3.18 A large orthopedic hospital has continued to experience an increased demand for cus- tomized knee implants. The administration is evaluating alternatives to meet this de- mand, including the purchase of 3D printers (and related software) and outsourcing to a manufacturer. Potential profits and losses under different case demand levels, as identi- fied through a feasibility analysis, are displayed in EX 3.18.1. Table EX3.18.1 Alternative Buy One 3D Printer Buy Two 3D Printers Outsource Payoff: Profit (in $000s) for Case Demand Levels High (20) (45) 10 Moderate 125 95 60 85 25 Suppose administrators believe that the most likely case level is moderate. Addition- ally, they estimate that low and high case demand levels are approximately four times less likely to occur than moderate case demand. Using this information, derive the subjective probability distribution for each case level. a. b. Develop a decision tree model, calculating expected values for each event node. Which alternative is selected? Suppose that administrators determine the profit estimates for the three 3D printing alternatives are unreliable, and would rather use the cost information associated with each alternative in their decision making. The total costs under each alternative are displayed in Table EX 3.18.2. Construct a regret table using the cost information. Will the selected alternative be different if the administration is pessimistic or opti- mistic? Explain. c. Table EX 3.18.2 Alternative Buy One 3D Printer Buy Two 3D Printers Outsource Cost (in $000s) for Case Demand Levels Moderate 415 775 60 OW 425 800 90 725 30 3.18 A large orthopedic hospital has continued to experience an increased demand for cus- tomized knee implants. The administration is evaluating alternatives to meet this de- mand, including the purchase of 3D printers (and related software) and outsourcing to a manufacturer. Potential profits and losses under different case demand levels, as identi- fied through a feasibility analysis, are displayed in EX 3.18.1. Table EX3.18.1 Alternative Buy One 3D Printer Buy Two 3D Printers Outsource Payoff: Profit (in $000s) for Case Demand Levels High (20) (45) 10 Moderate 125 95 60 85 25 Suppose administrators believe that the most likely case level is moderate. Addition- ally, they estimate that low and high case demand levels are approximately four times less likely to occur than moderate case demand. Using this information, derive the subjective probability distribution for each case level. a. b. Develop a decision tree model, calculating expected values for each event node. Which alternative is selected? Suppose that administrators determine the profit estimates for the three 3D printing alternatives are unreliable, and would rather use the cost information associated with each alternative in their decision making. The total costs under each alternative are displayed in Table EX 3.18.2. Construct a regret table using the cost information. Will the selected alternative be different if the administration is pessimistic or opti- mistic? Explain. c. Table EX 3.18.2 Alternative Buy One 3D Printer Buy Two 3D Printers Outsource Cost (in $000s) for Case Demand Levels Moderate 415 775 60 OW 425 800 90 725 30
