This paper presents a new multiple criteria optimization model of an assignment problem with imprecise coefficients. Besides, minimizing the total cost, total time of finishing jobs, and maximization of the overall achieved quality, we introduce a new criterion that minimizes the number of workers employed to finish all jobs. It contributes significantly in multi-job assignment to adjust the number of workers assigned to at least one job for balancing work allocation among the workers. Furthermore, we employ new diversification constraints to obtain a reasonable tradeoff between the number of workers employed and number of jobs assigned. A new interactive possibilistic programming approach is developed for trapezoidal possibility distributions, which uses α-level sets to incorporate confidence levels of the decision maker in his fuzzy judgments leading to α-efficient solutions. Numerical experiments are conducted using data coming from a manpower planning problem to demonstrate working of the proposed multiple criteria assignment model and effectiveness of the fuzzy interactive approach.

中文翻译：

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多准则分配问题的新可能性优化模型


本文提出了一种新的不精确系数分配问题的多标准优化模型。此外，为了最小化总成本、完成工作的总时间以及最大化总体质量，我们引入了一个新的标准，最小化完成所有工作所雇用的工人数量。在多工作分配中，调整分配给至少一项工作的工人数量以平衡工人之间的工作分配有很大贡献。此外，我们采用新的多元化约束，以在雇用的工人数量和分配的工作数量之间取得合理的权衡。针对梯形可能性分布开发了一种新的交互式可能性规划方法，该方法使用 α 水平集将决策者的置信水平纳入其模糊判断，从而产生 α 有效解决方案。使用来自人力规划问题的数据进行数值实验，以证明所提出的多标准分配模型的工作原理以及模糊交互方法的有效性。