Operations Management Core Concepts and Formulas Review

Posted on Nov 15, 2025 in Business Administration and Innovation Management

Operations Management Core Concepts Review

1. Competitive Dimensions and Key Performance Indicators (KPIs)

Competitive Dimensions: How a company positions itself in the market.

  • Cost / Price: Offering products/services at a low price (e.g., Commodities).
  • Product Quality & Reliability: Delivering high-quality, dependable products (e.g., Vehicles).
  • Delivery Speed: Quickly providing products/services (e.g., Fast food, Same-day delivery).
  • Delivery Reliability: Meeting promised delivery times (e.g., FedEx, JIT).
  • Coping with Changes in Demand: Adjusting production volume based on demand fluctuations (e.g., Seasonal businesses).
  • Flexibility & New Product Introduction Speed: Quickly changing products or introducing new ones (e.g., Intel).
  • Other Product-Specific Criteria: Supporting the product (e.g., Technical support, Installation, Maintenance).

Core Competency: What a company does uniquely well compared to competitors. Provides market access, increases customer value, and is hard to imitate.

Order Qualifiers: Minimum criteria a product/service must meet to be considered by a customer.

Order Winners: Criteria that differentiate a product/service and lead to customer purchase. Order winners can become order qualifiers over time.

Key Performance Indicators (KPIs): Metrics used to measure performance and drive behavior. Examples include Lead time, Total Inventory, Inventory turns, Utilization, Efficiency, Productivity, On-time delivery, Scrap/Rework cost % of Sales, and Warranty cost % of Sales. The concept of a Balanced Scorecard relates to using a mix of financial and non-financial KPIs.

2. Productivity Measurement and Calculation

Productivity = Output / Input

  • Productivity: Measure of resource utilization.
  • Total Measure Productivity: Goods/services produced / All resources used.
  • Partial Measure Productivity: Output / Single input (Labor, Capital, Materials, Energy).
  • Multifactor Measure Productivity: Output / Group of inputs (e.g., Labor + Capital).
  • Percent Change Calculation: [(New – Old) / Old] × 100%.

3. Process Performance: Special and Common Causes of Variation

  • Process Variation: All processes inherently have variation.
  • Common Cause (Random) Variation: Inherent to the system, affects all outcomes. Caused by system design/faults (e.g., poor training, equipment). Requires management action to change the system. Accounts for ≥ 85% of problems. A process is statistically in control when only common cause variation is present (predictable).
  • Special Cause (Assignable) Variation: Not inherent; arises from specific, identifiable circumstances (e.g., broken tool, material change). Can be corrected by the operator or supervisor. Accounts for ≤ 15% of problems. A process is not in statistical control when special cause variation is present (unpredictable).

4. Project Management: Critical Path Method (CPM)

  • Project: A series of related tasks directed towards a major output over time.
  • Project Management: Planning, directing, and controlling resources to meet time, cost, and technical goals.
  • Network-Planning Models (CPM/PERT): Represent projects as networks of activities.
  • Critical Path: The longest time path through the network, which determines the project duration. Activities on the critical path have zero slack.
  • CPM Steps:
    1. Identify activities and their duration.
    2. Sequence activities and build the network diagram.
    3. Determine the critical path (calculate Early Start (ES), Early Finish (EF), Late Start (LS), Late Finish (LF), and Slack).
  • Single Time Estimate CPM: Used when activity times are known with certainty.
  • Three Activity Time Estimates CPM: Used when activity times are uncertain (uses Beta distribution), providing probability information regarding completion time.
  • Time-Cost Models (Crashing): Analyze cost trade-offs required to reduce project time.
  • Work Breakdown Structure (WBS): A hierarchy of project tasks.
  • Earned Value Management (EVM): Objective measure of project progress concerning scope, schedule, and cost.
  • Project Structures: Pure Project, Functional Project, and Matrix Project.

5. Process Analysis: Flow, Waste, and Little’s Law

  • Process: Transforms inputs into outputs.
  • Process Flowcharting: Diagramming process elements (tasks, flows, decisions, storage) to understand, analyze, and improve the process. This technique helps identify waste.
  • Cycle Time: Average time between successive unit completions. Cycle Time = 1 / Throughput Rate.
  • Throughput Rate: The rate at which units are completed.
  • Blocking: A process stops because there is no place to put the completed item (downstream bottleneck).
  • Starving: A process stops because no work is available (upstream bottleneck).
  • Little’s Law: Applies to steady-state processes: Flow Time = Work-In-Process (WIP) / Throughput Rate.
  • Flow Time (Throughput Time): Total time for a unit to move through the system.
  • Scrap: Waste material that impacts the inputs needed for production.
  • Seven Classes of Waste (“Muda”): Excess Production, Waiting, Transportation, Processing, Inventory, Motion, Defects (often remembered by the acronyms TIM WOOD or DOWNTIME).
  • Process Improvement: Systematically analyzing activities to Eliminate, Simplify, Change sequence, Combine, or Standardize. Focus is on improving flow.

