INCORPORATING ENVIRONMENTAL CONCERNS IN SUPPLY CHAIN OPTIMIZATION - Environmentally Conscious Materials Handling - page 130

Robust optimization is an alternative to deal with the drawbacks of stochastic
optimization. Under robust optimization, uncertain parameters are known only to
belong to an “uncertainty” set (i.e., knowledge of their specific distributions is
not necessary). The focus is on generating solutions that are robust or immune
to parameter changes. Early concepts of robust optimization, such as the one
proposed by Soyster (1973) in the early 1970s, sought to construct optimization
models such that the solution would be feasible over entire uncertainty sets.
The drawback of such models is that solutions are too conservative in the sense
that the objective is sacrificed for robustness. Recent concepts of robustness
involve the consideration of worst-case scenarios. Mulvey et al. (1995) present a
min-max objective approach that integrates goal programming formulations with
scenario-based data descriptions for optimizing against worst-case scenarios.

5.5 Optimality Criteria

The concept of optimality in SCO may have to be recast in light of societal pres-
sures (such as issues of “fairness”) and due to concerns of supplier reliability
leading to diversification efforts. One approach in the literature is the concept
of equitable efficiency , which can be applied to both single and multiobjective
optimization problems. Traditionally, decision makers are interested in solutions
that are Pareto-optimal or efficient (i.e., no other solution yields a strictly better
result). However, this optimality criterion may not be appropriate when dealing
with environmental concerns or other issues that are difficult to quantify. Dur-
ing the past decade, an increasing interest in equity issues has resulted in new
methodologies in the area of operations research; equitable efficiency has been
proposed as one refinement to the concept of Pareto optimality.
To understand the concept of equitable efficiency, consider a typical optimiza-
tion problem. The optimality of a solution is traditionally determined by the
magnitude of the resulting objective value. In the case of equitable efficiency,
the decision maker not only is interested in the value of the objective but also
desires to achieve a balance or fairness among outcomes. Consider an illustrative
example of a multiobjective problem, similar to that in Kostreva et al. (2004).
Suppose two possible solutions exist, generating outcome vectors (6, 2, 6) and
(1, 3, 1), respectively (assume that the outcome vector elements are normalized
and are therefore comparable). Both solutions are Pareto-optimal (i.e., neither
solution strictly dominates the other). Though both solutions have two outcome
elements equal to each other, the second outcome vector is clearly better in terms
of distribution of outcomes (outcomes deviate by a maximum of 2 as opposed to
4), and the solution with outcome vector (1, 3, 1) is said to equitably dominate the
other solution. Thus, equitably efficient solutions are a subset of Pareto-optimal
solutions.
The concept of equitable efficiency can be also be applied to MOPs in which
the

objectives are incomparable or even conflicting. Traditional optimality