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Dynamic spare parts transportation model for Arctic production facility

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International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

Timely delivery of the required spare parts plays an important role in meeting the availability target and reducing the downtime of production facilities. Spare parts logistics is affected in complex ways while operating in the Arctic, since the area is sparsely populated and has insufficient infrastructure. It is also greatly affected by the distinctive operational environment of the region, such as cold temperature, varying forms of sea ice, blizzards, heavy fog, etc. Therefore, in order to have an effective logistic plan, the effect of all influencing factors, called covariates, on the transportation of the spare parts need to be identified, modelled and quantified by the use of an appropriate dynamic model. The traditional models, however, lack the comprehensive integration of the effect of covariates on the spare parts transportation. The purpose of this paper is to introduce the concept of a dynamic model for spare parts transportation in Arctic conditions by considering the time-independent and time-dependent covariates. The model continuously updates the prior probabilities according to the most recent time-dependent covariates to provide posterior probabilities. The application of the model is illustrated using a case study.

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Acknowledgments

The work has been funded by The Research Council of Norway and ENI Norge AS through the EWMA (Environmental Waste Management) project, facilitated at UiT The Arctic University of Norway. The financial support is gratefully acknowledged. The authors would like to thank all anonymous logistic companies, operating in northern Norway, for providing the data related to transportation time.

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Authors and Affiliations

  1. Department of Engineering and Safety, UiT The Arctic University of Norway, 9037, Tromsø, Norway

    Yonas Zewdu Ayele, A. Barabadi & J. Barabady

Authors
  1. Yonas Zewdu Ayele
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  2. A. Barabadi
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  3. J. Barabady
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Corresponding author

Correspondence to Yonas Zewdu Ayele.

Appendix

Appendix

Estimation of the probabilities \(P_{it}\) —for summer season, for transporting the spare parts from Dusavika to Veidnes via Honningsvåg.

Example The result from Weibull ++7 analysis shows that for air-cargo and ship-cargo the best-fit distribution is 3P—Weibull and for truck-cargo, it is Log-logistic. Then, to estimate the probability of using air-cargo (P AC ) from ship-cargo and truck-cargo, Eq. (6) can be re-written as follows:

$$P_{AC} = \frac{{\left( {1 - \exp^{ - } \left( {\frac{t - \gamma }{\eta }} \right)^{\beta } } \right)^{{^{{}} }} }}{{1 + \left[ {\left( {\frac{{\exp \left( {\frac{(\ln (t) - \mu }{\sigma }} \right)}}{{1 + \exp \left( {\frac{(\ln (t) - \mu }{\sigma }} \right)}}} \right) + \left( {1 - \exp^{ - } \left( {\frac{t - \gamma }{\eta }} \right)^{\beta } } \right)} \right]}}$$
(22)

By substituting the parameters from Table 5 into the Eq. (22), and since, according to the assumption, t equals the scheduled delivery time 1 [T SDT1 ], which is 95 h, then P AC can be calculated as:

$$P_{AC} = \frac{{\left( {1 - \exp^{ - } \left( {\frac{95 - 10.71}{2.07}} \right)^{1.42} } \right)^{{^{{}} }} }}{{1 + \left[ {\left( {\frac{{\exp \left( {\frac{(\ln (95) - 3.79}{0.04}} \right)}}{{1 + \exp \left( {\frac{(\ln (95) - 3.79}{0.04}} \right)}}} \right) + \left( {1 - \exp^{ - } \left( {\frac{95 - 94.15}{2.57}} \right)^{2.00} } \right)} \right]}} = 0.48$$
(23)

Subsequently, the probability of choosing ship-cargo (P SC ) can be calculated as:

$$P_{SC} = \frac{{\left( {1 - \exp^{ - } \left( {\frac{95 - 94.15}{2.57}} \right)^{2.00} } \right)}}{{1 + \left[ {\left( {\frac{{\exp \left( {\frac{(\ln (95) - 3.79}{0.04}} \right)}}{{1 + \exp \left( {\frac{(\ln (95) - 3.79}{0.04}} \right)}}} \right) + \left( {1 - \exp^{ - } \left( {\frac{95 - 10.71}{2.07}} \right)^{1.42} } \right)} \right]}} = 0.04$$
(24)

In the same approach, the probability of choosing truck-cargo (P TC ) can be calculated as:

$$P_{TC} = \frac{{\left( {\frac{{\exp \left( {\frac{(\ln (95) - 3.79}{0.04}} \right)}}{{1 + \exp \left( {\frac{(\ln (95) - 3.79}{0.04}} \right)}}} \right)}}{{1 + \left[ {\left( {1 - \exp^{ - } \left( {\frac{95 - 94.15}{2.57}} \right)^{2.00} } \right) + \left( {1 - \exp^{ - } \left( {\frac{95 - 10.71}{2.07}} \right)^{1.42} } \right)} \right]}} = 0.48$$
(25)

Afterwards, the basic principle of probabilities, which states that the summation of all of the probability has to be one, \(\sum\nolimits_{i = 0}^{N} {P_{it} = 1}\), needs to be verified, and Eq. (26) verifies that the calculated probabilities are summed to be 1.

$$\sum\limits_{n = 1}^{3} {\left( {P_{AC} + P_{SC} + P_{TC} } \right)} = \sum {(0.48 + 0.04 + 0.48)} = 1$$
(26)

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Ayele, Y.Z., Barabadi, A. & Barabady, J. Dynamic spare parts transportation model for Arctic production facility. Int J Syst Assur Eng Manag 7, 84–98 (2016). https://doi.org/10.1007/s13198-015-0379-x

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