Questions from Management Science

Q: On average, 100 customers arrive per hour at Gotham City Bank

On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two minutes to serve a customer. Interarrival and service times are exponentially distributed. The bank c...

Q: Consider the following two queueing systems. ■ System 1:

Consider the following two queueing systems. ■ System 1: An M/M/1 system with arrival rate  and service rate 3µ. ■ System 2: An M/M/3 system with arrival rate  and each server working at rate µ. Whi...

Q: Two one-barber shops sit side by side in Dunkirk Square

Two one-barber shops sit side by side in Dunkirk Square. Each shop can hold a maximum of four people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $15...

Q: The small mail-order firm Sea’s Beginning has one phone line

The small mail-order firm Sea’s Beginning has one phone line. An average of 60 people per hour call in orders, and it takes an average of one minute to handle a call. Time between calls and time to ha...

Q: The Smalltown Credit Union experiences its greatest congestion on paydays from 11

The Smalltown Credit Union experiences its greatest congestion on paydays from 11:30 a.m. until 1:00 p.m. During these rush periods, customers arrive according to a Poisson process at rate 2.1 per min...

Q: How long does it take to reach steady state? Use simulation

How long does it take to reach steady state? Use simulation, with the Multiserver Simulation.xlsm file, to experiment with the effect of warm-up time and run time on the key outputs. For each of the f...

Q: Do exponentially distributed random numbers have the memoryless property? Here is

Do exponentially distributed random numbers have the memoryless property? Here is one way to find out. Generate many exponentially distributed random numbers with mean 5, using the formula in the prev...

Q: The current spreadsheet model essentially finds the expected profit in several steps

The current spreadsheet model essentially finds the expected profit in several steps. It first finds the profit in cell B19 for a fixed value of demand. Then it uses a data table to find the profit fo...

Q: There are three factories on the Momiss River. Each emits two

There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be red...

Q: Given the model in the Multi-server Simulation.xlsm file

Given the model in the Multi-server Simulation.xlsm file, what unit cost parameters should be used if we are interested in “optimizing” the system? Choose representative inputs and unit costs, and the...