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On Strategic Planning of a Dynamic Allocation of Vehicles with Stochastic Breakdown to Destinations with Multiple Alternative Routes for Returns Maximization
Research Article | Published: 29 January 2026
ICCK Journal of Applied Mathematics Volume 2, Issue 1, 2026: 64-86
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ICCK Journal of Applied Mathematics, Volume 2, Issue 1, 2026: 64-86

Open Access | Research Article | 29 January 2026
On Strategic Planning of a Dynamic Allocation of Vehicles with Stochastic Breakdown to Destinations with Multiple Alternative Routes for Returns Maximization
by
Charles I. Nkeki Charles I. Nkeki 1 *
Chiedozie B. Ibe Chiedozie B. Ibe 1
1 Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria
* Corresponding Author: Charles I. Nkeki, [email protected]
DOI: 10.62762/JAM.2025.632255
ARK: ark:/57805/jam.2025.632255
Received: 12 December 2025, Accepted: 09 January 2026, Published: 29 January 2026  
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Abstract
This paper proposes a dynamic programming (DP) approach for a stochastic multi-period allocation problem, whereby fleet of vehicles are assigned from stations to destinations with multiple alternative routes in order to maximize returns, while the vehicles are subject to random failure. In the process of managing the business, the company is assumed to incur proportional management costs and pay tax to government. The expected returns is modelled as a function of random failure of vehicles due to bad roads and depreciation. The depreciation rate is assumed to follow a straight-line approach. The breakdown rate is modelled as function of the rate of bad roads on the fleets, depreciation rate and expiration time of the fleets. The sum of the probability rate of bad roads on the fleets and depreciation rate, is referred to in this paper, as "decay rate" of the fleets. This paper aim at: (i) modelling the breakdown rates of the vehicles over time; (ii) modelling a stochastic multi-period allocation of the vehicles from stations to destinations with multiple alternative routes and random breakdown of the vehicles; (iii) maximizing the expected net returns of the operations over a period of time; and (iv) determining the optimal management costs and tax payable to government over finite time horizon. Stochastic models and optimal policies of the fleet of vehicles allocation are considered, and problem is solved using DP approach. As a result, the optimal expected net returns from all the destinations and the sum total for all the stations, both for the absence and presence of stochastic break down are obtained. Also obtained are the optimal management costs and tax accrued to government from the investment process over time. Some sensitivity analysis are also carried out in this paper. It was found in this paper that as the breakdown rate of vehicles increases, the expected net returns decreases, and vice versa. Finally, the proposed models were validated using data from some of the transport companies in Nigeria.
Keywords
dynamic allocation of vehicles
stochastic breakdown
straight line depreciation
decay rate
destination
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
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Cite This Article
APA Style
Nkeki, C. I., & Ibe, C. B. (2026). On Strategic Planning of a Dynamic Allocation of Vehicles with Stochastic Breakdown to Destinations with Multiple Alternative Routes for Returns Maximization. ICCK Journal of Applied Mathematics, 2(1), 64–86. https://doi.org/10.62762/JAM.2025.632255
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TY  - JOUR
AU  - Nkeki, Charles I.
AU  - Ibe, Chiedozie B.
PY  - 2026
DA  - 2026/01/29
TI  - On Strategic Planning of a Dynamic Allocation of Vehicles with Stochastic Breakdown to Destinations with Multiple Alternative Routes for Returns Maximization
JO  - ICCK Journal of Applied Mathematics
T2  - ICCK Journal of Applied Mathematics
JF  - ICCK Journal of Applied Mathematics
VL  - 2
IS  - 1
SP  - 64
EP  - 86
DO  - 10.62762/JAM.2025.632255
UR  - https://www.icck.org/article/abs/JAM.2025.632255
KW  - dynamic allocation of vehicles
KW  - stochastic breakdown
KW  - straight line depreciation
KW  - decay rate
KW  - destination
AB  - This paper proposes a dynamic programming (DP) approach for a stochastic multi-period allocation problem, whereby fleet of vehicles are assigned from stations to destinations with multiple alternative routes in order to maximize returns, while the vehicles are subject to random failure. In the process of managing the business, the company is assumed to incur proportional management costs and pay tax to government. The expected returns is modelled as a function of random failure of vehicles due to bad roads and depreciation. The depreciation rate is assumed to follow a straight-line approach. The breakdown rate is modelled as function of the rate of bad roads on the fleets, depreciation rate and expiration time of the fleets. The sum of the probability rate of bad roads on the fleets and depreciation rate, is referred to in this paper, as "decay rate" of the fleets. This paper aim at: (i) modelling the breakdown rates of the vehicles over time; (ii) modelling a stochastic multi-period allocation of the vehicles from stations to destinations with multiple alternative routes and random breakdown of the vehicles; (iii) maximizing the expected net returns of the operations over a period of time; and (iv) determining the optimal management costs and tax payable to government over finite time horizon. Stochastic models and optimal policies of the fleet of vehicles allocation are considered, and problem is solved using DP approach. As a result, the optimal expected net returns from all the destinations and the sum total for all the stations, both for the absence and presence of stochastic break down are obtained. Also obtained are the optimal management costs and tax accrued to government from the investment process over time. Some sensitivity analysis are also carried out in this paper. It was found in this paper that as the breakdown rate of vehicles increases, the expected net returns decreases, and vice versa. Finally, the proposed models were validated using data from some of the transport companies in Nigeria.
SN  - 3068-5656
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -
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@article{Nkeki2026On,
  author = {Charles I. Nkeki and Chiedozie B. Ibe},
  title = {On Strategic Planning of a Dynamic Allocation of Vehicles with Stochastic Breakdown to Destinations with Multiple Alternative Routes for Returns Maximization},
  journal = {ICCK Journal of Applied Mathematics},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {64-86},
  doi = {10.62762/JAM.2025.632255},
  url = {https://www.icck.org/article/abs/JAM.2025.632255},
  abstract = {This paper proposes a dynamic programming (DP) approach for a stochastic multi-period allocation problem, whereby fleet of vehicles are assigned from stations to destinations with multiple alternative routes in order to maximize returns, while the vehicles are subject to random failure. In the process of managing the business, the company is assumed to incur proportional management costs and pay tax to government. The expected returns is modelled as a function of random failure of vehicles due to bad roads and depreciation. The depreciation rate is assumed to follow a straight-line approach. The breakdown rate is modelled as function of the rate of bad roads on the fleets, depreciation rate and expiration time of the fleets. The sum of the probability rate of bad roads on the fleets and depreciation rate, is referred to in this paper, as "decay rate" of the fleets. This paper aim at: (i) modelling the breakdown rates of the vehicles over time; (ii) modelling a stochastic multi-period allocation of the vehicles from stations to destinations with multiple alternative routes and random breakdown of the vehicles; (iii) maximizing the expected net returns of the operations over a period of time; and (iv) determining the optimal management costs and tax payable to government over finite time horizon. Stochastic models and optimal policies of the fleet of vehicles allocation are considered, and problem is solved using DP approach. As a result, the optimal expected net returns from all the destinations and the sum total for all the stations, both for the absence and presence of stochastic break down are obtained. Also obtained are the optimal management costs and tax accrued to government from the investment process over time. Some sensitivity analysis are also carried out in this paper. It was found in this paper that as the breakdown rate of vehicles increases, the expected net returns decreases, and vice versa. Finally, the proposed models were validated using data from some of the transport companies in Nigeria.},
  keywords = {dynamic allocation of vehicles, stochastic breakdown, straight line depreciation, decay rate, destination},
  issn = {3068-5656},
  publisher = {Institute of Central Computation and Knowledge}
}
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