Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

An emergency logistics distribution routing model for unexpected events

  • RAOTA-2016
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Though there are many specialities of logistics distribution in unexpected events, the greatest uniqueness of the problem should be the feature that no historical data about some parameters are available. The paper defines the emergency logistics as the one of which the parameters have no historical data due to the occurrence of the unexpected events, and discusses an emergency logistics distribution routing problem in which demands of the affected areas and road travel times lack historical data and are given by experts’ estimations. Uncertain variables are used to describe the experts’ estimates of the parameters and the use of them is justified. An emergency logistics distribution routing model is developed based on uncertainty theory. To solve the problem, the equivalent model is provided and a cellular genetic algorithm is designed. In addition, an example is presented to illustrate the application of the proposed model and the effectiveness of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Altay, N., & Green, W. G, I. I. I. (2006). OR/MS research in disaster operations management. European Journal of Operational Research, 175, 475–493.

    Article  Google Scholar 

  • Barbarosoǧlu, G., & Arda, Y. (2004). A two-stage stochastic programming framework for transportation planning in disaster response. The Journal of the Operational Research Society, 55, 43–53.

    Article  Google Scholar 

  • Caunhye, A. M., Nie, X., & Pokharel, S. (2012). Optimization models in emergency logistics: A literature review. Socio-Economic Planning Sciences, 46, 4–13.

    Article  Google Scholar 

  • Chandre, M., Baskett, P., & Gallaghter, G. (2007). The southeast Asian tsunami disaster—How resuscitation helped the recovery program. Resuscitation, 72, 6–7.

    Article  Google Scholar 

  • Chen, X. (2012). Variation analysis of uncertain stationary independent increment processes. European Journal of Operational Research, 222, 312–316.

    Article  Google Scholar 

  • Chen, X. W., & Ralescu, D. A. (2012). B-spline method of uncertain statistics with applications to estimate travel distance. Journal of Uncertain Systems, 6, 256–262.

    Google Scholar 

  • Coles, S., & Pericchi, L. (2003). Anticipating catastrophes through extreme value modelling. Journal of the Royal Statistical Society: Series C (Applied Statistics), 52, 405–416.

    Article  Google Scholar 

  • Ding, C., & Zhu, Y. (2015). Two empirical uncertain models for project scheduling problem. Journal of the Operational Research Society, 66, 1471–1480.

    Article  Google Scholar 

  • Fiedrich, F., Gehbauer, F., & Rickers, U. (2000). Optimized resource allocation for emergency response after earthquake disasters. Safety Science, 35, 41–57.

    Article  Google Scholar 

  • Gao, Y. (2011). Shortest path problem with uncertain arc lengths. Computers and Mathematics with Applications, 62, 2591–2600.

    Article  Google Scholar 

  • Han, S., Peng, Z., & Wang, S. (2014). The maximum flow problem of uncertain network. Information Sciences, 265, 167–175.

    Article  Google Scholar 

  • Huang, X. (2010). Portfolio analysis: From probabilistic to credibilistic and uncertain approaches. Berlin: Springer.

    Book  Google Scholar 

  • Huang, X. (2012). Mean-variance models for portfolio selection subject to experts’ estimations. Expert Systems With Applications, 39, 5887–5893.

    Article  Google Scholar 

  • Huang, X., Xiang, L., & Islam, S. M. N. (2014). Optimal project adjustment and selection. Economic Modelling, 36, 391–397.

    Article  Google Scholar 

  • Huang, X., & Zhao, T. (2014). Project selection and scheduling with uncertain net income and investment cost. Applied Mathematics and Computation, 247, 61–71.

    Article  Google Scholar 

  • Huang, X., & Di, H. (2015). Modeling uncapacitated facility location problem with uncertain customers’ positions. Journal of Intelligent & Fuzzy Systems, 28, 2569–2577.

    Article  Google Scholar 

  • Huang, X., Zhao, T., & Kudratova, S. (2016). Uncertain mean-variance and mean-semivariance models for optimal project selection and scheduling. Knowledge-Based Systems, 93, 1–11.

    Article  Google Scholar 

  • Huang, X., & Zhao, T. (2016). Project selection and adjustment based on uncertain measure. Information Sciences, 352–353, 1–14.

    Google Scholar 

  • Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263–292.

    Article  Google Scholar 

  • Ke, H., & Yao, K. (2016). Block repalcement policy in uncertain environment. Reliability Engineering & System Safety, 148, 119–124.

    Article  Google Scholar 

  • Kovács, G., & Spens, K. M. (2007). Humanitarian logistics in disaster relief operations. International Journal of Physical Distribution & Logistics Management, 37, 99–114.

    Article  Google Scholar 

  • Liberatore, F., Ortuño, M. T., Tirado, G., Vitoriano, B., & Scaparra, M. P. (2014). A hierarchical compromise model for the joint optimization of recovery operations and distribution of emergency goods in humanitarian logistics. Computers & Operations Research, 42, 3–13.

