Page 73 - DCAP208_Management Support Systems

Management Support Systems

Notes
It is necessary to resort to multi-objective techniques to generate or at least to approximate
the efficient set. There are basically three approaches to undertake that task: (a) the constraint
method, (b) the weighting method and (c) the multi-objective simplex method. Of these
three approaches only the last one can obtain an exact representation of the efficient set.
The Pay-Off Matrix in Mop
One way of obtaining the initial and useful information of an MOP problem is to optimize
each of the objectives separately over the efficient set and then to compute the value of
each objective at each of the optimal solutions. In this way a square matrix, called the ‘Pay-
off Matrix’ is obtained.
The Constraint Method
The basic idea of this method is to optimize one of the objectives while the others are
specified as constraints. The efficient set is then generated by parameterize the right hand
side of the objectives treated as restraints. Thus, for a MOP problem with q objectives to be
maximized, the constraint method leads to the following mathematical programming
problem:
Maximize Z (x)
k
Subject to: x ∈ F
Z (x) ≥ L, j = 1,2...k–1, k+1...q
j j
Being Z (x) the objective to be optimized. Through parametric variations of the right hand
j
sides L the efficient set is generated.
j
The Weighting Method
The basic idea of this method is to combine all the objectives in to a single objective
function. Each objective function is given a weight before all the objectives are added.
Subsequently, the efficient set is generated through parametric variation of weights. Zadeh
(1963) was first to propose this method. Thus, for a MOP problem with q objectives to be
maximized, the weighting method leads to the following mathematical programming
structure:
Maximize W Z (x) + W Z (x) + ...........+ W Z (x)
1 1 2 2 q q
Subject to x ∈ F
W > 0

Through parametric variations of the weights W the efficient set can be generated.
It should be noted that the weighting method guarantees efficient solutions only when the
weights are larger than zero (W > 0). If one of the weights is zero, and there are alternative
optimal solutions, then the corresponding optimal solution provided by the weighting
method can be inferior or non efficient. Further the weighting method can only generate
extreme efficient points and not both the extreme and inferior one as the constraint method
does.
India is predominantly an agricultural economy and thus prosperity to its people depends
upon the progress of its agricultural sector. Agriculture and allied activities contribute
29.1 percent to the gross domestic product of India as compared to 2 percent in U.S., France,
Norway, Japan, 5 percent in Korea and 49 percent in Ethiopia. Indian Agriculture employees
69 percent of total work force as compared to 2 percent in Tanzania, 93 percent in Nepal
and is a major source of poverty alleviation and empowerment of the agrarian folk. It is
also the major source of sustaining life for majority of its population by providing them
Contd....

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