Midterm Decision Analysis Exercises [PDF]

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MIDTERM DECISION ANALYSIS EXERCISES 1. Weenies and Buns is a food processing plant that manufactures hot dogs and hot dogs buns. They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week. Each hot dog buns requires 0.1 pound of flour. They currently have a contract with B-land, Inc., which specifies that a delivery of 800 pounds of beef product is delivered every Monday. Each hot dog requires ¼ pound of beef product. All the other ingredients in the hot dogs and hot dogs buns are in plentiful supply. Finally, the labor force at Weenies and Buns consists of five employees working full time (40 hours per week each). Each hot dog requires three minutes of labor, and each hot dog bun requires two minutes of labor. Each hot dog yield a profit of $0.20, and each bun yields a profit of $0.10. Weenies and Buns would like to know how many hot dogs and how many hot dogs buns they should produce each week so as to achieve the highest possible profit. a. Formulate and solve a linear programming model for this problem algebraically. b. Use the graphical method to solve this model. Solution : a.



x1 = hotdogs x2 = buns flour: pork: work hours: Nonnegativity:



0.1 x2 ≤ 200 0.25 x1 ≤ 800 3 x1 + 2 x2 ≤ 12,000 x1 ≥ 0, x2 ≥ 0



Profit = 0.2 x1 + 0.1 x2 b.



Optimal Solution: (x1, x2) = (3200, 1200) and P = $760.



2. The Graham Company has two factories producing a product that needs to be shipped to two customers. Here are some details. Factory 1 is producing 80 units. Factory 2 is producing 90 units. Customer 1 requires 100 units. Customer 2 requires 70 units. There are rail links directly from Factory 1 to Customer 1 and Factory 2 to Customer 2. Any amounts can be shipped along these rail links. Independent truckers are available to ship up to 60 units from each factory to the distribution center, and then 60 units from the distribution centre to each customer. Hint : 80 units should be shipped from Factory 1 to Customer 1 and 30 units should be shipped from Factory 2 to Customer 2.



$800



C



$600



C



a. How many units should be shipped along each shipping lane to minimize the total shipping cost? b. Write the spreadsheet model for Graham Company. Solution : a.



F1 -> C1 : 80 units F2 -> DC : 0 units DC -> C1 : 20 units DC -> C2 : 40 units F2 -> C2 : 30 units F2 -> DC : 60 units



b. Total shipping cost : (80 * $800) + (0 * $200) + (20 * $400) + (40 * $300) + (30 * $600) + (60 * $200) = $114000



3. The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows. Demand Bus Low Medium High Small 50 60 70 Medium 40 80 90 Large 20 50 120 Prior Probability 0.3 0.3 0.4 a. If he uses the maximum likelihood criterion, which size bus will he decide to purchase? b. If he uses Bayes’ decision rule, which size bus will he decide to purchase? c. What is the expected annual profit for the bus that he will decide to purchase using Bayes’ decision rule? d. What is his expected value of perfect information? Solution : a. Large b. Medium c. $72,000 d. $15,000 4. The comptroller of the Macrosoft Corporation has $100 million of excess funds to invest. She has been instructed to invest the entire amount for one year in either stocks or bonds (but not both) and then to reinvest the entire fund in either stocks or bonds (but not both) for one year more. The objective is to maximize the expected monetary value of the fund at the end of the second year. The annual rates of return on these investments depend on the economic environment, as shown in the following table.



The probabilities of growth, recession, and depression for the first year are 0.7, 0.3, and 0, respectively. If growth occurs in the first year, these probabilities remain the same for the second year. However, if a recession occurs in the first year, these probabilities change to 0.2, 0.7, and 0.1, respectively, for the second year.



Construct by hand the decision tree for this problem and then analyze the decision tree to identify the optimal policy. Solution :



The comptroller should invest in stocks the first year. If there is growth during the first year then she should invest in stocks again the second year. If there is a recession during the first year then she should invest in bonds for the second year. The expected payoff is $122.94 million.