The Avis car rental company successfully used the transportation method to move its inventory of cars efficiently.
Transportation and assignment problems are really linear programming techniques called network flow problems.
A typical transportation problem may ask the question, “How many of X should be shipped to point E from source A?”
The objective of a transportation problem solution is to schedule shipments from sources to destinations while minimizing total transportation and production costs.
Assignment problems involve determining the most efficient assignment of people to projects, salesmen to territories, contracts to bidders, and so on.
The objective of an assignment problem solution most often is to minimize total costs or time of performing the assigned tasks.
An important characteristic of assignment problems is that no less than two jobs or two workers are assigned to one machine or project.
The northwest corner rule, stepping-stone, MODI, and Vogel’s methods all produce integer solutions.
The MODI method is the Maximized Optimal Distribution method.
In the assignment problem, the costs for a dummy row will be equal to the lowest cost of the column for each respective cell in that row.
Linear programming techniques can be used to solve transportation problems and are more efficient than special purpose algorithms.
In finding the maximum quantity that can be shipped on the least costly route using the stepping-stone method, one examines the closed path of plus and minus signs drawn and selects the smallest number found in those squares containing minus signs.
In a transportation problem, the northwest corner rule is generally the most effective and efficient procedure to follow.
An advantage of the transportation and assignment problems is that the computational procedures virtually eliminate the possibility of multiple optimal solutions.
The Hungarian method is designed to solve transportation problems efficiently.
The transportation and assignment problems are the only linear programming problems for which we have special solution techniques.
From a practical perspective, it is always necessary to achieve an "optimal" solution to a complex assignment problem-a "very good" solution will simply not do.
In a transportation problem, each destination must be supplied by one and only one source.
In a transportation problem, a single source may supply something to all destinations.
One reason we choose not to apply the simplex method to the solution of assignment problems is that the Hungarian method is faster and easier.
A transportation model must have the same number of rows as columns.
The transportation method can be used to solve both minimization problems and maximization problems.
In the transportation model, we must always make the total supply equal to the total demand.
The stepping-stone method is simply an orderly process for investigating the solution at each possible "corner point" of the multidimensioned solution space.
In using the stepping-stone method, the path can turn at any box or cell which is unoccupied.
Using the stepping-stone...
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