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 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.

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.

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.

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?

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 $\$15/\text{hour}$. 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 $\$20/\text{hour}$. 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 pesos 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 $\$35$ 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 $\$38$ per pair.

• Alternative 2: Vertically integrate production by setting up its own plant. This would entail annual fixed costs of $\$240,000$ (facility rent, machinery depreciation, and insurance) and a unit variable manufacturing cost of $\$24$ 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.