transportation, transshipment and assignment problems
CHAPTER 6:
TRANSPORTATION, TRANSSHIPMENT AND ASSIGNMENT PROBLEMS
Transportation Problem - A distribution-type problem in which supplies of goods that are held at various locations are to be distributed to other receiving locations. - The solution of a transportation problem will indicate to a manager the quantities and costs of various routes and the resulting minimum cost - Used to compare location alternatives in deciding where to locate factories and warehouses to achieve the minimum cost distribution configuration
Formulating the model
Transportation
-Typically involves a set of locations which referred to as origins, and a set of receiving locations which referred to as destinations
-To develop a model of transportation problem, following information are needed:
1. Supply quantity (capacity) of each origin
2. Demand quantity of each destination
3. Unit transportation cost for each origin-destination route
Special Cases of Transportation Problems:
Maximization Problems
- A transportation-type problems that concern profits or revenues rather than costs.
-objective to maximize profits rather than to minimize costs.
Unacceptable Routes
-Certain origin-destination combinations may be unacceptable due to weather factors, equipment breakdowns, labor problems, or skill requirements that either prohibit, or make undesirable, certain combinations (routes).
Unequal supply and Demand
- Situations in which supply and demand are not equal. In such case, it is necessary to modify the original problem so that supply and demand are equalized
- Modify by adding dummy column (if demand if less than supply) or dummy row (if supply is less than demand). Dummy is assigned unit cost of zero for each cell, and it is given a supply or demand equal to the difference between supply and demand
-Quantities in dummy routes in the optimal solution are not shipped and serve to indicate which supplier will hold the excess supply, and how much, or which
TRANSPORTATION, TRANSSHIPMENT AND ASSIGNMENT PROBLEMS
Transportation Problem - A distribution-type problem in which supplies of goods that are held at various locations are to be distributed to other receiving locations. - The solution of a transportation problem will indicate to a manager the quantities and costs of various routes and the resulting minimum cost - Used to compare location alternatives in deciding where to locate factories and warehouses to achieve the minimum cost distribution configuration
Formulating the model
Transportation
-Typically involves a set of locations which referred to as origins, and a set of receiving locations which referred to as destinations
-To develop a model of transportation problem, following information are needed:
1. Supply quantity (capacity) of each origin
2. Demand quantity of each destination
3. Unit transportation cost for each origin-destination route
Special Cases of Transportation Problems:
Maximization Problems
- A transportation-type problems that concern profits or revenues rather than costs.
-objective to maximize profits rather than to minimize costs.
Unacceptable Routes
-Certain origin-destination combinations may be unacceptable due to weather factors, equipment breakdowns, labor problems, or skill requirements that either prohibit, or make undesirable, certain combinations (routes).
Unequal supply and Demand
- Situations in which supply and demand are not equal. In such case, it is necessary to modify the original problem so that supply and demand are equalized
- Modify by adding dummy column (if demand if less than supply) or dummy row (if supply is less than demand). Dummy is assigned unit cost of zero for each cell, and it is given a supply or demand equal to the difference between supply and demand
-Quantities in dummy routes in the optimal solution are not shipped and serve to indicate which supplier will hold the excess supply, and how much, or which