Shapley value cost allocation model for multimodal freight transport carriers

TT.
2024;
: 53-63
https://doi.org/10.23939/tt2024.01.053
Received: March 26, 2024
Accepted: April 24, 2024
1
Federal University of Technology Owerri
2
Federal University of Technology Owerri
3
Federal University of Technology Owerri
4
Federal College of Fisheries and Marine Technology
5
Federal University of Technology Owerri
6
Ibrahim Badamasi Babangida University

The downstream petroleum products distribution is beset with significant challenges due to ageing pipeline infrastructure, pipeline vandalism and other logistical constraints. These challenges have given rise to soaring pump prices of premium motor spirit (PMS), product shortages and unavailability across some locations in Nigeria. Thus, deploying alternative transport modes for PMS distribution is explored to improve product distribution efficiency. The decision to combine inland waterway transport (instead of pipeline network) and road transport modes would activate the intrinsic advantages inherent in the multimodal transport system. However, the efficiency outcome of using multi-modes may be eroded if the multimodal transport operators compete (instead of collaborating) in service provisions. This research investigated cost efficiency in cooperative collaboration among multimodal transport carriers. We proposed collaboration among six multimodal transport operators. The aim of encouraging such a large-scale coalition (S) is the expectation that costs emanating from their joint operation would be reduced. We applied the Shapley value cost allocation method to distribute the costs of operation and profit to the collaborators. After the analysis, we observed that the unit cost for coalition S1 was reduced by N17.16 (5.10 %) million naira. Similarly, we observed respective reductions in unit costs for coalitions S2, …, S10. We observed a reduction in cost by N107.84 million naira, which represents a 6.15 % reduction in total unit cost for the multimodal transportation carriers. Thus, the observed cost efficiency represents savings due to distribution chain efficiency if the multimodal transport carriers collaborate to improve product availability. Working as a coalition would offset PMS pump price variation attributable to distribution chain inefficiency.

1. Cruijssen, F., Cools, M., & Dullaert, W. (2007). Horizontal cooperation in logistics: opportunities and impediments. Transportation Research Part E: Logistics and Transportation Review, 43(2), 129-142. doi: 10.1016/j.tre.2005.09.007 (in English).
https://doi.org/10.1016/j.tre.2005.09.007
2. Wang, Y. (2023). A collaborative approach based on Shapley value for carriers in the supply chain distribution. Heliyon, 9(7). e17967. doi: 10.1016/j.heliyon.2023.e17967 (in English).
https://doi.org/10.1016/j.heliyon.2023.e17967
3. Agarwal, R., & Ergun, Ö. (2010). Network design and allocation mechanisms for carrier alliances in liner shipping. Operations research, 58(6), 1726-1742. doi: 10.1287/opre.1100.0848 (in English).
https://doi.org/10.1287/opre.1100.0848
4. Ivanov, D., Pavlov, A., & Sokolov, B. (2014). Optimal distribution (re) planning in a centralized multi-stage supply network under conditions of the ripple effect and structure dynamics. European Journal of Operational Research, 237(2), 758-770. doi: 10.1016/j.ejor.2014.02.023 (in English).
https://doi.org/10.1016/j.ejor.2014.02.023
5. Kayikci, Y. (2020). Analysis of Cost Allocation Methods in International Sea-Rail Multimodal Freight Transportation. Yaşar Üniversitesi E-Dergisi, 15(57), 129-142. doi: 10.19168/jyasar.568692 (in English).
https://doi.org/10.19168/jyasar.568692
6. Audy, J. F., D'Amours, S., & Rousseau, L. M. (2010). Erratum: Cost allocation in the establishment of a collaborative transportation agreement-an application in the furniture industry. Journal of the operational research society, 61(10), 1559-1559. doi: 10.1057/jors.2010.139 (in English).
https://doi.org/10.1057/jors.2010.139
7. Zaremba, L., Zaremba, C. S., & Suchenek, M. (2017). Modification of shapley value and its implementation in decision making. Foundations of Management, 9(1), 257-272. doi: 10.1515/fman-2017-0020 (in English).
https://doi.org/10.1515/fman-2017-0020
8. Thomas, L. (1986). Games, Theory & Applications. Chichester: Ellis Horwood (in English).
9. Aziz, H., Cahan, C., Gretton, C., Kilby, P., Mattei, N., & Walsh, T. (2014). A Study of Proxies for Shapley Allocations of Transport Costs. Computer Science and Game Theory, 51, 1-35. doi: 10.48550/arXiv.1408.4901 (in English).
10. Li, J., Cai, X., & Zeng, Y. (2016). Cost allocation for less-than-truckload collaboration among perishable product retailers. OR spectrum, 38(1), 81-117. doi: 10.1007/s00291-015-0424-9 (in English).
https://doi.org/10.1007/s00291-015-0424-9
11. Aloui, A., Hamani, N., & Delahoche, L. (2021). An integrated optimization approach using a collaborative strategy for sustainable cities freight transportation: A Case study. Sustainable Cities and Society, 75, 103331. doi: 10.1016/J.SCS.2021.103331 (in English).
https://doi.org/10.1016/j.scs.2021.103331
12. Pavlidis, K., Ioannis, P., & Folinas, D. (2016). Application of game theory in multimodal transport operator processes. Retrieved from: https://www.zbw.eu/econis-archiv/handle/11159/686 (in English).
13. Masimli, A. (2023). Shapley Value for Shortest Path Routing in Dynamic Networks. Retrieved from: https://www.preprints.org/manuscript/202304.1115/v1 (in English).
https://doi.org/10.20944/preprints202304.1115.v1
14. Amuji, H. O., Ugwuanyim, G. U., & Anyiam, K. E. (2019). Application of game theory in maintaining the academic standard in the Nigerian Universities. World Scientific News, (125), 72-82. (in English).
15. Young, H. P. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14(2), 65-72. doi: 10.1007/BF01769885 (in English).
https://doi.org/10.1007/BF01769885
16. Shapley, L. S. (1953). A value for n-person games. (in English).
https://doi.org/10.1515/9781400881970-018
17. Dai, B., & Chen, H. (2012). Profit allocation mechanisms for carrier collaboration in pickup and delivery service. Computers & Industrial Engineering, 62(2), 633-643. doi: 10.1016/j.cie.2011.11.029 (in English).
https://doi.org/10.1016/j.cie.2011.11.029
18. Malawski, M., Wieczorek, A., & Sosnowska, H. (2006). Konkurencja i kooperacja - teoria gier w ekonomii i naukach społecznych (Competition and Cooperation - Theory of Games in Economics and Social Science), Warszawa: Wydawnictwo Naukowe PWN.