Explanation of Solution
Given:
- The total cost of employing a teller at a bank is $100 per day.
- A teller can serve an average of 60 customers per day.
- An average of 50 customers per day arrives at the bank.
- Both service times and inter arrival times are exponential.
- The delay cost per customer day is $100.
To determine
The number of tellers that the bank should hire is to be determined.
Calculating the number of tellers, the bank should hire:
The queuing system is a
Here,
Arrival rate,
Service rate,
Also, if there are s servers, then,
In queuing optimization problem, the component of cost due to customers waiting in line is referred to as the delay cost. Thus, the bank wants to minimize,
Since, the total cost of employing a tell at a bank is $100 per day, then,
Case 1:
For number of servers,
The Hourly delay cost is defined as follows:
Now, the delay cost per customer day is
Also,
Hence,
Now, the average hours the customer spends in the system
Substituting
Now, substitute the value obtained from equation 2 and equation 4 in equation 1,
Hence, the total cost per day for one server is
Case 2:
For number of servers,
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Chapter 20 Solutions
Operations Research : Applications and Algorithms
- This is the question. I am unsure how to begin on - Acme Parts runs a small factory and employs workers who are paid one of three hourly rates depending on their shift: first shift, $17 per hour; second shift, $18.50 per hour; third shift, $22 per hour. Each factory worker might work any number of hours per week; any hours greater than 40 are paid at one and one-half times the usual rate. In addition, second- and third-shift workers can elect to participate in the retirement plan for which 3% of the worker’s gross pay is deducted from the paychecks. Write a program that prompts the user for hours worked, shift, and, if the shift is 2 or 3, whether the worker elects the retirement (1 for yes, 2 for no). Display: Hours worked Shift Hourly pay rate Regular pay Overtime pay Total of regular and overtime pay Retirement deduction, if any Net pay. This is the way the code starts - import java.util.*; public class AcmePay { public static void main(String[] args) throws Exception {…arrow_forwardA call center has 60 employees on‐line, each of whom make one phone call every 3 min on average, and talk on average for 2 min. Each call costs 15¢. What is the total traffic in erlangs? How many circuits are required for a GoS of 1%? How much should the yearly (250 working days, 8 working hours a day) lease price be for the company to make a 50% saving in its telephone bills over the first 3 years? Assume the lease set‐up fee of $30,000 should be paid over a period of 3 years.arrow_forwardAssume now that there are 12 people initially on the yacht with 6 women and 6 men, and that exploration teams consist of six people. How many exploration teams have more women than men?arrow_forward
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- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole