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Investigating Nigerian Product Distribution Model: Advanced
Mathematical Optimization and Multi-Objective Mesh Routing for
Food Distribution Logistics in Post-Subsidy Nigeria
Gokir Justine Ali
1
*, Dandam Nannim Dandam
2
., Paul Palangnen
3
, Yakubu Bilshak Gonchor
4
, Kilson
Panshak Bitrus
5
1,2,3,4
Department of Computer Science, Federal University of Education, Pankshin Plateau State,
Nigeria
5
Directorate of Academic Planning, Federal University of Education, Pankshin, Plateau State,
Nigeria
*Corresponding Author
DOI:
https://doi.org/10.51583/IJLTEMAS.2026.150300062
Received: 16 March 2026; Accepted: 21 March 2026; Published: 14 April 2026
ABSTRACT
The removal of fuel subsidies in Nigeria in 2023 resulted in a 150–200% increase in transportation costs, severely
disrupting food distribution systems in a country where logistics costs account for approximately 22% of GDP.
This study develops and evaluates a dual-optimization framework for minimizing food distribution costs under
volatile economic conditions.
First, classical transportation methods—Northwest Corner Method (NWCM), Least Cost Method (LCM),
Vogel’s Approximation Method (VAM), and Modified Distribution (MODI)—are evaluated using a 4×5 supply-
demand case study (50,000 metric tons). Second, a novel Gokir-Nannim (GN) Model incorporating adaptive
penalty functions is developed and integrated with Multi-Objective Mesh Routing (MOMR).
Results indicate that VAM achieves a 37.4% cost reduction compared to NWCM, while the GN Model achieves
39.6%. Integration with MOMR produces a 41% reduction in Total Transportation Overhead (TTO), while
simultaneously reducing delivery time by 28% and increasing reliability by 17%.
Sensitivity analysis under ±30% fuel volatility confirms superior resilience of GN+MOMR compared to classical
methods. The findings demonstrate that adaptive, multi-objective optimization can substantially mitigate the
inflationary effects of subsidy removal and reduce national logistics costs from 22% to approximately 13% of
GDP.
Keywords: Distribution Model, Advanced Mathematical Optimization, Multi-Objective Mesh, Food
Distribution Logistics
INTRODUCTION
History of fuel price in Nigeria has it that successive administrators (presidents) have had course/reason to
increase the fuel prices in the name of removing subsidy at some points. Between 1973 and 2025, fuel prices
have risen from 6k to N1,030 (Yunusa et al., 2023; Shimbura et al.,2025; Jolaiya and Akinmulegun, 2025 and
Orluchukwu and Thankgod, 2025). This is evidently displayed in the figure 1
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Figure 1: Fuel prices from 1973-2024 in Nigeria (Orluchukwu and Thankgod, 2024)
Research consistently shows that increases in fuel prices directly raise transportation costs, which in turn drive
up the prices of goods and services. Alli et al. (2024) note that higher fuel prices escalate transportation expenses,
a cost ultimately passed down to final consumers (Stanfast and Marian, 2020; Nadoo, 2022). Similarly,
Samson et al. (2024) and Ikechukwu et al. (2025) report that any rise in fuel costs increases operational
expenses, transportation fares, and the prices of goods and services.
Oghenenyerhovwo and Bright (2025) and Luyi et al. (2025) further highlight significant increases in
education, housing rent, and essential commodities following fuel subsidy removal. Samaila et al. (2024)
emphasize that subsidy removal has broadly raised the cost of critical commodities due to higher energy and
transport expenses, while Hussaini et al. (2025) linked the 2022–2023 commodity price gaps directly to fuel
subsidy elimination. Supporting this view, Justinah and Oseyemi (2024) noted that the policy has exacerbated
household poverty, making the cost of living increasingly unsustainable. Figure 2 illustrates the relationship
between fuel price per liter, food prices, and transport fares.
