Page 74 - DCAP208_Management Support Systems

Unit 5: Modeling and Analysis

Notes
food stuff, which is one of the basic needs for human existence. The classical economists
have assigned a central plane to food in their growth model. Starting from Malthus, the
question of feeding the ever growing population has been engaging the attention of
politicians and academicians alike. Food grains occupies an important place in human
food so as self-sufficiency in food grain production was the derived goal of planned
development.
For instance, a subsistence farmer may be interested in securing adequate food supplies
for the family, maximizing cash income, increasing leisure, avoiding risk, etc. but not
necessarily in that order. Similarly a commercial farmer may wish to maximize gross
margin, minimize his indebtedness, acquire more land, reduce fixed costs, etc.

Technique of Analysis
The objective functions are optimized simultaneously in the multiple objective
programming farm planning model. First, the pay-off matrix has been constructed using
‘ideal point’ which represents the optimum values of the objectives under consideration.
In fact, this ideal point is not feasible because the objectives are in conflict, we select the
efficient farm plans closest to it or best compromise by using compromise programming
techniques. The worst element from each column of the pay-oft matrix will be the ‘Anti-
Ideal Point’. Among the different techniques to generate the efficient set, a variant of the
weighting method has been chosen known as Non-Inferior Set Estimation (NISE) method,
as the most suitable multiple objective programming technique for generating the efficient
set (Cohan, Church and Steer, 1979).

For some value of and different values of P different compromise solution for distant
function Lp were obtained and the farmer/nation can chose any one solution for a given
preferences of the different objectives out of the various compromise solutions. However
the distance function Lp is usually used for P=1 and P2=α which shows a longest and the
chebyshev distance in the geometric sense respectively (greater weight is given to the
largest deviation). Therefore, maximum of the individual deviations is minimized with p
= α For different values of P and j, we can generate different compromise solutions. The
alternate with the lowest value for the distance function will be the best compromise
solution because it is the nearest solution with respect to the ideal point. For L1 metric
(P=1), the best compromise solution to the ideal point can be obtained by solving the
following linear programming problems.
*
Zj – Zj(x)
MinL = ∑ δ subject to (X) ∈F
i.e. 1 j Z– Z *
*
j j
For L α matrix (P=α), the minimised by minimum of the individual deviation is minimized
by solving the following linear programming model.
Min L = d
e e
Such that
*
Zj – Zj(x)
δ= ≤ d
*
1 Z– Z * e
j j
*
Zj – Zj(x)
δ= ≤ d e
2
Z– Z * j
*
j
: : :
: : :
. . .
Contd....
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