    Article  Google Scholar 

  • Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.

    Google Scholar 

  • Liu, B. (2009a). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3, 3–10.

    Google Scholar 

  • Liu, B. (2009b). Theory and practice of uncertain programming (2nd ed.). Berlin: Springer.

    Book  Google Scholar 

  • Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.

    Book  Google Scholar 

  • Liu, B. (2012). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6, 3–10.

    Google Scholar 

  • Liu, B. (2014). Uncertainty distribution and independence of uncertain processes. Fuzzy Optimization and Decision Making, 13, 259–271.

    Article  Google Scholar 

  • Liu, S., Huang, W., & Ma, H. (2009). An effective genetic algorithm for the fleet size and mix vehicle routing problems. Transportation Research Part E: Logistics and Transportation Review, 45, 434–445.

    Article  Google Scholar 

  • Özdamar, L., Ekinci, E., & Küçükyazici, B. (2004). Emergency logistics planning in natural disasters. Annals of Operations Research, 129, 217–245.

    Article  Google Scholar 

  • Özdamar, L., & Demir, O. (2012). A hierarchical clustering and routing procedure for large scale disaster relief logistics planning. Transportation Research Part E: Logistics and Transportation Review, 48, 591–602.

    Article  Google Scholar 

  • Peng, Z. X., & Iwamura, K. (2010). A sufficient and necessary condition of uncertainty distribution. Journal of Interdisciplinary Mathematics, 13, 277–285.

    Article  Google Scholar 

  • Qin, Z., & Kar, S. (2013). Single-period inventory problem under uncertain environment. Applied Mathematics and Computation, 219, 9630–9638.

    Article  Google Scholar 

  • Qin, Z. (2015). Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns. European Journal of Operational Research, 245, 480–488.

    Article  Google Scholar 

  • Shi, Y., Liu, H., Gao, L., & Zhang, G. (2011). Cellular particle swarm optimization. Information Sciences, 181, 4460–4493.

    Article  Google Scholar 

  • Smith, K., & Petley, D. (2009). Environmental hazards: Assessing risk and reducing disaster. Abingdon: Taylor & Francis.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristic and biases. Science, 185, 1124–1131.

    Article  Google Scholar 

  • Vidal, T., Crainic, T. G., Gendreau, M., Lahrichi, N., & Rei, W. (2012). A hybrid genetic algorithm for multidepot and periodic vehicle routing problems. Operations Research, 60, 611–624.

    Article  Google Scholar 

  • Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013). A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows. Computers & Operations Research, 40, 475–489.

    Article  Google Scholar 

  • Waller, S. T., & Ziliaskopoulos, A. K. (2006). A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms. Transportation Research Part C, 14(6), 418–427.

    Article  Google Scholar 

  • Wang, G., Tang, W., & Zhao, R. (2013). An uncertain price discrimination model in labor market. Soft Computing, 17, 579–585.

    Article  Google Scholar 

  • Xu, X., Qi, Y., & Hua, Z. (2010). Forecasting demand of commodities after natural disasters. Expert Systems with Applications, 37, 4313–4317.

    Article  Google Scholar 

  • Yazici, M. A., & Ozbay, K. (2007). Impact of probabilistic road capacity constraints on the spatial distribution of hurricane evacuation shelter capacities. Transportation Research Record: Journal of the Transportation Research Board, 2022, 55–62.

    Article  Google Scholar 

  • Yan, H., & Zhu, Y. (2015). Bang–bang control model for uncertain switched systems. Applied Mathematical Modelling, 39, 2994–3002.

    Article  Google Scholar 

  • Yuan, Y., & Wang, D. (2009). Path selection model and algorithm for emergency logistics management. Computers & Industrial Engineering, 56, 1081–1094.

    Article  Google Scholar 

  • Zhang, Q., Huang, X., & Tang, L. (2011). Optimal multinational capital budgeting under uncertainty. Computers and Mathematics with Applications, 62, 4557–4567.

    Article  Google Scholar 

  • Zhang, Q., Huang, X., & Zhang, C. (2015). A mean-risk index model for uncertain capital budgeting. Journal of the Operational Research Society, 66, 761–770.

    Article  Google Scholar 

  • Zhang, X., Zhang, Z., Zhang, Y., Wei, D., & Deng, Y. (2013). Route selection for emergency logisctics management: A bio-inspired algorithm. Safety Science, 54, 87–91.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by National Natural Science Foundation of China Grant No. 71171018 and Specialized Research Fund for the Doctoral Program of Higher Education No. 20130006110001.

Author information

Authors and Affiliations

  1. Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, 100083, China

    Xiaoxia Huang & Liying Song

Authors
  1. Xiaoxia Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liying Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoxia Huang.

