Introduction:
A model, which is used for optimum allocation of scarce or limited resources to competing products or activities under such assumptions as certainty, linearity, fixed technology, and constant profit per unit, is linear programming.
Comparison between transportation model and general linear programming model:
Similarities
1. Both have objective function.
2. Both have linear objective function.
3. Both have non - negativity constraints.
4. Both can be solved by simplex method. In transportation model it is laborious.
5. A general linear programming problem can be reduced to a transportation problem if (a) the aij's (coefficients of the structural variables in the constraints) are restricted to the values 0 and/or 1 and (b) There exists homogeneity of units among the constraints.
Differences
1. Transportation model is basically a minimization model; whereas general linear programming model may be of maximization type or minimization type.
2. The resources, for which, the structural constraints are built up is homogeneous in transportation model; where as in general linear programming model they are different. That
3. is one of the constraint may relate to machine hours and next one may relate to man-hours etc. In transportation problem, all the constraints are related to one particular resource or commodity, which is manufactured by the factories and demanded by the market points.
4. The transportation problem is solved by transportation algorithm; whereas the general linear programming problem is solved by simplex method.
5. The values of structural coefficients (i.e. xij) are not restricted to any value in general linear programming model, where as it is restricted to values either 0 or 1 in transportation problem.
for example:
Let one of the constraints in general linear programming model is: 2x –3y 10z ≤ 20. Here the coefficients of structural variables x, y and z may negative numbers or positive numbers of zeros. Where as in transportation model, say for example x11 x12 x13 x14 = bi = 20. Suppose the value of variables x11, and x14 are 10 each, then 10 0. x12 0. x13 10 = 20.
Hence the coefficients of x11 and x14 are 1 and that of x12 and x13 are zero.
