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The tradeoff between solution robustness and model robustness is also analyzed in the obtained results.

Our analysis on the tradeoff between solution robustness and model robustness arrives at important practical insights.

As mentioned earlier, tradeoff between solution robustness and model robustness can be derived by penalty parameter ( gamma ). Figure 1 illustrates the effects of the penalty function on the expected value of efficiency of DMUs.

Tradeoff between solution robustness (expected total costs) and model robustness (expected under-fulfillment) can be found using different values of (omega) in the objective function (28).

Next, sensitivity analysis has been presented for solution robustness and model robustness.

Since the objective function has been influenced by (omega), the relationship between the model robustness and solution robustness has been analyzed only for the objective function value.

As the value of (omega) increases, the expected total costs representing solution robustness increases exponentially, and the expected under-fulfilled demand representing model robustness drops.

These problems are handled formally in the paradigm of optimization under uncertainty where uncertainty propagation of these parameters through model equations is reflected in terms of system constraints and objectives that facilitate a designer to unveil the tradeoff between solution optimality and robustness.

One of the main advantages of this approach is that it enables decision makers to draw a tradeoff between expected value and variance of DMUs' efficiency under probable scenarios, and a tradeoff between solution and model robustness.

Otherwise, the RO model proposed by Mulvey et al. (1995) enables us to measure the tradeoff between solution and model robustness.

This creates a compromise between shaper robustness and rise time.