).

The DMAIC Methodology:

A closed-loop, data-driven 5-phase quality improvement framework:

1. Define: Explicitly define customer Critical-to-Quality (CTQ) parameters, project boundaries, and business goals using a Project Charter.
2. Measure: Quantify current baseline performance by gathering data on defect frequencies and process cycle times.
3. Analyze: Identify root causes of variation and defects using Ishikawa (Fishbone) diagrams, 5-Whys, and Pareto charts.
4. Improve: Develop, pilot, and deploy targeted solutions to eliminate root causes; optimize settings using Design of Experiments (DOE).
5. Control: Institute Statistical Process Control (SPC) charts, standard operating procedures, and mistake-proofing (Poka-Yoke) to ensure process gains are permanently sustained.

Chase Strategy vs. Level Strategy:

Step 1: Forward Pass (ES & EF)

• A (Dur=3): $ES = 0, \; EF = 0 + 3 = 3$
• B (Dur=4): $ES = 3, \; EF = 3 + 4 = 7$
• C (Dur=2): $ES = 3, \; EF = 3 + 2 = 5$
• D (Dur=6): $ES = 7, \; EF = 7 + 6 = 13$
• E (Dur=3): $ES = 7, \; EF = 7 + 3 = 10$
• F (Dur=4, Pred: C, D): $ES = \max(5, 13) = 13, \; EF = 13 + 4 = 17$
• G (Dur=2, Pred: E, F): $ES = \max(10, 17) = 17, \; EF = 17 + 2 = 19$

Total Project Duration = 19 weeks.

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Step 2: Backward Pass (LF & LS)

• G (Dur=2): $LF = 19, \; LS = 19 - 2 = 17$
• F (Dur=4, Succ: G): $LF = 17, \; LS = 17 - 4 = 13$
• E (Dur=3, Succ: G): $LF = 17, \; LS = 17 - 3 = 14$
• D (Dur=6, Succ: F): $LF = 13, \; LS = 13 - 6 = 7$
• C (Dur=2, Succ: F): $LF = 13, \; LS = 13 - 2 = 11$
• B (Dur=4, Succ: D, E): $LF = \min(7, 14) = 7, \; LS = 7 - 4 = 3$
• A (Dur=3, Succ: B, C): $LF = \min(3, 11) = 3, \; LS = 3 - 3 = 0$

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Step 3: Slack (Total Float) & Critical Path Table

Conclusions:

• Critical Path: A $\rightarrow$ B $\rightarrow$ D $\rightarrow$ F $\rightarrow$ G
• Total Project Completion Time: 19 weeks
• Non-critical activities C and E possess 8 weeks and 7 weeks of slack respectively, allowing resource leveling without delaying the completion date.

1. Total Quality Management (TQM):

An organization-wide management philosophy aimed at continuously improving the quality of products, processes, and corporate culture to exceed customer expectations.

• Core pillars: Customer focus, Total employee involvement, Process-centered thinking, Integrated system, Continuous improvement (Kaizen), and Data-based decision making.

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2. The Seven Basic Quality Control (QC) Tools (Ishikawa’s Tools):

1. Check Sheet: Structured form for real-time manual defect logging.
2. Histogram: Visual graphic showing frequency distributions and central tendencies of measurements.
3. Pareto Chart: Bar chart illustrating the 80/20 rule (vital few causes produce majority of defects).
4. Cause-and-Effect (Fishbone / Ishikawa) Diagram: Maps categorized root causes (Man, Machine, Material, Method, Measurement, Milieu).
5. Scatter Diagram: Graphical plot testing mathematical correlation between two variables.
6. Flowchart / Process Map: Visual sequence of process steps highlighting bottlenecks.
7. Control Chart (Shewhart Chart): Time-series plot with statistical Upper and Lower Control Limits ($UCL, LCL$) to monitor process stability.

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3. Statistical Process Control (SPC) & Control Charts:

SPC uses statistical sampling to monitor a process over time and distinguish between two types of variation:

• Common Cause (Random) Variation: Natural, inherent background noise of a stable system (e.g. slight temperature fluctuations). Cannot be eliminated without fundamentally redesigning the process.
• Assignable (Special Cause) Variation: Specific, identifiable anomalies that shift the process out of control (e.g. worn machine tool, operator fatigue, bad raw material batch).

$\bar{X}$ and $R$ Charts:

• $\bar{X}$ Chart (Mean Chart): Monitors changes in the central process average over time.

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  $$UCL_{\bar{X}} = \bar{\bar{X}} + A_2 \bar{R}, \quad LCL_{\bar{X}} = \bar{\bar{X}} - A_2 \bar{R}$$
• $R$ Chart (Range Chart): Monitors process dispersion and variability.

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  $$UCL_R = D_4 \bar{R}, \quad LCL_R = D_3 \bar{R}$$
  If sample points fall within bounds without non-random trends, the process is deemed in statistical control; any point crossing $UCL/LCL$ triggers immediate root-cause intervention before defective output reaches customers.