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.

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.

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.

One delivery driver delivers all the day's packages 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.

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 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 labor; 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.

A business can manufacture 100 lamps with two technically efficient processes: process A uses 10 kg of material and 8 hours of labor; process B, 12 kg of material and 5 hours of labor. The material costs $\$4$ per kg and the hour of labor, $\$15$. 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 cookie factory produces 3.600 boxes in an 8-hour shift with 3 workers. a) Calculate labor 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 organization), reasoning what effect each would have on output per hour worked.

A print shop 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.

An online store prepares 960 orders a day with 4 operators on 8-hour shifts. a) Calculate labor 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 labeling 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.

A workshop produces 640 T-shirts a week with 2 workers working 40 hours a week each. a) Calculate the labor 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.

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: $TV = \frac{P_1 - P_0}{P_0} \times 100$. 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 labor productivity of each week. b) Calculate its rate of change: $TV = \frac{P_1 - P_0}{P_0} \times 100$. c) Comment on two possible causes of the change.

A factory produced 20 000 units last year, which it sold at $\$25$ each. It employed 5 workers at a cost of $\$30,000$ per worker and raw materials worth $\$200,000$. 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 dollars obtained per dollars of cost. c) Name two reasons why overall productivity can rise even if production barely changes.

An industrial company presents the following situation: in the last fiscal year, it generated sales revenue of $\$540,000$ with a total cost of the factors employed of $\$450,000$. 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?

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 bicycle factory produced $12,000$ units last year at a price of $\$300/\text{unit}$. It employed $8$ workers ($1,600$ annual hours each with a labor cost of $\$25/\text{hour}$), machinery for $3,200$ hours at $\$40/\text{hour}$, and raw materials for an amount of $\$900,000$.

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 spending on raw materials by $15\ \%$, requiring an investment in labor training that raises the hourly labor cost to $\$26/\text{hour}$ (worked hours and machine hours do not change).

• Plan 2 (Assembly robotization): Halves the necessary labor hours ($6,400$ total hours at $\$25/\text{hour}$), but increases machine hours to $4,500$ annual hours and the hourly depreciation/maintenance cost of machinery to $\$50/\text{hour}$ (spending 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.