Exercises: Production process, efficiency and productivity

Identify the inputs, transformation, and outputs of the production process of a juice factory, naming at least two elements from each group.

Production can be job/unit production (custom-made), batch production, or continuous production (uninterrupted). Classify these cases: a shipyard building custom-made vessels, an industrial bakery baking batches of the same bread, and a refinery operating 24 hours a day.

The figure shows the production process as a three-link chain. State which link is missing, marked with "?", and describe what it contains in the case of a juice factory.

A biscuit factory produces 3 600 boxes in an 8-hour shift with 3 workers. a) Calculate labour productivity in boxes per hour worked. b) Explain in your own words what that figure measures.

Explain what productivity is and name three ways to improve it in a furniture factory (training the workforce, improving the machines, work organisation), reasoning what effect each would have on output per hour worked.

Two bakeries bake the same bread every day: one uses 5 kg of flour and 2 hours of oven time and the other, 6 kg of flour and 1.5 hours of oven time. a) Reason whether it is possible to decide which is technically more efficient with that data. b) Explain what additional information would be needed to know which is economically more efficient.

A printing house has a machine that runs 6 hours a day and produces 9 000 posters a day. a) Calculate the machine's productivity per hour. b) If it replaces it with another that produces 12 000 posters in the same 6 hours, calculate the new productivity and its percentage change.

One delivery driver delivers all the day's parcels but takes an enormous detour; another uses the optimal route and also delivers them all. a) Explain which of the two is effective and which is efficient. b) Reason whether one can be effective without being efficient and vice versa, with an example of a business you know.

A workshop produces 640 T-shirts a week with 2 workers working 40 hours a week each. a) Calculate the labour productivity in T-shirts per hour: $P = \frac{\text{units produced}}{\text{hours worked}}$. b) If the following week they produce 680 T-shirts with the same number of hours, calculate the new productivity and comment on the change.

A business can manufacture a part using two processes that yield the same quantity and quality: process A uses 4 kg of material and 2 hours of labour; process B uses 3 kg of material and 3 hours. a) Which process is technically more efficient? b) Explain what price data you would need to know which process is economically more efficient.

The productivity of a factory was 10 units per hour last year and 11 units per hour this year. a) Calculate the rate of change of productivity: $TV = \frac{P_1 - P_0}{P_0} \cdot 100$. b) Comment on two reasons that could explain this improvement.

A garment workshop produced 4 200 polo shirts in one week with 3 workers who worked 35 hours each; the following week it produced 4 600 polo shirts with the same workers and the same hours. a) Calculate the labour productivity of each week. b) Calculate its rate of change: $TV = \frac{P_1 - P_0}{P_0} \cdot 100$. c) Comment on two possible causes of the change.

A business can manufacture 100 lamps with two technically efficient processes: process A uses 10 kg of material and 8 hours of labour; process B, 12 kg of material and 5 hours of labour. The material costs $4\ \text{€}$ per kg and the hour of labour, $15\ \text{€}$. a) Calculate the cost of each process. b) State which is economically more efficient and explain why the answer depends on the prices of the factors.

A factory produced 20 000 units last year, which it sold at $25\ \text{€}$ each. It employed 5 workers at a cost of $30.000\ \text{€}$ per worker and raw materials worth $200.000\ \text{€}$. a) Calculate the value of production and the total cost of the factors. b) Calculate the overall productivity: $PG = \frac{\text{production value}}{\text{factor costs}}$. c) Interpret the result.

A company had an overall productivity of $1,2$ last year and it has been $1,32$ this year. a) Calculate the rate of change of overall productivity. b) Interpret the result: what an overall productivity of $1,32$ means, in euros obtained per euro of cost. c) Name two reasons why overall productivity can rise even if production barely changes.

An online shop prepares 960 orders a day with 4 operators on 8-hour shifts. a) Calculate labour productivity in orders per hour. b) Management expects to reach 1 320 orders a day and is undecided between hiring two more operators or buying a labelling system with which the current four would reach that volume in the same working day: calculate the resulting productivity in each option. c) Comment on what other variables, besides productivity, the decision should consider.

An industrial company presents the following situation: in the last fiscal year, it generated sales revenue of $540.000\ \text{€}$ with a total cost of the factors employed of $450.000\ \text{€}$. For the next fiscal year, management is debating two mutually exclusive strategic options:

• Option A: Maintain the current price and production volume, but reorganize shifts and processes to reduce the total cost of inputs by $10\ \%$.

