Problem 1 Payoffs Decision Table 13 Points A Small Building

Problem 1 Payoffsdecision Table 13 Points A Small Building Contrac

Problem 1: Payoffs/Decision Table (13 points) A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. Estimated profits (in $ thousands) under each of the two possible states of nature are as shown in the table below. NEXT YEAR’S DEMAND Alternative Low High Do nothing Expand Subcontract $50 20 40

Which alternative should be selected if the decision criterion is:

a. The optimistic approach? (3 points)

b. The conservative approach? (3 points)

c. Minimize the regret? (7 points)

Paper For Above instruction

The decision-making process for the small building contractor involves evaluating potential strategies based on different decision criteria under uncertainty about future demand. The scenario presents three alternatives: doing nothing, expanding capacity, or subcontracting, with estimated profits depending on whether demand turns out to be low or high. This paper analyzes optimal choices using three decision approaches—the optimistic, conservative, and regret minimization criteria.

Decision Alternatives and Payoffs:

• Do nothing: Profit of $50,000 if demand is low; profit drops to $20,000 if demand is high.
• Expand: Profit of $20,000 if demand is low; profit of $40,000 if demand is high.
• Subcontract: Profit of $40,000 regardless of demand level.

**a. Optimistic Approach (Maximax Criterion):

The optimistic approach aims to maximize potential gains by selecting the strategy with the highest possible payoff. Analyzing the payoffs:

• Do nothing: maximum profit is $50,000.
• Expand: maximum profit is $40,000.
• Subcontract: maximum profit is $40,000.

Based on the maximax criterion, the contractor should choose to do nothing, as it offers the highest possible payoff in the best-case scenario ($50,000).

**b. Conservative Approach (Maximin Criterion):

The conservative approach seeks to maximize the minimum guaranteed payoff, emphasizing risk aversion. The minimum payoffs for each alternative are:

• Do nothing: minimum profit is $20,000.
• Expand: minimum profit is $20,000.
• Subcontract: minimum profit is $40,000.

Therefore, the subcontracting alternative guarantees at least $40,000, making it the preferred choice under the maximin approach, given its higher minimum payoff.

**c. Minimize the Regret (Minimum Regret Criterion):

This approach involves calculating the regret associated with each decision, which is the difference between the payoff of the best decision in each state and the payoffs of others. First, determine the best payoffs in each state:

• Low demand: best payoff is $50,000 (do nothing).
• High demand: best payoff is $40,000 (subcontract).

Now, compute the regret table:

Identify the maximum regret for each decision:

• Do nothing: maximum regret is $0.
• Expand: maximum regret is $30,000.
• Subcontract: maximum regret is $10,000.

To minimize regret, the contractor should choose the alternative with the smallest maximum regret, which is to subcontract, resulting in a maximum regret of $10,000.

Summary:

Under the optimistic criterion, doing nothing is optimal. The conservative (risk-averse) approach recommends subcontracting, as it guarantees the highest minimum profit. The regret minimization approach also favors subcontracting to minimize potential regret in the worst-case analysis.

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