IDIS 343 Exam 3 Questions with Correct Answers| Latest Update Guaranteed Success
1. Driving Force: - Plant/Warehouse location: economic factors dominate
- Retail location: Revenue generated - cost dominates
- Service operations (hospital, charity collection center, maintenance facility): accessibility to
the site dominates
2. Number of Facilities: - Single facility location: avoids the need to consider competitive
forces, division of demand among facilities, inventory consolidation effects, and facility costs.
- Multiple facility location: significantly more complex.
3. Discreteness of the Choice: - Continuous location methods: Space is a continuum
- Discrete location methods: List of possible choices, more common
4. Degree of Data Aggregation: - Using aggregate data may be necessary but it limits
accuracy.
- Little aggregation is better for retail location, intracity location, and making final plant and
warehouse site selection
5. Time Horizon: - Static horizon: Covers single period
- Dynamic horizon: Covers multiple periods
Key Questions •How many facilities should there be?
•Where should they be located?
•What size should they be?
Single Facility Location Location model for a single plant, terminal, warehouse, retail, service
point...
,• Method we will cover is known as center of gravity approach, p-median, the grid method, and
the centroid method.
• This model is classified as a static continuous location model.
Center of Gravity (CoG) Method Where should the facility be located given a set of points
representing source points and demand points, their volumes, and their transportation rates?
Minimizing the sum of the volume at a point multiplied by the transportation rate to ship to the
point multiplied by the distance to the point (i.e., total transportation cost).
Steps of CoG Method
Notation: • TC: total transportation cost
• Vi : volume (demand or supply) at point i
• Ri : transportation rate per unit volume to point i
• di : distance to point i from the facility to be located
• Xi : horizontal coordinate of source or demand point
• Yi : vertical coordinate of source or demand point
• X^-,Y^- : coordinates of the located facility
Steps of CoG Method
Steps 1-3 1. Identify the coordinates of each source and demand point, along with their
volumes and transportation rates.
2. Approximate the initial location from the center of gravity formulas by omitting the distance
term di as follows:
X^- = (SUM Vi*Ri*Xi)/SUMVi*Ri
Y^- = (SUM Vi*Ri*Yi)/SUMVi*Ri
3. Using the solution for X^- and Y^- from step 2, calculate di according to the following
equation:
di=sqrt((Xi-X^-)^2+(Yi-Y^-)^2)
, Steps of CoG Method
Steps 4-7 4. Substitute di into the following equations and solve for the revised X^- and Y^-
coordinates
X^- =(SUMViRiXi/di)/(SUMViRi/di)
Y^- =(SUMViRiYi/di)/(SUMViRi/di)
5. Recalculate di based on the revised X^- and Y^&coordinates.
6. Repeat steps 4 and 5 until the X^- and Y^ coordinates do not change for successive iterations,
or they change very little.
7. Calculate the total cost for the best location.
Discrete Location Problem (Single Facility)
Solution Methods - Heuristics -Qualitative Analysis
• Weighted Scores
-Quantitative Analysis
• Transportation Models
Heuristics Choice of an appropriate heuristic depends on many factors:
- How are the distances measured?
-What is the objective?
Measuring the Distance 1. Rectilinear distance
2. Euclidean distance
1. Rectilinear distance - Distances are measured along the paths that are orthogonal (or
perpendicular) to each other.
- Best for the cities with perpendicular streets.
1. Driving Force: - Plant/Warehouse location: economic factors dominate
- Retail location: Revenue generated - cost dominates
- Service operations (hospital, charity collection center, maintenance facility): accessibility to
the site dominates
2. Number of Facilities: - Single facility location: avoids the need to consider competitive
forces, division of demand among facilities, inventory consolidation effects, and facility costs.
- Multiple facility location: significantly more complex.
3. Discreteness of the Choice: - Continuous location methods: Space is a continuum
- Discrete location methods: List of possible choices, more common
4. Degree of Data Aggregation: - Using aggregate data may be necessary but it limits
accuracy.
- Little aggregation is better for retail location, intracity location, and making final plant and
warehouse site selection
5. Time Horizon: - Static horizon: Covers single period
- Dynamic horizon: Covers multiple periods
Key Questions •How many facilities should there be?
•Where should they be located?
•What size should they be?
Single Facility Location Location model for a single plant, terminal, warehouse, retail, service
point...
,• Method we will cover is known as center of gravity approach, p-median, the grid method, and
the centroid method.
• This model is classified as a static continuous location model.
Center of Gravity (CoG) Method Where should the facility be located given a set of points
representing source points and demand points, their volumes, and their transportation rates?
Minimizing the sum of the volume at a point multiplied by the transportation rate to ship to the
point multiplied by the distance to the point (i.e., total transportation cost).
Steps of CoG Method
Notation: • TC: total transportation cost
• Vi : volume (demand or supply) at point i
• Ri : transportation rate per unit volume to point i
• di : distance to point i from the facility to be located
• Xi : horizontal coordinate of source or demand point
• Yi : vertical coordinate of source or demand point
• X^-,Y^- : coordinates of the located facility
Steps of CoG Method
Steps 1-3 1. Identify the coordinates of each source and demand point, along with their
volumes and transportation rates.
2. Approximate the initial location from the center of gravity formulas by omitting the distance
term di as follows:
X^- = (SUM Vi*Ri*Xi)/SUMVi*Ri
Y^- = (SUM Vi*Ri*Yi)/SUMVi*Ri
3. Using the solution for X^- and Y^- from step 2, calculate di according to the following
equation:
di=sqrt((Xi-X^-)^2+(Yi-Y^-)^2)
, Steps of CoG Method
Steps 4-7 4. Substitute di into the following equations and solve for the revised X^- and Y^-
coordinates
X^- =(SUMViRiXi/di)/(SUMViRi/di)
Y^- =(SUMViRiYi/di)/(SUMViRi/di)
5. Recalculate di based on the revised X^- and Y^&coordinates.
6. Repeat steps 4 and 5 until the X^- and Y^ coordinates do not change for successive iterations,
or they change very little.
7. Calculate the total cost for the best location.
Discrete Location Problem (Single Facility)
Solution Methods - Heuristics -Qualitative Analysis
• Weighted Scores
-Quantitative Analysis
• Transportation Models
Heuristics Choice of an appropriate heuristic depends on many factors:
- How are the distances measured?
-What is the objective?
Measuring the Distance 1. Rectilinear distance
2. Euclidean distance
1. Rectilinear distance - Distances are measured along the paths that are orthogonal (or
perpendicular) to each other.
- Best for the cities with perpendicular streets.