• Option B: Lower the selling price by $5\ \%$ to raise the quantity demanded and produced by $15\ \%$, which would require increasing the use of productive factors by $12\ \%$ (keeping their unit costs constant).

1. a) Calculate the current Total Factor Productivity and predict the value of Total Factor Productivity that would be achieved under each of the two options (calculating output at constant prices to isolate real efficiency).
2. b) Justify which of the two options represents a greater real gain in technical and economic efficiency. Refute the argument of the commercial director, who claims that "Option B is always superior because it maximizes total sales revenue."
3. c) What market and operational risks would the company assume if it chooses the option that offers higher total factor productivity?

A garment manufacturing company has two production plants with the following characteristics:

• North Plant: 25 workers produce $50.000$ garments per year, working $1.600$ hours per worker per year at a wage cost of $15\ \text{€}/\text{hour}$. Its defect rate is $1\ \%$.

• South Plant: 20 workers produce $42.000$ garments per year with part-time contracts of $1.200$ hours per year at a wage cost of $20\ \text{€}/\text{hour}$. Its defect rate is $7\ \%$.

The management committee proposes closing the production line at the North Plant, claiming that "its labor productivity per employee is lower than that of the South Plant ($2.000$ garments/worker compared to $2.100$)."

1. a) Calculate labor productivity per actual hour worked and per euro of wage cost invested in each plant. Is the committee's initial statement technically supported?
2. b) Interpret the impact of the defective parts rate on the real productivity of market-ready garments and calculate the net usable output per hour in each factory.
3. c) Draft a reasoned report for general management evaluating whether closing the North Plant is appropriate or what corrective measures should be required from each of the two plants.

An emerging footwear brand designs its models in Spain but outsources $100\ \%$ of manufacturing to external workshops in Portugal, paying $35\ \text{€}$ per pair produced. Annual sales are $20.000$ pairs. In the face of recurring delivery delays and quality discrepancies, management is studying two alternatives:

• Alternative 1: Maintain outsourcing but require quality audits at origin and late-delivery penalties, which would raise the agreed price to $38\ \text{€}$ per pair.

• Alternative 2: Vertically integrate production by setting up its own plant. This would entail annual fixed costs of $240.000\ \text{€}$ (facility rent, machinery depreciation, and insurance) and a unit variable manufacturing cost of $24\ \text{€}$ per pair.

1. a) Calculate the production threshold (the make-or-buy break-even point) above which it becomes economically more advantageous to produce in-house compared to audited outsourcing (Alternative 1). Justify which option is preferable for the current sales volume ($20.000$ pairs).
2. b) Evaluate the operational and strategic risks the company would assume if it decides to internalize production, paying special attention to flexibility in the event of demand drops and to exit barriers.
3. c) If the company expects demand to drop next year to $14.000$ pairs due to a recession, predict how this reduction would affect the decision and indicate which production model would offer greater adaptability.

A company that manufactures ceramic pieces presents the following data between 2024 (base year) and 2025:

• Year 2024: produced $10.000$ pieces at a unit price of $60\ \text{€}$, using $2.000$ hours of labor at $20\ \text{€}/\text{hour}$, $40.000\ \text{kg}$ of clay at $8\ \text{€}/\text{kg}$ and $60.000\ \text{kWh}$ of gas at $2\ \text{€}/\text{kWh}$.

• Year 2025: produced $10.500$ pieces that it sold at $68\ \text{€}/\text{unit}$, using $2.200$ hours of labor at $23\ \text{€}/\text{hour}$, $46.000\ \text{kg}$ of clay at $9\ \text{€}/\text{kg}$ and $64.000\ \text{kWh}$ of gas at $2,2\ \text{€}/\text{kWh}$.

The financial director claims: "Our overall productivity has grown remarkably because the value of production increased by $19\ \%$."

1. a) Calculate the Overall Productivity for 2024 and 2025 both at current prices and at constant base-year prices.
2. b) Calculate the rate of change of real Overall Productivity (at constant prices). Justify whether the company has improved or worsened its real technical efficiency and refute the financial director's conclusions using these data.
3. c) Interpret what has happened to the unit consumption of clay and energy per piece produced and explain why selling price inflation can mask losses in productive efficiency.

