In some processes and systems, undesirable inputs and outputs may be presented along with desirable measures. Undesirable factors play a significant role to calculate the accurate efficiency of Decision Making Units (DMUs). Furthermore, analyzing the impact of a throughput on another throughput in economics and production management gives useful information in order to make a better decision. Therefore, the current paper proposes a linear programming approach based on Data Envelopment Analysis (DEA) to compute the marginal rates of substitution for single throughput and multi-throughput of efficient DMUs while undesirable inputs and outputs are present simultaneously. To address undesirable input and output measures, the assumption of the weak disposability of both inputs and outputs is considered. The proposed approach is illustrated with numerical examples and an application of wastewater treatment plants. The results show that the provided approach is applicable and suitable to assess the marginal rates of substitution in the presence of undesirable input–output measures.

在某些过程和系统中，不希望的输入和输出可能会与希望的措施一起出现。不良因素在计算决策单元 (DMU) 的准确效率方面起着重要作用。此外，在经济学和生产管理中分析一个吞吐量对另一个吞吐量的影响可以提供有用的信息，以便做出更好的决策。因此，当前的论文提出了一种基于数据包络分析 (DEA) 的线性规划方法，以计算有效 DMU 的单吞吐量和多吞吐量的边际替代率，同时不希望的输入和输出同时存在。为了解决不受欢迎的输入和输出措施，考虑了输入和输出的弱可处置性的假设。数值算例和废水处理厂的应用说明了所提出的方法。结果表明，所提供的方法适用于评估存在不良投入产出措施时的边际替代率。