Reference no: EM131780503

A certain small car-wash business is currently being analyzed to see if costs can be reduced. Customers arrive according to a Poisson process at a mean rate of 15 per hour, and only one car can be washed at a time. At present the time required to wash a car has an exponential distribution, with a mean of 4 minutes. It also has been noticed that if there are already 4 cars waiting (including the one being washed), then any additional arriving customers leave and take their business elsewhere. The lost incremental profit from each such lost customer is $6.Two proposals have been made. Proposal 1 is to add certain equipment, at a capitalized cost of $6 per hour, which would reduce the expected washing time to 3 minutes. In addition, each arriving customer would be given a guarantee that if she had to wait longer than ½ hour (according to a time slip she receives upon arrival)before her car is ready, then she receives a free car wash (ata marginal cost of $4 for the company). This guarantee would bewell posted and advertised, so it is believed that no arriving customerswould be lost.Proposal 2 is to obtain the most advanced equipment available,at an increased cost of $20 per hour, and each car would besent through two cycles of the process in succession. The time requiredfor a cycle has an exponential distribution, with a mean of1 minute, so total expected washing time would be 2 minutes. Becauseof the increased speed and effectiveness, it is believed thatessentially no arriving customers would be lost.The owner also feels that because of the loss of customergoodwill (and consequent lost future business) when customershave to wait, a cost of $0.20 for each minute that a customer hasto wait before her car wash begins should be included in the analysisof all alternatives.Evaluate the expected total cost per hourof the statusquo, proposal 1, and proposal 2 to determine which one should bechosen. At the back of this page, construct a table breaking down the cost components. Indicate the Kendall-Lee notation of the queueing systemfor each configuration.