Problem P 8-14
Steve's Mountain Bicycle Shop is considering three options for its facility next year. Steve can expand his current shop, move to a larger facility, or make no change. With a good market, the annual payoff would be $76,000 if he expands, $90,000 if he moves, and $40,000 if he does nothing. With an average market, his payoffs will be $30,000, $41,000, and $15,000, respectively. With a poor market, his payoff will be - +17,000, - +28,000, and $4,000, respectively.
(a) Which option should Steve choose if he uses the maximax criterion?
(b) Which option should Steve choose if he uses the maximin criterion?
(c) Which option should Steve choose if he uses the equally likely criterion?
(d) Which option should Steve choose if he uses the criterion of realism with a = 0.4?
(e) Which option should Steve choose if he uses the minimax regret criterion?
Question
Problem P 8-28
Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because there will be a five-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision.
Jerry has done some analysis about the profit-ability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $60,000 if the market is good, but he will lose $40,000 if the market is bad. The small shop will return a $30,000 profit in a good market and a $10,000 loss in a bad market. At the present time, he believes that there is a 59% chance that the market will be good.
Jerry also has the option of hiring his old marketing professor for $5,000 to conduct a marketing research study. If the study is conducted, the results could be either favorable or unfavorable. It is estimated that there is a 0.6 probability that the survey will be favorable. Furthermore, there is a 0.9 probability that the market will be good, given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of 0.12 of a good market if the marketing research results are not favorable.
(a) Develop a decision tree for Jerry and help him decide what he should do.
(b) How much is the marketing professor's information worth? What is the efficiency of this information?
Problem P 9-16
The wheat harvesting season in the U.S. Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two- week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin.
The central bin is owned cooperatively, and it is to every farmer's benefit to make the unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the cooperative members.
Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. The storage bin is open and operated 16 hours per day, seven days per week during the harvest season and is capable of unloading 35 trucks per hour, according to an exponential distribution. Full trucks arrive all day long (during the hours the bin is open), at a rate of about 30 per hour, following a Poisson pattern.
To help the cooperative get a handle on the problem of lost time while trucks are waiting in line or unloading at the bin, find the
(a) average number of trucks in the unloading system
(b) average time per truck in the system
(c) utilization rate for the bin area
(d) probability that there are more than three trucks in the system at any given time
(e) total daily cost to the farmers of having their trucks tied up in the unloading process
(f) The cooperative, as mentioned, uses the storage bin only two weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off-season. Would it be worth the cooperative's while to enlarge the storage area?
Problem P 9-20
Carlos Gomez is the receiving supervisor for a large grocery store. Trucks arrive to the loading dock at an average rate of four per hour, according to a Poisson distribution, for 8 hours each day. The cost of operating a truck is estimated to be $80 per hour. Trucks are met by a three-person crew, which is able to unload a truck in an average of 12 minutes, according to an exponential distribution. The payroll cost associated with hiring a crew member, including benefits, is $22 per hour.
Carlos is now considering the installation of new equipment to help the crew, which would decrease the average unloading time from 12 minutes to 9 minutes. The cost of this equipment would be about $500 per day. Is the installation of the new equipment economically feasible?