6. Work Measurement Techniques and Time Standards

  • Work Measurement: Analyzing jobs to set time standards. Used for scheduling, capacity planning, performance evaluation, and benchmarking.
  • Production/Time Standard: The time required for a trained worker using a prescribed method with normal effort/skill to complete a task. Normal performance equals 100% efficiency.
  • Time Study: Directly observing and timing tasks.
    1. Select elements of the task.
    2. Time elements (using continuous or snap-back methods).
    3. Determine the required sample size (based on confidence and accuracy formulas).
    4. Set the standard (apply performance rating to get Normal Time, then add allowances for Standard Time).
    • Normal Time (NT): Observed Time × Performance Rating.
    • Standard Time (ST): NT × (1 + Allowances) or NT / (1 – Allowances).
  • Work Sampling: Estimating the proportion of time spent on various activities through random observations. Used for utilization studies and setting allowances. Requires truly random observations.
  • Predetermined Time Systems (e.g., MTM, MOST, MODAPTS): Analyzing tasks into basic motions and using pre-set times for those motions. No direct timing is needed. Standards can be set before the job starts. These systems use Time Measurement Units (TMU).

7. Breakeven Analysis for Decision Making

  • Breakeven Analysis: A method for choosing among alternatives by finding the point where total revenue equals total cost, or where profit begins.
  • Breakeven Demand Formula: (Total Fixed Costs) / (Price per unit – Variable costs per unit).

8. Assembly Line Balancing and Efficiency

  • Assembly Line Balancing: Assigning tasks to workstations so that each station takes no more time than the workstation cycle time.
  • Workstation Cycle Time: The time interval between successive units coming off the line. This is limited by the longest task time (the bottleneck).
  • Precedence Relationship: The required order in which tasks must be performed.
  • Steps in Line Balancing:
    1. Specify relationships (precedence diagram).
    2. Determine the required cycle time.
    3. Determine the theoretical minimum number of workstations (Σ Task Times / Cycle Time).
    4. Select assignment rules (heuristics).
    5. Assign tasks to workstations.
    6. Evaluate efficiency.
  • Bottleneck: The station with the longest task time, which limits the line’s output.
  • Efficiency: (Σ Task Times) / (Actual Workstations × Cycle Time).
  • Strategies for Task Time > Cycle Time: Splitting tasks or using parallel stations.
  • Mixed-Model Line Balancing: Producing different products on the same line, requiring reduced setup times.

9. Process Capability: Cp and Cpk Ratios

Remember: Control limits are not the same as specification limits.

  • Statistical Control vs. Process Capability: Control means the process is predictable (only common cause variation); Capability means the process meets customer specifications. A process can be in control but not capable.
  • Specification Limits (USL, LSL): Customer or design requirements for individual units. These are NOT the same as Control Limits.
  • Control Limits: Based on process variation, used for Statistical Process Control (SPC) charts to detect special causes.
  • Cp (Process Capability Index): Potential capability when the process is perfectly centered.
    • Formula: Cp = (USL – LSL) / (6 × σ).
    • Needs to be > 1.0, ideally ≥ 1.33.
  • Cpk (Process Capability Ratio): Actual capability, which considers process centering.
    • Formula: Cpk = Min[(USL – &bar;X) / (3 × σ), (&bar;X – LSL) / (3 × σ)].
    • Cpk ≤ Cp.
    • A Cpk = 1.0 means the mean is 3 standard deviations from the nearest specification limit.
  • Assumptions for Capability Analysis: Process is in control, data is normally distributed, specifications reflect customer needs, the target is the center, and measurement error is small.
  • Troubleshooting (In Control but Not Capable): Strategies include reducing variability, shifting the mean, or widening specifications.

