Mathematical Models for Performance Measurement and Benchmarking in Organizations

绩效衡量和基准是我们经济体系的重要基础，尤其是加拿大庞大的服务业。银行、医院和学校只是可以从基准和效率评估中受益的组织的几个例子。通过拥有有效的工具来衡量任何组织相对于其同行或竞争对手的绩效，该组织可以更好地了解它目前所处的位置与其潜力所在之间可能存在的任何差距。提出的研究旨在开发决策支持工具，以建模性能并确定组织中的最佳实践。要使用的模型结构是数据包络分析（DEA），它属于更广泛的多标准决策方法。DEA的研究跨越了40年；拟议的研究计划审查了在将DEA应用于现实世界问题的过程中出现的一些主要问题。供应链管理是当前研究的一个重要领域。拥有分析供应链和对供应商及其相关供应链进行绩效比较的手段，现在在“盈利”和“非盈利”设置中都成为绝对必要的。DEA方法有可能成为这里的一种选择工具，但目前的形式还不够强大，无法提供所需的详细分析。拟议研究的主要部分侧重于解决DEA方法中的一些缺点。该研究的一个重要特征涉及非同质多阶段问题（包括供应链）的绩效/效率的测量和建模。这意味着要考虑并非所有链条都具有相同数量的阶段的设置。此外，该研究将探讨建立伙伴关系/联盟的问题，并考虑到资源汇集。另一个研究领域涉及等级情况。需要审查的一个重要应用是涉及一组发电厂的应用，每一个发电厂都在一个管理下作为一组发电机组或子机组的保护伞。这种结构是许多问题设置的特征，因为它允许在不同的聚合和分解级别上进行效率度量。

Performance measurement and benchmarking are important underpinnings of our economic system, particularly the large Canadian service sector. Banks, hospitals and schools are but a few examples of organizations that can benefit from benchmarking and efficiency evaluation. By having effective tools for measuring the performance of any organization relative to its peers or competitors, that organization can have a better understanding of any gaps that may exist between where it currently stands and where its potential lies. The proposed research is aimed at developing decision support tools for modeling performance and identifying best practice in organizations. The model structure to be used is data envelopment analysis (DEA), which falls within the broader set of multi-criteria decision-making methodologies. DEA research has spanned 4 decade; the proposed research program examines some of the major issues that have arisen in the process of applying DEA to real world problems. An important area of current research is supply chain management. Having the means for analyzing supply chains and making performance comparisons between vendors and their associated supply chains , is now becoming an absolute necessity in both 'for profit' and 'not for profit' settings. The DEA methodology has the potential to become a tool of choice here, but is not robust enough in its current form to provide the detailed analysis needed. A major portion of the proposed research focuses on addressing some of these shortcomings in the DEA methodology. One important feature of the research involves the measurement and modeling of performance/efficiency in non-homogeneous multistage problems (including supply chains). This means considering settings where not all chains have the same number of stages. Furthermore, the research will look into the problem of forming partnerships/coalitions, taking into consideration pooling of resources. Another area of study involves hierarchical situations. An important application to be examined is that involving a set of electric power plants, each of which acts as an umbrella for a set of power units or sub-units under one management. This structure is characteristic of a number of problem settings in that it allows for efficiency measurement at different levels of aggregation and disaggregation.