A factory produces $50.000$ parts per year, which it sells at $12\ \text{€}/\text{unit}$. It employs $10$ workers at an annual wage cost of $28.000\ \text{€}$ per worker, consumes $150.000\ \text{€}$ in raw materials, and $50.000\ \text{€}$ in energy.

The company is evaluating an automation plan with two impacts: reducing the workforce to $4$ workers and increasing production to $55.000$ parts per year. However, raw material consumption would increase to $170.000\ \text{€}$, energy costs to $75.000\ \text{€}$, and the annual depreciation of the new equipment would amount to $65.000\ \text{€}$. The selling price and the wage per worker remain constant.

1. a) Calculate the productivity of the labor factor (in parts/worker) and the total factor productivity of the company before and after automation.
2. b) Calculate the rate of change of labor productivity and compare it with the rate of change of total factor productivity.
3. c) Interpret the contrast between both results: justify why replacing labor with capital can dramatically increase the partial productivity of labor without necessarily meaning a proportional advance in overall resource efficiency.

The management team of a factory celebrates the results of the fiscal year, claiming that “the company has experienced a productivity success because the physical volume of production ($Q$) grew by $20\ \%$ at constant prices.” However, the internal audit reveals that to achieve this increase, the total cost of the productive factors consumed (also at constant prices) increased by $35\ \%$.

1. a) Formally demonstrate, using the Total Factor Productivity Index ($TFP_I = TFP_1 / TFP_0$) or through a rigorous algebraic approach, what the percentage rate of change in Total Factor Productivity has been.
2. b) Interpret the results in the light of returns to scale: why can an increase in productive scale lead to a drop in overall efficiency? Describe two real organizational problems in a factory (such as bottlenecks or managerial diseconomies) that explain this discrepancy.
3. c) Design a set of three control indicators that management should incorporate before authorizing future capacity expansions to ensure that growth generates value rather than efficiency losses.

A company manufactures an electronic component with an annual demand of $20.000$ units. To manufacture it internally, it incurs annual fixed costs of $60.000\ \text{€}$ (machinery and structure). Regarding variable costs, each component requires $0,2$ labor hours (with a wage cost of $20\ \text{€}/\text{hour}$) and $3\ \text{€}$ of materials.

An external supplier offers to supply this component for $6,5\ \text{€}/\text{unit}$.

1. a) Calculate the unit cost of producing the $20.000$ units internally and compare it with the supplier's price. Analytically find the break-even production threshold (the volume from which it is better to make rather than buy) and interpret the result for the company's situation.
2. b) Assume that the supplier has delivery times that would force the company to maintain an additional safety stock with a financing and storage cost of $0,6\ \text{€}$ per component, and that $3\ \%$ of the parts received from the supplier are defective and cannot be used. Evaluate whether outsourcing is still advantageous with these new data.
3. c) Design two concrete organizational proposals that allow the company to reduce its internal manufacturing costs without resorting to staff layoffs, improving its productivity to be competitive against the external supplier.

A bicycle factory produced $12.000$ units last year at a price of $300\ \text{€}/\text{unit}$. It employed $8$ workers ($1.600$ annual hours each with a labor cost of $25\ \text{€}/\text{hour}$), machinery for $3.200$ hours at $40\ \text{€}/\text{hour}$, and raw materials for an amount of $900.000\ \text{€}$.

For the next fiscal year, management is evaluating two alternative modernization plans for the same volume of $12.000$ bicycles:

• Plan 1 (Materials reengineering): Through ecodesign agreements and waste reduction, it reduces expenditure on raw materials by $15\ \%$, requiring an investment in labor training that raises the hourly labor cost to $26\ \text{€}/\text{hour}$ (worked hours and machine hours do not change).

• Plan 2 (Assembly robotization): Halves the necessary labor hours ($6.400$ total hours at $25\ \text{€}/\text{hour}$), but increases machine hours to $4.500$ annual hours and the hourly depreciation/maintenance cost of machinery to $50\ \text{€}/\text{hour}$ (expenditure on raw materials does not change).

1. a) Calculate the total factor productivity of the initial year and the partial productivities of labor (bicycles/hour) and machinery (bicycles/hour).
2. b) Calculate the projected Total Factor Productivity for Plan 1 and Plan 2 at constant prices. Determine which of the two plans achieves a greater percentage increase in overall efficiency.
3. c) Interpret the results: justify why acting on the factor with the highest relative weight in costs (raw materials) can be more effective for overall productivity than automating labor, and explain what strategic risks each plan entails.