10. Six Sigma and Lean Manufacturing Principles

  • Quality Management (TQM): Managing the organization for excellence in dimensions important to the customer.
  • Costs of Quality: Prevention, Appraisal, Internal Failure, and External Failure. Costs increase significantly at later stages.
  • Six Sigma: A data-driven approach to reduce defects (targeting 3.4 Defects Per Million Opportunities – DPMO). Uses the DMAIC methodology (Define, Measure, Analyze, Improve, Control). Focuses primarily on reducing variation.
  • Lean Manufacturing (Just-In-Time – JIT): A philosophy of minimizing waste (muda) to achieve high volume production with minimal inventory.
    • Toyota Production System: Built on the elimination of waste and respect for people.
    • Push vs. Pull Systems: Push systems are forecast-based; Pull systems are demand-based and limit Work-In-Process (WIP). Lean/JIT utilizes a Pull system.
    • Waste Elimination: Targeting the 7 classes of waste (TIM WOOD).
    • Setup Reduction (Quick Changeovers): Crucial for enabling smaller batches and reduced inventory (SMED – Single-Minute Exchange of Die). Strategies involve converting internal setup activities to external ones and standardizing processes.
    • Inventory Reduction: Lean aims to minimize inventory because it hides problems and is a form of waste.
    • Value Stream Mapping: Visualizing and analyzing material and information flow to identify and eliminate waste.
    • Respect for People: Empowering employees and utilizing quality circles.
    • 5S: Workplace organization methodology (Sort, Straighten, Shine, Standardize, Sustain).
  • Lean Supply Chains: Extending Lean principles throughout the entire supply chain.

11. Aggregate Planning Strategies

  • Sales and Operations Planning (S&OP) / Aggregate Operations Plan: Medium-range planning (3-18 months) used to match supply with demand. It balances production rate, workforce level, and inventory.
  • Aggregation: Planning for product groups rather than individual items.
  • Objective: Minimize the cost of resources required to meet forecasted demand.
  • Key Strategies:
    • Chase Strategy: Matches the production rate exactly to demand by hiring and firing workers. Minimizes inventory but results in high labor costs and HR issues.
    • Level Strategy: Maintains a constant production rate and workforce level. Uses inventory and backorders to absorb demand fluctuations. Provides a stable workforce but incurs higher inventory costs.
    • Mixed Strategy: A combination of chase and level approaches (e.g., using overtime, subcontracting, and limited hiring/firing). This is the most common strategy in practice.
  • Cut-and-Fit Approach: Costing out different planning scenarios.
  • Relevant Costs: Production (labor, overtime, subcontracting), Inventory (holding, shortage), and Workforce (hiring, layoff).

12. Inventory Metrics: Turnover and Days of Supply

  • Inventory Turnover: Calculated as Cost of Goods Sold / Average Aggregate Inventory Value. Measures how many times inventory is sold and replaced per year. A higher turnover rate is generally better.
  • Days/Weeks of Supply: Calculated as (Average Aggregate Inventory Value / COGS) × 365 (or 52). Indicates how many days or weeks of sales can be met with current inventory levels.

13. Inventory Management Models

  • Inventory: Stock of items or resources held.
  • Inventory System: Policies and controls for monitoring inventory levels and determining when and how much to order.
  • Purposes of Inventory: To decouple operations, meet demand variation (safety stock), buffer against lead time variation (safety stock), provide production scheduling flexibility (cycle inventory), and take advantage of order size (cycle inventory).
  • Inventory Costs: Holding, Setup/Production Change, Ordering, and Shortage costs.
  • Independent Demand: Demand for final products, unrelated to other items (managed by multi-period models).
  • Dependent Demand: Demand derived from the demand for another item (managed by Material Requirements Planning – MRP).
  • Single-Period Model (Newsvendor): Used for one-time orders of perishable or limited-life items. Balances overstock (Co) and understock (Cu) costs. The optimal quantity is based on the critical ratio Cu / (Cu + Co).
  • Multi-Period Models:
    • Fixed-Order Quantity (Q-model / EOQ): Event triggered (reorder point R). Orders a fixed quantity Q. Requires continuous monitoring. Favors expensive or important items.
      • EOQ Formula: Optimal Q minimizing holding and ordering costs: EOQ = √((2DS) / H). Assumes constant demand, lead time, price, and no stockouts.
      • Reorder Point (R): Inventory level that triggers an order. R = (Average daily demand × Lead time) + Safety Stock. Safety stock buffers variability, based on the desired service level.
    • Fixed-Time Period (P-model / Periodic): Time triggered (regular review). Orders vary to bring inventory up to a target level. Requires less monitoring but necessitates higher safety stock. Favors less expensive items.
  • Price Break (Quantity Discounts): Lower price offered for larger orders. Requires comparing the total cost at the EOQ quantity and at the price break quantities.

