An intuitive way to handle optimization problems with data affected by the uncertainty set is to undergo a robust optimization problem where the solution must be satisfied for any possible realization of the data in the uncertainty set. In this work, we addressed an uncertain linear programming problem in which some constraints involves the product of two uncertain parameters that are robust in nature. Hereafter, we discuss the max-min regret approach and subsequently with the help of Lagrangian duality, establish an equivalent approximation of the robust counterpart of such types of uncertain programming problems. Further, for the application purpose, we propose a multi-objective, multi-product production planning model of a captive repair shop for overhauling and repairing products or machines which indicates the relevance of the theoretical performance.

处理受不确定性集合影响的数据的优化问题的一种直观方法是进行鲁棒的优化问题，其中对于不确定性集合中数据的任何可能实现都必须满足解决方案。在这项工作中，我们解决了一个不确定的线性规划问题，其中一些约束条件涉及两个不确定参数的乘积，这些参数本质上是可靠的。此后，我们讨论最大-最小后悔方法，然后借助拉格朗日对偶性，建立此类不确定规划问题的鲁棒对应物的等效近似值。此外，出于应用目的，我们提出了一个多目标，