Productivity and its measurement

Partial, multi-factor and total productivity, productivity indices, the ILO work-content model, and why inputs must be valued at base-period prices.

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Why it matters

Every work-study, layout or incentive decision in a plant is finally judged by one question: did we get more output from the same resources? Productivity measurement gives that answer in numbers, lets you compare a month with the previous one or a plant with its competitor, and shows which input (labour, material, machines, energy) is holding performance back.

Key ideas

Productivity is the ratio of output produced to the input used to produce it. It is a measure of how well resources are used, not of how much is produced.

  • Production vs productivity. Production is the quantity of output. Production can rise while productivity falls (for example, by adding overtime and extra workers that produce proportionally less).
  • Efficiency vs effectiveness. Efficiency is doing things right (low input per unit of output); effectiveness is doing the right things (meeting the target or customer need). Productivity combines both: an efficient plant making unwanted products is not productive.

Kinds of productivity measure

  • Partial (single-factor) productivity = output / one input. Examples: labour productivity (units per labour-hour), machine productivity (units per machine-hour), material productivity (units per kg or per ₹ of material), energy productivity (units per kWh). Easy to measure and understand, but can mislead: buying a robot raises labour productivity while capital productivity may fall.
  • Multi-factor productivity (MFP) = output / (sum of two or more inputs). The inputs must be added in a common unit, which is money at base-period (constant) prices.
  • Total productivity = total tangible output / total tangible input, where the inputs are human, material, capital, energy and other expenses, all in money at base-period prices (Sumanth's total productivity model). This is the best single indicator of overall performance.

Units matter. You cannot add labour-hours to rupees. If inputs are in different physical units, either use partial measures or convert every input (and the output) to money using constant prices, so that price inflation is not mistaken for productivity change.

Productivity index. To track change, divide the current-period productivity by the base-period productivity: PI = P_current / P_base. A PI of 1.12 means a 12 % improvement.

Why productivity is lost: the work-content model (ILO). Total time of an operation = basic work content + excess work content due to poor product design or specification + excess work content due to inefficient methods + ineffective time due to management shortcomings + ineffective time within the worker's control. Method study attacks excess work content; work measurement exposes ineffective time. This connects this topic to the method study, time study and work sampling topics that follow.

Ways to raise the ratio. Increase output with the same input; same output with less input; output rising faster than input; or input falling faster than output. Typical levers: better methods and layout, standard times and incentives, training, maintenance (less downtime), lower scrap and rework, and better scheduling.

Formulas

Partial productivity = O / I_k

  • O = output (units, or ₹ at base-period prices); I_k = one input (labour-hours, machine-hours, kg, kWh or ₹). Units of the result follow, e.g. units/labour-hour.

Labour productivity = O / L

  • L = labour-hours (h) = number of workers × hours per worker.

Multi-factor productivity = O / (I_1 + I_2 + … )

  • All inputs in ₹ at base-period prices. Result in units per ₹ (often quoted per ₹1,000) or dimensionless if output is also in ₹.

Total productivity TP = O_T / (H + M + C + E + X)

  • O_T = total tangible output value (₹); H = human (labour) input; M = material; C = capital (depreciation or capital charge for the period); E = energy; X = other expenses, all in ₹ at base-period prices. TP is dimensionless.

Productivity index PI = P_current / P_base; % change = (PI − 1) × 100

  • Use the same measure (same inputs, same price base) in both periods.

Worked examples

Example 1 (standard). A firm sells 2,000 units in a month at ₹50 each. Inputs for the month at base prices: labour ₹20,000, material ₹35,000, capital charge ₹15,000, energy ₹5,000, other expenses ₹5,000. Find total productivity, labour (partial) productivity in ₹/₹ and the labour + material multi-factor productivity.

  1. Output value: O_T = 2,000 × 50 = ₹1,00,000.
  2. Total input: 20,000 + 35,000 + 15,000 + 5,000 + 5,000 = ₹80,000.
  3. Total productivity: TP = 1,00,000 / 80,000 = 1.25.
  4. Labour productivity: 1,00,000 / 20,000 = 5.0 ₹ of output per ₹ of labour.
  5. Multi-factor (labour + material): 1,00,000 / (20,000 + 35,000) = 1,00,000 / 55,000 = 1.82.

Example 2 (GATE level). Base month: 6 workers each working 160 h produce 4,800 units. After a method improvement: 5 workers each working 168 h produce 5,400 units. Labour costs ₹150/h, material ₹40 per unit, and fixed overhead is ₹60,000 per month in both months (base prices). Find (a) the % change in labour productivity and (b) the % change in multi-factor productivity (units per ₹1,000 of labour + material + overhead).

  1. Labour-hours: base L_b = 6 × 160 = 960 h; current L_c = 5 × 168 = 840 h.
  2. Labour productivity: base 4,800 / 960 = 5.00 units/h; current 5,400 / 840 = 6.43 units/h.
  3. % change = (6.4286 / 5.00 − 1) × 100 = +28.6 %.
  4. Input cost, base: 960 × 150 + 4,800 × 40 + 60,000 = 1,44,000 + 1,92,000 + 60,000 = ₹3,96,000.
  5. Input cost, current: 840 × 150 + 5,400 × 40 + 60,000 = 1,26,000 + 2,16,000 + 60,000 = ₹4,02,000.
  6. MFP: base 4,800 / 3,96,000 × 1,000 = 12.12 units per ₹1,000; current 5,400 / 4,02,000 × 1,000 = 13.43 units per ₹1,000.
  7. % change = (13.433 / 12.121 − 1) × 100 = +10.8 %.

