Reference no: EM131921959

Part -1: Excel Simulation Assignment

Question 1: The chief of staff in the emergency room of Exercise 6.22 is considering the computerization of the admissions process. This change will not reduce the 10 min service time, but it will make it constant. Develop a spreadsheet simulation to compare the performance of the proposed automated process with the performance of the manual existing process. Hint: Note that interarrival and service times that follow an exponential distribution can be generated with the Excel functions RAND() and LNQ and the following expressions:

A_j = -(1/λ) x LN(RAND(η))
S_j = -(1/μ) x LN(RAND(η))
where
μ is the mean service rate

λ is the mean arrival rate

The Excel formula RAND() generates a random number between 0 and 1. The natural logarithm of the random number is found to transform this number into an exponentially distributed value. The transformation to an exponential distribution is completed when the value is divided by the appropriate mean rate and the negative sign is applied. (Simulate 500 patients in each case.)

Question 2: At Letchworth Community College, one person, the registrar, registers students for classes. Students arrive at a rate of 10/h (Poisson arrivals), and the registration process takes 5 min on the average (exponential distribution).

The registrar is paid $5 per hour, and the cost of keeping students waiting is estimated to be $2 for each student for each hour waited (not including service time). Develop a process-driven spreadsheet simulation to compare the estimated hourly cost of the following three systems. (See the hint in Exercise 7.3 and simulate 500 students in each case.)

a. The current system.

b. A computerized system that results in a service time of exactly 4 min. The computer leasing cost is $7 per hour.

c. Hiring a more efficient registrar. Service time could be reduced to an average of 3 min (exponentially distributed), and the new registrar would be paid $8 per hour.

Part -2: ExtendSim Simulation Assignment

Question 1. Airline ticket counter - At an airline ticket counter, the current practice is to allow queues to form in front of each ticket agent. Time between arrivals to the agents is exponentially distributed with a mean of 5 minutes. Customer join the shortest queue at the time of their arrival. The service time for the ticket agents is uniformly distributed between 2 and 10 minutes.

a. Develop an ExtendSim model to determine the minimum number of agents that will result in an average waiting time of 5 min or less.

b. The airline has decided to change the procedure involved in processing customers by the ticket agents. A single line is formed, and customers are rooted to the ticket agent who becomes free next. Modify the simulation model in part (a) to simulate the process change. Determine the number of agents needed to achieve an average waiting time of 5 min or less.

c. Compare the systems in parts (a) and (b) in terms of the number of agents needed to achieve a maximum waiting time of 5 minutes.

d. It has been found that a subset of the customers purchasing tickets is taking a long period of time.

By separating ticket holders from non-ticket holders, management believes that improvements can be made in the processing of customers. The time needed to check back in a person is uniformly distributed between 2 and 4 min. The time to purchase a ticket is uniformly distributed between 12 and 18 min. Assume that 15% of the customers will purchase tickets and develop a model to simulate this situation. As before, the time between all arrivals is exponentially distributed with a mean of 5 min. Suggest staffing levels for both counters, assuming that the average waiting time should not exceed 5 min.

Question 2. A bank with five tellers opens its doors at 9 a.m. and closes its doors at Spm, but it operates until all the customers inline by5 p.m. have been served. Assume that the interarrival times of customers are exponentially distributed with a mean of 1 min and that the service times of customers are exponentially distributed with a mean of 4.5 min. In the current configuration, each teller has a separate queue (see figure 8.64). An arriving customer joins the shortest queue, choosing the shortest queue furthest to the left in case of ties.

The bank's management team is concerned with operating costs as well as the quality of service currently being provided to customers, and they are thinking about changing the system to a single queue. In the proposed system, all arriving customers would join single queue. The first customer in the queue goes to the first available teller. Simulate 5 days of operation of the current and proposed systems and compare their expected performance.