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Designing a humanitarian relief network considering governmental and non-governmental operations under uncertainty

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Abstract

This study addresses a humanitarian supply chain network that includes locating relief centers, pre-positioning and distributing relief items, and providing medical treatment in affected regions to help people suffering. Also, the role of non-governmental organizations along with governmental organizations and disruption in relief centers is examined. The objective of the model is to minimize total costs. The problem is formulated as a mixed-integer linear mathematical model. A two-stage mixed fuzzy-stochastic approach is developed to capture the uncertainty. To solve the model on a large scale, grasshopper optimization algorithm is utilized, and its performance is examined through computational experiments. To assess the applicability of the proposed model, it is applied to Tehran as a real case study. According to the numerical examples and sensitivity analysis, fruitful managerial insights are provided to help decision-makers increase relief operations' efficiency. The results indicate that non-governmental organizations' contribution significantly enhances the performance of the humanitarian supply chain while disruption has an adverse impact.

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adopted from http://atlas.tehran.ir)

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Acknoledgements

The authors would like to thank the editor-in-chief and the anonymous referees for their perceptive comments and valuable suggestions on a previous draft of this paper to improve its quality.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, College of Engineering, University of Tehran, P. O. Box, Tehran, 11155-4563, Iran

    Seyed Reza Abazari, Fariborz Jolai & Amir Aghsami

  2. School of Industrial Engineering, K. N. Toosi University of Technology (KNTU), Tehran, Iran

    Amir Aghsami

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  1. Seyed Reza Abazari
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Appendix A

Appendix A

In order to survey the equality of the objective function's value obtained by GAMS and GOA, a statistical hypothesis test is conducted. For this purpose, a test problem has been solved 30 times with GAMS and GOA. First, the Kolmogorov–Smirnov test in MINITAB software has been used for the normality test of obtained values. According to the probability plot and p-value in Fig. 

Fig. 27
figure 27

Probability plot of the objective function values

Full size image

27, it can be concluded that the objective function's values have a normal distribution. Therefore, the hypothesis test is as follows (Montgomery 2009):

$$\left\{\begin{array}{c}{H}_{0}: {Z}_{GOA}={Z}_{GAMS}\\ {H}_{1}: {Z}_{GOA}>{Z}_{GAMS}\end{array}\right.$$

A statistic for this test could be calculated using the following equation:

$${t_0} = \frac{{\overline {{Z_{GOA}}} - {Z_{GAMS}}}}{{{\raise0.7ex\hbox{$S$} \!\mathord{\left/ {\vphantom {S {\sqrt n }}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${\sqrt n }$}}}}$$
$$S=\sqrt{\frac{\sum_{i=1}^{n}{({Z}_{{\left(GOA\right)}_{i}}-\overline{{Z }_{GOA}})}^{2}}{n-1}}$$

For a minimization problem, the acceptance region would be \(\left(-\infty , {t}_{\alpha ,n-1}\right]\). The results of the statistical hypothesis test are specified in Table

Table 5 Results of the statistical hypothesis test
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5. Based on results shown in Table 5 and the significance level of 0.05, the statistic is in the acceptance region and the null hypothesis cannot be rejected, which means that results obtained with GOA and GAMS have no significant difference.

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Abazari, S.R., Jolai, F. & Aghsami, A. Designing a humanitarian relief network considering governmental and non-governmental operations under uncertainty. Int J Syst Assur Eng Manag 13, 1430–1452 (2022). https://doi.org/10.1007/s13198-021-01488-y

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