Recourse penalty cost

Tables 6.3-6.5 show the computational results for Risk Model II over a range of values of risk parameter 02 with respect to different recourse penalty costs, for three representative cases of 0 = 1E — 10, IE — 7, and 1.55E — 5, respectively. An example of the detailed results is presented in Table 6.6 for 02 = 50 of the first case. Figure 6.2 illustrates the corresponding efficient frontier plot for Risk Model II while Figure 6.3 provides the plot of the expected profit for different levels of risk.

Although increasing 02 with fixed value of 0 corresponds to decreasing expected profit, it generally leads to a reduction in expected production shortfalls and surpluses. Therefore, a suitable operating range of 02 values should be selected to achieve a proper trade-off between expected profit and expected production feasibility. Increasing 02 also reduces the expected deviation in the recourse penalty costs under different scenarios. This, in turn, translates to increased solution robustness. In that sense, the selection of 0j and 02 values depends primarily on the policy adopted by the decision maker. 

Operational risk factor 02 Optimal objective value Expected variation in profit V(z0)(E + 8) Expected total unmet demand/ production shortfall Expected total excess production/ production surplus Expected recourse penalty costs Es Expected variation in recourse penalty costs Vs p = E[z ] - Es c a P... 

Operational Risk Trade-off Parameter <9 for Recourse Penalty Costs... 

One of the reasons why the pair of decreasing values of 0, with a fixed value of 03 leads to increasing profit is due to the decrease in production shortfalls and, at the same time, increase in production surpluses. Typically, the fixed penalty cost for shortfalls is lower than surpluses. A good start would be to select a lower operating value of 0 j to achieve both high model feasibility as well as increased profit. Moreover, lower values of 03 correspond to decreasing variation in the recourse penalty costs, which implies solution robustness. 

The corresponding expected recourse penalty for the second-stage costs is given by ... 

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