(max, +)-linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form f(x1, …, xh) = max(aj + xj), where aj, j = 1, …, h, are real numbers. Similarly (min, +)-linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have (max, +)-linear functions of variables x on one side and (min, +)-linear functions of variables y on the other side. Such systems can be applied e.g. to operations research problems in which we need to coordinate or synchronize release and completion times of operations or departure and arrival times of passengers. A motivation example is presented and the proposed solution method is demonstrated on a small numerical example.

中文翻译：

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两侧$(\max,+)/(\min,+)$不等式约束下的优化问题

(max, +)-线性函数是可以表示为一个变量的有限数量线性函数的最大值的函数，其形式为 f(x1, …, xh) = max(aj + xj)，其中 aj, j = 1, ..., h, 是实数。类似地，定义了 (min, +)-线性函数。我们将考虑优化问题，其中可行解集是有限不等式系统的解集，其中不等式在一侧具有变量 x 的 (max, +)-线性函数和 (min, +)-线性函数另一边的变量 y。例如，此类系统可以应用于运营研究问题，在这些问题中我们需要协调或同步运营的发布和完成时间或乘客的出发和到达时间。提出了一个动机示例，并在一个小的数值示例上演示了所提出的解决方法。