There are 3 different fire alarm systems in the store. System A detects fire with a probability of 0.6 and costs $40, the B detects fire with a probability of 0.91 and costs $100, the C detects fire with a probability of 0.8 and costs $60. Which option is better: to set one system B or two systems A and C?

There are 3 different fire alarm systems in the store. System A detects fire with a probability of 0.6 and costs $40, the B detects fire with a probability of 0.91 and costs $100, the C detects fire with a probability of 0.8 and costs $60. Which option is better: to set one system B or two systems A and C?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 17P

See similar textbooks

Similar questions

It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. Is Ben Gibson acting legally? Is he acting ethically? Why or why not?
Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. As the Marketing Manager for Southeastern Corrugated, what would you do upon receiving the request for quotation from Coastal Products?
A firm produces 2 different alarm systems A and B. System A detects withprobability 0.93 and costs 2 times expensive then system B. System B detectsfire with probability 0.8. Which option is better: to set two systems B or onesystem A?
A hospital has three independent fire alarm systems, with reliabilities of .95, .97, and .99. In the event of a fire, what is the probability that a warning would be given?
The number of hybrid cars that have be requested for rental from a car rental office during a 50 day sample period is given in the following table. Demand for Cars Number of Days Probability 3 3 0.06 4 7 0.14 5 12 0.24 6 14 0.28 7 10 0.20 8 4 0.08 50 1.00What is the expected (mean) number of hybrid rentals per day? Compute to one decimal place.
A machine can be purchased at t = 0 for $20,000. The estimated life is 5 years, with an estimated salvage value of zero at that time. The average annual operating and maintenance expenses are expected to be $5,500. If MARR = 10%, what must the average annual revenues be in order to be indifferent between (a) purchasing the machine or (b) doing nothing?
a. Mayers & Smith Corp. has a fertilizer plant. The probability of an explosion at the plant depends on how much the firm spends on safety as given by the table below. If an explosion occurs, the loss to society (damaged equipment, death of employees, etc.) is expected to be $250 million. Safety Expenditure $ millions) 0.0 0.5 1.0 1.5 2.0 2.5 Probability of Loss 0.030 0.020 0.016 0.013 0.011 0.010 Find the optimal level of safety from a societal perspective. marginal cost and marginal benefit; optimal amount. Suppose Mayers & Smith has to pay only one half of the losses that occur. How much would Mayers & Smith spend on safety?
You have two design options for your new line of high-resolution monitors for Computer-Aided Design (CAD)workstations. The production run is for 110,000 units. Design option A has a .90 probability of yielding 65good monitors per 100 and a .10 probability of yielding 70good monitors per 100. This design will cost $1,000,000. Design option B has a .80 probability of yielding 65good units per 100 and a .20 probability of yielding 60good units per 100. This design will cost $1,350,000. Good or bad, each monitor will cost $75. Each good monitor will sell for $150. Bad monitors are destroyed and have no salvage value. We ignore any disposal costs in this problem. Demonstrate how decision trees can be used in order to choose the design option based on the above situation. Calculate the expected monetary value (EMV) of each option and determine which option you will propose.
The Platinum Star Hotel in Kingston, NY, is considering doing overbooking in order to deal with the constant problem they have with no-shows. The table given below presents the number of no-shows and the probability of each occurring. Number of Shows (d) Probability of No-shows Occurring P(d) 0 0.10 1 0.07 2 0.12 3 0.02 4 0.07 5 0.01 6 0.04 7 0.19 8 0.22 9 0.16 a) What would be your recommendation for overbooking if the average rate per room per night is S125 and the cost of not honoring a reservation is $155? b) What is the expected loss for your overbooking choice? c) State the reasoning for selecting your overbooking choice?