A note on a minimax linear programming model for dispatching rule selection

초록

Dispatching rules are essential for scheduling tasks in dynamic environments. When multiple performance criteria are involved, selecting an appropriate rule becomes challenging, as optimizing one criterion may deteriorate another. To address this issue, Amin and El-Bouri (2018) proposed a minimax linear programming (LP) model that selects a dispatching rule performing consistently well across all criteria, thereby avoiding the pitfalls of traditional aggregation methods. By reformulating the selection task as a voting problem, their approach seeks to minimize the worst-case undesirable score based on ranked criteria. In this note, we demonstrate that their two-stage LP model can be equivalently solved using a single LP formulation. Moreover, we derive a closed-form solution to the problem using convex analysis, which clarifies the model’s structure and enhances its practical usability.

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