Appendix: Fundamentals of uncertainty theory

Appendix: Fundamentals of uncertainty theory

Uncertainty theory is a branch of mathematics based on the following four axioms.

Definition 1

Let \(\mathcal{L}\) be a \(\sigma \)-algebra over a nonempty set \(\Gamma \). Each element \(\Lambda \in \mathcal{L}\) is called an event. A set function \(\mathcal{M} \{\Lambda \}\) is called an uncertain measure if it satisfies the following four axioms (Liu 2007, 2009a):

  • (i) \(\mathcal{M} \{\Gamma \}=1.\)

  • (ii) \(\mathcal{M} \{\Lambda \}+\mathcal{M} \{\Lambda ^c\}=1.\)

  • (iii) For every countable sequence of events\(\{\Lambda _i\}\), we have

    $$\begin{aligned} \mathcal{M}\displaystyle \left\{ \bigcup \limits _{i=1}^{\infty }\Lambda _i\right\} \le \sum \limits _{i=1}^{\infty } \mathcal{M}\{\Lambda _i\}. \end{aligned}$$

The triplet \((\Gamma , \mathcal{L}, \mathcal{M})\) is called an uncertainty space.

  • (iv) Let \((\Gamma _k, \mathcal{L}_k, \mathcal{M}_k)\) be uncertainty spaces for \(k=1, 2, \ldots \) The product uncertain measure is

    $$\begin{aligned} \displaystyle \mathcal{M}\left\{ \prod _{k=1}^{\infty }\Lambda _k\right\} =\bigwedge _{k=1}^{\infty } \mathcal{M}_k\{\Lambda _k\} \end{aligned}$$

where \(\Lambda _k\) are arbitrarily chosen events from \(\mathcal{L}_k\) for \(k=1,2,\ldots ,\) respectively.

Definition 2

(Liu 2007) An uncertain variable is a measurable function \(\xi \) from an uncertainty space \((\Gamma , \mathcal{L}, \mathcal{M})\) to the set of real numbers.

In application, an uncertain variable is characterized by an uncertainty distribution function.

Definition 3

(Liu 2007) The uncertainty distribution \(\Phi : \mathfrak {R}\rightarrow [0,1]\) of an uncertain variable \(\xi \) is defined by

$$\begin{aligned} \Phi (t)=\mathcal{M}\{\xi \le t\}. \end{aligned}$$

For example, a normal uncertain variable has the following uncertainty distribution

$$\begin{aligned} \Phi (t)=\displaystyle \left( 1+\exp \left( \frac{\pi (\mu -t)}{\sqrt{3}\sigma } \right) \right) ^{-1},\quad t\in \mathfrak {R}, \end{aligned}$$

where \(\mu \) and \(\sigma \) are real numbers and \(\sigma >0.\) In the paper, we denote it by \(\xi \sim N(\mu , \sigma )\).

Definition 4

(Liu 2010) An uncertainty distribution \(\Phi (t)\) is said to be regular if it is a continuous and strictly increasing function with respect to t at which \(0<\Phi (t)<1,\) and

$$\begin{aligned} \lim \limits _{t\rightarrow -\infty }\Phi (t)=0, \, \lim \limits _{t\rightarrow +\infty }\Phi (t)=1. \end{aligned}$$

It is seen that the distribution of a normal uncertain variable is regular. In application, we often suppose that all uncertainty distributions are regular. Otherwise, we can give some perturbations to get a regular one.

Definition 5

(Liu 2010) Let \(\xi \) be an uncertain variable with regular uncertainty distribution \(\Phi (t).\) Then the inverse function \(\Phi ^{-1}(\alpha )\) is called the inverse uncertainty distribution of \(\xi .\)

The operational law of the uncertain variables is given by Liu (2010) as follows:

Theorem 2

(Liu 2010) Let \(\xi _1, \xi _2, \ldots , \xi _n\) be independent uncertain variables with regular uncertainty distributions \(\Phi _1, \Phi _2,\ldots , \Phi _n,\) respectively. If \(f(t_1,t_2,\ldots ,t_n)\) is strictly increasing with respect to \(t_1,t_2,\ldots ,t_n,\) then

$$\begin{aligned} \xi =f(\xi _1,\xi _2,\ldots ,\xi _n) \end{aligned}$$

is an uncertain variable that has the following inverse uncertainty distribution function

$$\begin{aligned} \Psi ^{-1}(\alpha )=f(\Phi ^{-1}_1(\alpha ), \Phi ^{-1}_2(\alpha ), \ldots , \Phi ^{-1}_n(\alpha )), \quad 0< \alpha <1. \end{aligned}$$
(19)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, X., Song, L. An emergency logistics distribution routing model for unexpected events. Ann Oper Res 269, 223–239 (2018). https://doi.org/10.1007/s10479-016-2300-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-016-2300-7

Keywords

Search

Navigation