Social efficiency forecasting based on social sustainability practices in the service supply chain

Abstract

This study tries to provide a system to predict social efficiency (SOE) by relying on internal social sustainability practices (ISSPs) in the service supply chains (SCs). Because of the unclear notion of an emerging issue, this study applied the fuzzy set theory to extract the experts’ opinions and overcome the vague nature of this problem. So, the ISSPs were identified by literature review and confirmed as schedulable and budgetable practices in service SCs by the fuzzy Delphi method (FDM). The extracted ISSPs and SOE were, respectively, applied in the role of inputs and output of the adaptive neuro-fuzzy inference system (ANFIS). The data from 70 hospital SCs were collected to design the knowledge base. The proposed system would help service SC managers to foresee if they are performing in an efficient way regards to social sustainability. Also, predicting the impact of adopting different levels of social practices on SOE enables managers to make a conscious decision about prioritizing and budgeting those practices. According to the extensive literature review, the research on the relationship between social sustainability practices-performance is emerging and limited. Also, one of the most important contribution of the paper is to consider the service SCs characteristics in this issue. This paper is a preliminary effort and scientific contribution to empirically determine the relations between social practices and social efficiency, especially in service SCs, along with applying FDM and ANFIS for answering this research questions.

Appendix 1

The steps for FDM calculations (Wang and Durugbo 2013):

• 1. The triangular fuzzy numbers (TFNs) were determined for index $O_{i} = \left( {L_{i} , M_{i} ,U_{i} } \right)$ for each i-factor. L_i represents the minimum value provided by the experts:

  $${\text{LC}}_{i} = \min \left( {L_{ik} } \right)$$

M_i is the geometric mean of the experts’ opinions and is determined as follows:

$$M_{i} = \left( {R_{i1} \times R_{i2} \times \cdots \times R_{ik} } \right)^{\frac{1}{k}}$$

U_i represents the maximum value provided by the experts:

$$U_{i} = \max \left( {L_{ik} } \right)$$

A fuzzy number is a special fuzzy set in which $\tilde{A} = \left\{ {\left( {x, \mu_{A} \left( x \right),x \in R} \right)} \right\}$ that x value is in R → [0, 1]. The fuzzy number ($\tilde{A}$) is defined on R, so that is a TFN and the membership function can be defined as follows:

$$\mu_{A} \left( x \right) = \left\{ {\begin{array}{*{20}l} {\frac{x - L}{{M - L}},} \hfill & {x \in \left[ {L,M} \right]} \hfill \\ {\frac{U - x}{{U - M}},} \hfill & {x \in \left[ {M, U} \right]} \hfill \\ {0,} \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right..$$

In this case, L ≤ M ≤ U, L and U are the smallest and highest values, respectively, and M represents the most probability of value.

• 2. When the TFNs are set for all factors, the center of area (COA) method is used for the defuzzification and determine the G_i value:

  $$G_{i} = \frac{{\left( {U_{i} - L_{i} } \right) + \left( {M_{i} - L_{i} } \right)}}{3} + L_{i}$$

• 3. The factors are screened by determining α. The basis for screening is as follows: Factors whose G_i are greater than or equal to the threshold (α = 3.5) remain, and other factors are eliminated.

  $$\left\{ {\begin{array}{*{20}l} {{\text{If}}\;G_{i} \ge \alpha \;{\text{Then}}\;{\text{select}}\;{\text{No}}.\;i\;{\text{factor}}} \hfill \\ {{\text{If}}\;G_{i} < \alpha \;{\text{Then}}\;{\text{delete}}\;{\text{No}}.\;i\;{\text{factor}}} \hfill \\ \end{array} } \right.$$