14. Material Requirements Planning (MRP) and Lot Sizing

MRP is a system for managing dependent demand inventory, determining what, how much, and when components are needed for finished goods.

MRP Inputs:

  • Master Production Schedule (MPS): Specifies when and how many finished goods are needed (derived from the Aggregate Plan).
  • Bill of Materials (BOM): The structure of components and materials required for a product, including the production sequence. Low Level Coding is essential.
  • Inventory Records: On-hand inventory, lead times, and lot-sizing rules.

MRP Process and Lot Sizing:

The MRP process explodes the MPS/BOM, calculates gross requirements, adjusts for on-hand inventory and scheduled receipts to determine net requirements, and then plans orders based on lot sizing and lead times.

  • MRP Table: Shows planned order releases and receipts over time for each item.
  • Lot Sizing Rules: Determine how much to order when needed in MRP.
    • Lot-for-Lot (L4L): Order the exact net requirement. Minimizes inventory holding costs.
    • Economic Order Quantity (EOQ): Uses the standard EOQ formula.
    • Least Total Cost (LTC): Chooses the lot size where ordering/setup costs approximate holding costs.
    • Least Unit Cost (LUC): Chooses the lot size that results in the lowest cost per unit.
  • Closed Loop MRP: Includes capacity planning feedback mechanisms.
  • Time Fences: Controls allowed changes to the MPS (Frozen, Slushy, Liquid zones).

15. Scheduling and Assignment Techniques

Workcenter Scheduling Objectives:

Meet due dates, minimize lead time, minimize setup time, minimize Work-In-Process (WIP), and maximize utilization. It is difficult to optimize all objectives simultaneously.

  • Priority Rules (n jobs on 1 machine): Sequencing jobs. Examples include:
    • FCFS (First-Come, First-Served)
    • SPT (Shortest Processing Time – minimizes average flow time and WIP)
    • EDD (Earliest Due Date – minimizes lateness)
    • STR (Slack Time Remaining), CR (Critical Ratio), LCFS (Last-Come, First-Served)
  • Johnson’s Rule (n jobs on 2 machines): Minimizes total completion time. Sequence jobs based on the shortest processing time on either machine (schedule the shortest time on machine 1 first, and the shortest time on machine 2 last).
  • Assignment Method (Hungarian Method): Assigning n tasks to n resources to minimize total cost or time. Uses a cost matrix and row/column reductions.
  • Work Center: An area containing resources where work is performed.
  • Shop-Floor Control: Managing work in the shop (priority, WIP tracking, status updates, data collection).
  • Input/Output Control: Managing the flow of work into and out of work centers, focusing particularly on bottlenecks.
  • Capacity & Scheduling:
    • Infinite Loading: Scheduling based on need (e.g., MRP), ignoring capacity constraints.
    • Finite Loading: Creating feasible schedules based on actual capacity limitations.
  • Scheduling Directions:
    • Forward Scheduling: Determines the earliest completion date.
    • Backward Scheduling: Starts from the due date and works backward (used in MRP).

16. Theory of Constraints (TOC)

  • Theory of Constraints (TOC): A management philosophy focused on identifying and managing constraints (bottlenecks) to achieve the organizational goal (making money).
  • Constraint (Bottleneck): Anything that limits the system’s performance. Constraints can be physical or non-physical.
  • TOC Steps (The Five Focusing Steps):
    1. Identify the constraint.
    2. Exploit the constraint (maximize its use).
    3. Subordinate everything else to the constraint.
    4. Elevate the constraint (invest to increase capacity).
    5. If the constraint is broken, repeat the process (do not allow inertia to set in).
  • Financial Metrics: Net Profit, Return on Investment (ROI), and Cash Flow (all are necessary).
  • Operational Metrics (TOC):
    • Throughput: Money generated by sales.
    • Inventory: Money tied up in things intended to be sold.
    • Operating Expenses: Money spent to convert inventory into throughput.
  • Goal (Operations Standpoint): Increase Throughput, reduce Inventory, and reduce Operating Expense.
  • Unbalanced Capacity: TOC emphasizes balancing flow, not capacities. Bottlenecks determine the system output.
  • Dollar Days: A measure combining inventory value and time ($$ × Days).
  • Synchronous Manufacturing: TOC-based scheduling that balances flow. Often uses forward scheduling.