The labour figure (28.6 %) overstates the real gain, because material is the largest cost and material per unit did not change. This is exactly why multi-factor and total measures are preferred.

Common mistakes

  • Adding inputs with different units (hours + rupees). Convert everything to money at base-period prices first.
  • Using current prices in both periods, so inflation looks like a productivity change.
  • Treating a rise in production as a rise in productivity without checking the inputs.
  • Judging a change by one partial measure only (automation raises labour productivity but may lower capital productivity).
  • Forgetting that labour-hours = workers × hours each, or counting idle paid hours inconsistently between periods.
  • Computing % change as (new − old)/new instead of (new − old)/old.

For GATE PI

Expect short numericals: labour productivity from workers, shifts and output; % change in productivity between two periods; total or multi-factor productivity from cost data; and conceptual one-mark questions on partial vs total productivity, production vs productivity, and the work-content model. Practise converting every input to the same money basis and computing indices to two decimals.

Quick check

  1. 12 workers work 8 h a day for 25 days and make 9,600 units. What is the labour productivity?
  2. Output value ₹6,00,000; total inputs ₹4,80,000. What is the total productivity?
  3. Labour productivity goes from 4.0 to 4.6 units/h. What is the % change?
  4. Why must inputs be valued at base-period prices for multi-factor productivity?

Answers: 1. 9,600 / (12 × 8 × 25) = 4 units per labour-hour; 2. 1.25; 3. +15 %; 4. So that different inputs can be added in one unit and price changes are not counted as productivity changes.

Interview questions

All Work Systems and Facility Design interview questions

Try answering each one aloud before you open it.

  1. 1.What is productivity in the context of work systems and facility design?Concept

    Productivity in work systems and facility design refers to the efficiency with which inputs are converted into outputs. It is a measure of how effectively resources such as labor, materials, and energy are utilized to produce goods and services. Higher productivity indicates more efficient use of resources.

  2. 2.Explain the importance of measuring productivity in industrial settings.Concept

    Measuring productivity is crucial in industrial settings because it helps identify areas where efficiency can be improved, leading to cost savings and increased competitiveness. It also aids in setting performance benchmarks, evaluating employee performance, and making informed decisions about resource allocation and process improvements.

  3. 3.What are some common methods used to measure productivity?Concept

    Partial (single-factor) productivity divides output by one input, such as units per labour-hour, per machine-hour or per kWh. Multi-factor productivity divides output by the sum of two or more inputs, and total productivity divides total tangible output by all tangible inputs (labour, material, capital, energy, other expenses). For multi-factor and total measures every input must be converted to money at base-period prices, because hours and rupees cannot be added and inflation must not look like a productivity gain. Change over time is tracked with a productivity index, current productivity divided by base productivity.

  4. 4.Why is labor productivity often used as a key performance indicator in manufacturing?Application

    Labor productivity is often used as a key performance indicator in manufacturing because it directly relates to the efficiency of the workforce, which is a significant cost component. By measuring output per labor hour, companies can assess how effectively their workforce is being utilized and identify opportunities for training or process improvements.

  5. 5.What happens if a facility consistently shows low productivity levels?Application

    If a facility consistently shows low productivity levels, it may face higher operational costs, reduced competitiveness, and lower profitability. This situation could lead to a need for process re-engineering, workforce training, or investment in new technologies to improve efficiency and output.

  6. 6.How can technology impact productivity in industrial facilities?Application

    Technology can significantly impact productivity by automating repetitive tasks, reducing errors, and speeding up production processes. Advanced technologies like robotics, AI, and IoT can optimize resource use, enhance quality control, and provide real-time data for better decision-making, leading to improved productivity.

  7. 7.Explain how facility layout can influence productivity.Application

    Facility layout influences productivity by affecting the flow of materials and workers. An efficient layout minimizes movement, reduces bottlenecks, and ensures smooth transitions between different stages of production. Poor layout design can lead to wasted time, increased handling costs, and reduced output.

  8. 8.Calculate the labor productivity if a factory produces 500 units of a product using 250 labor hours.Numerical

    Labor productivity is calculated as the total output divided by the total labor hours. In this case, labor productivity = 500 units / 250 labor hours = 2 units per labor hour.

  9. 9.A company uses 1000 units of raw material to produce 800 units of finished goods. What is the material productivity?Numerical

    Material productivity is calculated as the total output divided by the total input of materials. Here, material productivity = 800 units of finished goods / 1000 units of raw material = 0.8 units of finished goods per unit of raw material.

  10. 10.Discuss the role of employee training in enhancing productivity.Application

    Employee training plays a crucial role in enhancing productivity by equipping workers with the necessary skills and knowledge to perform their tasks efficiently. Training can lead to improved job performance, reduced errors, and increased innovation. It also helps in adapting to new technologies and processes, ultimately contributing to higher productivity levels.

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