CONCEPTS : TRANSPORTATION PROBLEM
1. Balanced Transportation Problem : A transportation problem in which the total supply available
(at all the origins) exactly satisfies the total demand required (at the destinations.)
2. Degeneracy : A condition that occurs when the number of occupied cells ( stone Squares) is less
than the number of rows plus number of columns minus 1 in a transportation table. This
degeneracy can be sorted out by selecting a water cell having lowest transportation cost &
assigning it a small quantity (epsilon, which not zero but nearer to zero) for converting it in to
stone square to meet test of feasibility of M + N -1 = stone squares
3. Dummy Destination : An extra / additional location added when total supply is greater total
demand The demand at the dummy location is adjusted so that total supply and demand are
equal.
Dummy Source : An artificial source when total demand is greater than total the supply at the
dummy source is so that total demand and supply are equal.
4. Initial Feasible Solution: A solution that satisfies supply and demand conditions and yet it may
or may not be optimal. There are five different methods to find an initial feasible solutions ( Row
minima method, Column minima method, North West corner method, Least cost method and
VAM method).
5.
Least Cost Method: A systematic procedure to obtain an initial feasible solution by allocating
as many units as possible to the lowest cost cell in the transportation table, then to the next
lowest, and so on.
6. Looping : It is a process of effecting improvement in the initial feasible solution wherein a closed
path is established from the selected water square having largest net opportunity cost ( highest –
ve figure) and assigning alternate + or – signs to the cells selected for a closed path. On doing
so, the requisite numbers of units are shifted in to or from each cell on the closed path depending
upon the signs.
7. Modified Distribution Method (MODI) : Another algorithm for finding the optimal solution to a
transportation problem. It can be used in place of the stepping stone method.
8. North West Corner Method : Systematic allocation to cells beginning in the upper left hand
corner of the transportation table to obtain an initial feasible solution.
9. Opportunity Cost (Regret Cost): The cost savings ( if any ) foregone by not using an empty cell
of transportation matrix.
10. Origins : The multiple sites for facilities location which are analyzed by the transportation
method.
11. Optimality Test In Transportation Problem: Where the values of water squares are negative
then they are selected for converting in to stone squares. A situation where all the values of water
square are positive, we assume the solution to e an optimal .Therefore finding out values of water
square is called as “optimality Test” The optimal solution is one in which there is no opportunity
cost, i.e. there is no other set of transportation route that will reduce the total transportation cost.
12. Prohibited Transportation Problem: In many practical solutions, some of the routes in a
transportation are prohibited due to certain operational problems such as flood situation, road
conditions, government restrictions etc.Such restrictions can be handled for solving transportation
problem by converting these operational problems in to mathematical problem by assigning very
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high cost of transportation to these prohibitive routes to ensure that these routes will not be
included in the final optimal solution.
13. Rim Requirements : The total quantities of the product which are supplied by each origin and the
total quantities demanded at each destination in the transportation method.
14. Stepping-Stone Method : An iterative technique for moving from an initial feasible solution to an
optimal solution in transportation problems.
15. Stepping-Stone Path : A series of adjustments in a feasible solution to a
transportation problem that incorporates a new route and retains a feasible solution.
16. Significance of Time Minimisation in Transportation Problem:
Transportation problems exist where the objective is to minimize the time rather than cost of
transportation, required to fill all the demand at the destinations. Typical examples occur in
transporting military supplies, perishable goods, and life saving drugs etc. where the speed of
delivery is more important than the transportation cost.
The structure of this type of problem is the same as in the regular transportation problem except
that for each route the cost of unit is replaced by the total time required to effect a complete
shipment. Here the transportation time is assumed independent of the size of shipment.
17. Sensitivity In Transportation Problem: It is a study of the effect of changes in re-distribution of
allocated quantities on the total transportation cost / expected profit. The study of how sensitive
an optimal solution is to the model assumptions and to data changes.
18. Transportation Problem : A specific case of linear programming concerned with scheduling
shipments from sources to destinations so that total transportation costs are minimized.
19. Transportation Table : A table used to display or summarize all transportation data to help keep
track of all algorithm computations by storing information on demands, supplies, shipping costs,
units shipped, origins and destinations.
20. Unbalanced Transportation Problem : A transportation problem where the total availability at
the origins is different from the total requirement at the destinations.
21. Vogel’s Approximation Method (VAM : An algorithm used to find a relatively efficient initial
feasible solution to a transportation problem by considering the ‘penalty cost’ of not using the
cheapest available route.
CONCEPTS : ASSIGNMENT PROBLEM
1. Assignment Problem : It is a special type of linear programming problem where the objective is
to minimize the cost or time of completing a number of jobs by a of persons in such a way that
only one resource is assigned to one activity.
2. Assignment Method : A scheduling method used for assigning individual jobs to individual
processing components on a one-to one basis, with the goal of minimizing the total cost or time
for accomplishing all of the jobs.
3. Balanced assignment problem : It is an assignment Problem where the number of activities is
exactly equal to the number of resources.
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4. Dummy rows or columns are extra rows or columns added in order to ‘balance’ an assignment
problem so that the number of rows equals the number of columns.
5. Dummy Job is an imaginary job with cost or time zero introduced to make an unbalanced
assignment problem balanced.
6. Hungarian Method is a technique (or an efficient solution procedure) of solving assignment
problems.
7. Multiple Optimal Solution: Sometimes, it is possible to have more than one alternative to
allocate the task to the facilities available. In such cases there will be more than one solution for
assigning the task to the respective facilities, however the total cost involved or profits generated
will be the same. In such type of situation, the management may exercise their preferences which
is suited to their requirements.
8. Infeasible Assignment :It is sometimes possible that a particular person is incapable of doing
certain work or a specific job cannot be performed on a particular machine. The solution of the
assignment problem should take into account these restrictions so that the infeasible
assignments can be avoided. This can be achieved by assigning a very high cost to the cells
where assignments are prohibited.
9. Prohibited Assignment Problem: In many practical solutions, some of the tasks cannot be
performed by certain facilities due to certain operational problems. Such restrictions can be
handled for solving assignment problem by converting these operational problems in to
mathematical problem by assigning very high cost of operations to these tasks to ensure that
these tasks will not be awarded to these facilities in the final optimal solution.
10. Regret / Reduced Matrix: It is an approach of the assignment method which reduces the original
assignment profits to a table of opportunity costs, the costs associated with a scarified opportunity
in order to make a particular decision The new matrix is also called as Regret Matrix.
11. Unbalanced Assignment Problem is an assignment problem where the number of resources
(or persons) is not equal to the number of activities (or jobs).
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