Chapter 10 Exercise 10.2 - Page 208 Of The Text

Chapter 10 Exercise 10 2 Page 208 Of The Text10 2 In The Clinic Ren

In this exercise, the focus is on decision-making under uncertainty concerning clinic renovation options in response to varying demand forecasts. The scenario involves choosing among doing nothing, a minor renovation, or a major renovation, with each option affecting the clinic's capacity to serve patients and, consequently, its revenue. The problem explores how management can evaluate these options considering different future demand scenarios and associated payoffs, emphasizing the use of expected total payoff calculations to guide decision-making.

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Effective management decision-making, especially under conditions of uncertainty, is critical in healthcare operations to optimize resource utilization and financial outcomes. The clinic renovation scenario provides a practical case for applying decision analysis techniques, notably the expected value approach, to select the most beneficial course of action considering different potential future states of demand.

The case presents three alternatives: doing nothing, implementing a minor renovation, or undertaking a major renovation, each with distinct costs and capacity implications. The "do nothing" option maintains the current capacity to serve 20 patients per day at a cost of $0, which effectively keeps the operating status quo but limits potential revenue if demand increases. The minor renovation costs $225,000 and raises capacity to 35 patients per day, while the major renovation costs $700,000 and allows for 50 patients daily. The earnings per patient are $75, and the clinic operates 300 days annually, generating revenue proportional to patient volume and capacity.

Analyzing this scenario involves assessing three possible demand states: demand remaining at 20 patients per day, increasing to 35 patients, or reaching 50 patients. These states represent the uncertain future environments influencing the profitability of each alternative. The outcomes are then quantified through the calculation of potential revenue for each demand level, with the payoffs tabulated accordingly.

The core method for evaluating these decisions is to compute the expected payoff for each alternative based on the likelihood of each demand state. For example, if management believes that the demand will stay at current levels (20 patients) with a certain probability, and increase to moderate (35 patients), or large increase (50 patients), with other probabilities, then the expected revenue from each renovation option can be calculated as a weighted average of the payoffs, reflecting these probabilities.

Suppose management's subjective probabilities are that there is a 30% chance that demand remains at 20 patients, a 25% chance of a moderate increase to 35 patients, and a 45% chance of a large increase to 50 patients. Using these probabilities, the expected payoff for each alternative can be determined. For instance, the expected revenue from the 'do nothing' option would be calculated by multiplying the revenue in each demand state by its probability and summing these products. Similar calculations are done for the minor and major renovation options.

Let us perform these calculations explicitly. First, we determine the revenue payoffs for each demand state and renovation alternative:

  • Do nothing:
    • 20 patients demand: Revenue = 20 x $75 x 300 days = $450,000
    • 35 patients demand: Revenue is capped at 20 patients, so also $450,000
    • 50 patients demand: Revenue is capped at 20 patients, so again $450,000
  • Minor renovation:
    • 20 patients demand: $75 x 20 x 300 = $450,000
    • 35 patients demand: $75 x 35 x 300 = $787,500
    • 50 patients demand: Cap at 35 patients, so $75 x 35 x 300 = $787,500
  • Major renovation:
    • 20 patients demand: $450,000
    • 35 patients demand: $75 x 35 x 300 = $787,500
    • 50 patients demand: $75 x 50 x 300 = $1,125,000

Next, these revenue figures are multiplied by the respective probabilities to determine the expected payoffs:

  • Expected payoff for 'do nothing': 0.30 x $450,000 + 0.25 x $450,000 + 0.45 x $450,000 = $450,000
  • Expected payoff for minor renovation: 0.30 x $450,000 + 0.25 x $787,500 + 0.45 x $787,500 = (0.30 x $450,000) + (0.25 + 0.45) x $787,500 = $135,000 + 0.70 x $787,500 = $135,000 + $551,250 = $686,250
  • Expected payoff for major renovation: 0.30 x $450,000 + 0.25 x $787,500 + 0.45 x $1,125,000 = $135,000 + $196,875 + $506,250 = $838,125

Based on these expected payoffs, the management should opt for the major renovation, which yields the highest expected revenue of $838,125, assuming their probability estimates are accurate. This approach illustrates the use of expected value decision criterion, a fundamental concept in decision analysis, to inform strategy under uncertainty.

Many factors influence the accuracy of these probabilistic assessments, including market trends, competitive dynamics, and healthcare policy changes. Sensitivity analysis, which explores how variations in probabilities affect the decision, can further enhance decision robustness. In practice, managers might also consider factors such as cash flow, funding availability, and strategic priorities beyond simple expected value calculations.

In conclusion, applying expected total payoff calculations to the clinic renovation decision allows management to quantify potential benefits and make informed choices under uncertainty. This analytical approach supports balancing risk and reward, ultimately aiming to align operational capacity with future demand patterns effectively.

References

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