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- Napa Air Express decided to offer direct service from Denver to Napa Valley. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller-capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Napa Air Express offers. Management developed estimates of the contribution to profit for each type of service based on two possible levels of demand for service to Napa Valley: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
|Demand for Service|
- If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches and why?
- Suppose that management of Napa Air Express believes that the probability of strong demand is 0.6 and the probability of weak demand is 0.4. Construct a decision tree and use the expected value approach to determine an optimal decision.
- Geniue Antique Egyptian Artifacts, Inc. produces three varieties of antique artifacts for sale to tourists: statuettes, lamps, and urns. All of the artifacts include special clay. A statuette requires 13 ounces of clay, a lamp uses 18 ounces, and each urn takes 17 ounces. Existing capacity of clay is 28,000 ounces per month. A special material is also used to produce the three artifacts, with each statuette needing 0.8 ounces, each lamp 0.7 ounces, and a typical urn requiring 1.0 ounces. The company has inventory of 1,200 ounces of special material per month.
The owner of the company wishes to maintain a balanced marketing program, and has ordered that production of statuettes to be limited to 275. The overall per unit profit for artifacts is the following: $199 per statuette, $99 per lamp, and $145 per urn. The owner wants to know how much of each type of antique to fabricate monthly in order to optimize profit.
- What are the objective function, decision variables, and constraints for this optimization problem?
- Develop an Excel spreadsheet and use Excel-Solver to find an optimal solution for this problem.
- Describe the optimal solution in words.
- Consider the following quarterly time series.
|Quarter||Year 1||Year 2||Year 3|
- Construct a time series plot. What type of pattern exists in the data?
- Use a multiple regression model to develop an equation to account for seasonal and trend effects in the data.
- Compute the quarterly forecasts for next year based on the model developed in part (b).
- Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table:
|Potential Locations for Substations||Areas Covered|
|A||1, 5, 7|
|B||1, 2, 5, 7|
|C||1, 3, 5|
|D||2, 4, 5|
|E||3, 4, 6|
|F||4, 5, 6|
|G||1, 5, 6, 7|
Formulate an integer programming model that could be used to find the minimum number of location necessary to provide coverage to all areas. Solve your model.