International Journal of Industrial Engineering & Production Research (2019) 30: 507- 528 DOI: 10.22068/ijiepr.30.4.507 Multi-Period Sustainability Performance in the Presence of Discrete and Bounded Measures Monireh Jahani Sayyad Noveiri 1 & Sohrab Kordrostami *2 Received 01 October 2019; Revised 01 November 2019; Accepted 10 November 2019; Published online 01 December 2019 © Iran University of Science and Technology 2019 ABSTRACT Sustainability performance assessment is a significant aspect of making sustainable decisions for organizations. Measuring sustainability performance of firms in a time span, covered in several periods, leads to more rational decision-making and planning by managers. Furthermore, in many application fields, there are discrete and bounded measures. However, there has been no systematic effort to analyze sustainability performance of Decision-Making Units (DMUs) in multiple periods of time when discrete and bounded factors are presented. Therefore, approaches based on Data Envelopment Analysis (DEA) are proposed in this paper to tackle this problem. To illustrate this issue in more detail, the performance of systems is measured for all dimensions, including economic, social, and environmental ones and for each period. Moreover, the overall multi-period sustainability performance and sustainability performance of each period are estimated using the suggested one- stage methods. Then, the sustainability performance is investigated for conditions in which internal relationships among economic, social, and environmental indicators are presented. Moreover, sustainability performance changes and performance changes of dimensions are addressed. An example and a case study are provided to explain our proposed approach. Results show that the introduced ideas are practical and effective. KEYWORDS: Sustainability Performance, Data Envelopment Analysis, Multi-Period, Discrete, Bounded. 1. Introduction1 Sustainable development is an important aspect in today’s societies. Forwarding sustainable growth needs to follow economic, social, and environmental goals, simultaneously. Measuring the sustainability of systems can facilitate determining the sustainability level and the efficiency in each sustainability dimension. Obviously, more beneficial information can be obtained from sustainability performance analysis in a time span containing multiple periods of time. In the literature, there are approaches to measuring sustainability performance. Readers can refer to [1] for more information. One of the prevailing approaches for this purpose is Corresponding author: Sohrab Kordrostami * kordrostami@liau.ac.ir 1. Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. 2. Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. the non-parametric Data Envelopment Analysis (DEA) approach, originally proposed by Charnes et al. [2]. Zhou et al. [3] provided an organized investigation on DEA utilizations in sustainability. Galán-Martín et al. [4] proposed an enhanced DEA method that applied the concept of ‘order of efficiency’ to assess sustainability. In their approach, sustainability has been analyzed in a specific period of time. Zhao et al. [5] developed a method based upon DEA to measure the performance of systems that each of them designed as an economic and environmental subunit and a social subunit. Hassanzadeh et al. [6] introduced input-oriented and output- oriented inverse semi-oriented models and measured the sustainability of countries in the presence of negative data. Tajbakhsh and Shamsi [7] designed a non-parametric index to assess the sustainability performance of countries in one period when undesirable and integer materials are presented. Amirteimoori et al. [8] assessed the sustainability RESEARCH PAPER [ DOI: 10.22068/ijiepr.30.4.507 ] [ Downloaded from ijiepr.iust.ac.ir on 2021-12-13 ] 1 / 22