Other Relevant Operations Management Concepts

Transformation Processes and Manufacturing Structures

  • Transformation Processes: How inputs become outputs (Physical, Locational, Exchange, Storage, Physiological, Informational).
  • Manufacturing Process Structures: Related to product variety and volume. Includes Job Shop, Batch, Assembly Line, Continuous Flow, Group Technology/Cellular, and Fixed Position.

Facility Layout Planning

Arranging departments and workstations. Inputs include objectives, demand, process requirements, and space.

  • Process Layout: Grouping similar equipment (used in Job Shop, Batch). Characterized by low volume, high variety, flexibility, high WIP, and high material handling. Planning uses From-To Charts and Relationship Charts (Vowel Coding).
  • Product Layout: Arranging resources by product flow (Assembly Line, Continuous). Characterized by high volume, low variety, inflexibility, and low WIP. The bottleneck is the slowest station.
  • Cellular Layout (Group Technology): Uses dissimilar machines grouped for specific part families. Combines benefits of product and process layouts: better human relations, less WIP/handling, faster setup. Involves part family grouping and cell formation.
  • Fixed Position Layout: The product stays put, and resources move to it.

Product Design and Development

  • Phases: Planning, Concept Development, System-Level Design, Detail Design, Testing and Refinement, Production Ramp-Up.
  • Concurrent Engineering: Simultaneous development by cross-functional teams to reduce time and cost while improving quality.
  • Quality Function Deployment (QFD) / House of Quality: Translating customer requirements into technical design requirements.
  • Value Analysis/Value Engineering (VA/VE): Systematically simplifying products or processes to improve performance at a lower cost.
  • Design for Manufacturability (DFM) / Design for Manufacturing and Assembly (DFMA): Designing products for ease of production and assembly.
  • Ecodesign: Considering environmental impact throughout the product lifecycle.

Statistical Process Control (SPC)

Using control charts to monitor processes and identify special causes of variation.

  • Variable Data: Measurable data (e.g., length, weight). Charts used:
    • &bar;X (Mean) and R (Range) charts.
    • X-Rm (Individual and Moving Range) charts.
  • Attribute Data: Classified data (e.g., go/no-go, counts). Charts used:
    • P (Proportion defective) chart.
    • np (Number defective) chart.
    • c (Number of defects per unit) chart.
    • u (Average number of defects per unit) chart.
  • WECO Rules: Additional criteria used for detecting out-of-control patterns on &bar;X charts (e.g., 8 points in a row above the mean).
  • Rational Sampling: Ensuring samples within a subgroup have minimal special cause variation.

Job Design and Work Analysis

  • Job Design: Specifying work activities, considering worker characteristics, tasks, and the environment. Trends include Quality at the Source, job enrichment, and automation.
  • Worker-Machine Chart: Analyzes working and idle time for both a worker and a machine.

Acceptance Sampling

  • Acceptance Sampling: Inspecting a sample to decide whether to accept or reject an entire lot. Used when 100% inspection is impractical or costly.
  • Risks: Producer’s Risk (α, rejecting a good lot) and Consumer’s Risk (β, accepting a bad lot).
  • Terms: Acceptable Quality Level (AQL), Lot Tolerance Percent Defective (LTPD).
  • Single Sampling Plan: Defined by sample size (n) and acceptance number (c).
  • Operating Characteristic (OC) Curves: Show the probability of accepting lots with different defect rates.

Strategic Sourcing and Supply Chain Management

  • Strategic Sourcing & Procurement: Managing supplier relationships effectively.
  • Outsourcing: Moving internal activities to external providers.
  • Specificity: How common or unique an item is, which impacts sourcing complexity.
  • Request for Proposal (RFP): Used for complex sourcing requirements.
  • Vendor-Managed Inventory (VMI): The supplier manages inventory levels at the customer’s location.
  • Total Cost of Ownership (TCO): Considering all costs associated with an item (acquisition, ownership, and post-ownership).
  • Green Sourcing: Incorporating environmental factors into procurement decisions.
  • Mass Customization: Delivering customized products efficiently at high volume. Requires modular design and postponed differentiation.
  • The Bullwhip Effect: The amplification of demand variability as it moves upstream through the supply chain. Caused by lack of synchronization, batching, and forward buying. Reduced by supply chain visibility and continuous replenishment.
  • Hau Lee’s Supply Chain Framework: Aligning supply chains based on demand and supply uncertainty. Classifies supply chains as Efficient, Responsive, Risk-Hedging, or Agile.