Abstract

The classical assignment problem is considered. A third index is introduced, which can characterize, for example, the location of the work carried out. An iterative decomposition algorithm is proposed. At each step, a problem is solved with three constraints from different groups of conditions and with one connecting variable. The triples of problems are also solved with one restriction, and according to certain rules, the coefficients of the objective functions change. The iterative process that is monotonic in the objective function either arrives at the exact optimum solution of the original problem or indicates the nonuniqueness of the solution. In the latter case, a simple procedure finds the optima.

中文翻译：

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解决三指标平面分配问题的分解方法

摘要

考虑经典分配问题。引入了第三索引，其可以表征例如所进行的工作的位置。提出了一种迭代分解算法。在每个步骤中，都需要通过来自不同条件组的三个约束和一个连接变量来解决问题。问题的三元组也可以有一个限制来解决，并且根据某些规则，目标函数的系数会发生变化。在目标函数中单调的迭代过程要么达到原始问题的精确最优解，要么表明解的非唯一性。在后一种情况下，一个简单的过程即可找到最佳值。