+1-415-670-9189
info@expertsmind.com
Formulate an integer linear programming model
Course:- Other Engineering
Reference No.:- EM13517701




Assignment Help
Expertsmind Rated 4.9 / 5 based on 47215 reviews.
Review Site
Assignment Help >> Other Engineering

PROBLEM 

Dr. Konur is the Sherriff of Rolla and right now he needs to assign policemen to the different shifts.

There are 50 policemen he can assign a shift. There are 4 different shifts:
- Shift 1: Starts at 6:00am and ends at 6:00pm
- Shift 2: Starts at noon and ends at midnight
- Shift 3: Starts at 6:00pm and ends at 6:00am
- Shift 4: Starts at midnight and ends at noon
Since different shifts have different start and end times, assigning a policeman to different shifts has different costs. Specifically, a policeman costs $100, $110, $150, and $175 in shifts 1, 2, 3, and 4, respectively. Also, there should be a specific number of policemen available in different time periods to make Rolla safe. The minimum numbers of policemen needed for each time period are given in the table below.

53_Systems Engineering6.png

Since Rolla is on a tight budget, Dr. Konur wants to minimize the total cost of the police station he is managing by determining the integer number of policemen to assign to each shift such that at least the minimum number of policemen required in each time period is available for each time period.

a) Mathematically formulate an integer linear programming model for Dr. Konur's problem by defining your decision variables, and expressing your objective and objective function, and constraints using your decision variables. Combine everything to get the final formulation.

b) Answer the following questions independent of each other and without solving the problem and explain your reasoning briefly.

a. If Dr. Konur could assign a fractional number of policemen to any shift, would that increase costs? Yes or No or Maybe? Explain your answer briefly.

b. If Dr. Konur had to assign at least 20 policemen to shift 1, would that increase costs? Yes or No or Maybe? Explain your answer briefly.




Put your comment
 
Minimize


Ask Question & Get Answers from Experts
Browse some more (Other Engineering) Materials
What is an open collector input why is it used on some sensors. List three types of vibration sensors and discuss how they operate. What effect will temperature change have on
Environmental engineering, CEE 357 Winter 2014. HW#6 Assignment: -  Find the ultimate BOD of the river water as it enters the lake. Find the value of the rate constant for BOD
If the temperatures of the inner and outer surfaces of the bottom of the pan are 104°C and 105°C, respectively, determine the rate of energy destruction within the bottom of
If the inverter is operated from a 1.8-V power supply, find the energy needed to charge and discharge the load capacitance. If the IC chip has 2 million of these inverters o
Your company, Tom-Tom Consulting, has been asked by the president of a large fast growing multi-faceted corporation to research three of the areas discussed in the course; h
The table below shows readings for three different cases where the circuit above, was malfunctioning. Find the fault, assuming only one device in each case has a problem. Li
In general, you will have one other classmate in your team. Each of you will design and simulate an instrumentation circuit with different specifications though you will cho
Determine the transfer function of the system and determine and plot the amplitude response of the system - Sketch the poles and zeros of the transfer function in the complex