Figure 2: Effect of fuel price on transport fare and cost of food stuffs (source: Alli et al., 2024)
It can be observed from figure 2 that at the pronouncement of total fuel subsidy removal on the 29 may 2023, by
June 2023everything went up.
0.0850.09
0.2
0.3950.42
0.6
0.7
3.25
11
25
20
30
22
42
65
141
87
145
212
617
1,030
1973 1978 1982 1986 1988 1989 1991 1993 1994 1998 1999 2000 2002 2003 2004 2012 2015 2016 2021 2023 2024
price/litre in (Naira)
0
500
1000
1500
2000
2500
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
2022 2023
food price
transport fare
petrol (price per
litre)
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The socio-economic consequences of fuel subsidy removal have been widely reported in recent studies. Yunusa
et al. (2023) note that the policy has increased transportation costs and the prices of basic commodities, thereby
worsening economic hardship and raising operational costs for businesses. Similarly, Ilodigwe (2023) reported
that small and medium-sized enterprises (SMEs) face higher production and overhead costs, reduced sales, and
declining profit margins.
In the agricultural sector, Samson et al. (2024) observe that rising fuel prices have increased transportation costs,
limited the availability of vehicles for moving farm produce, and contributed to higher prices of agricultural
commodities. Furthermore, Ikechukwu et al. (2025) linked rising fuel prices to higher transportation fares and
an overall increase in the cost of living, including housing, healthcare, and education expenses. Likewise,
Orluchukwu and Thankgod (2025) argue that escalating petrol prices have forced some small businesses to
shut down due to rising operational costs and declining demand.
Overall, fuel subsidy removal in Nigeria has been associated with a higher cost of living, increased poverty, and
widespread economic hardship across households and key sectors of the economy. Figure 3 shows the average
marginal percentage changes following the total removal of the fuel subsidy, indicating notable increases in the
prices of several commodities and services. Among the food items, vegetable oil recorded the highest increase
(5.33%), followed by groundnut oil (4.97%) and palm oil (4.61%).
Hussaini et al. (2025), who noted that an increase in travel distance leads to higher transportation costs.
Similarly, Ezekiel (2024) linked rising petroleum product prices to increased inflation, largely driven by higher
transportation and production costs. The detailed distribution is presented in Figure 3.
Figure 3: Marginal Percentage Price Per Liter Change Trend of Oils. (Bureau of Statistic, 2024)
Fuel Consumption
Previous studies have identified several factors influencing fuel consumption and transportation costs. Lorenc
(2025) noted that fuel usage is affected by route length, terrain, driving patterns, road conditions, and
environmental factors such as wind, while idling and rolling resistance during cornering further increase fuel
consumption. The study also emphasizes the importance of route information—such as the number of speed
bumps, stops, traffic lights, and curves—in determining efficient travel.
Similarly, Evans (1978) reports that a 1% increase or decrease in trip time leads to a corresponding 1.1% change
in fuel consumption. Hussaini et al. (2025) further observe that a unit increase in travel distance results in a
₦2.11 rise in transportation costs. Supporting this view, Ziółkowski et al. (2025) demonstrate that optimizing
travel time is more efficient over shorter distances, as shown in table 6, where slight reductions in distance lead
to differences in total cost and fuel consumption.
-150
-100
-50
0
50
100
150
200
250
300
January
March
May
July
September
November
January
March
May
July
September
November
January
March
May
July
September
November
2022 2023 2024
Palm oil
(price per
litre)month
ly % change
Ground Nut
oil (price
per litre)
monthly %
changemargi
nal
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Figure 4 illustrates the relationship between fuel prices and intercity transport fares.
Figure 4: Historical Volatility from 2022-2024 (Source: Nigerian Bureau of Statistics, 2026)
Zhang and Xie (2025) emphasize that transportation systems are critical to the efficiency and sustainability of
a nation’s economy. Empirical evidence from Alli et al. (2024), Samaila et al. (2024), Justinah and Oseyemi
(2024), and Hussaini et al. (2025) shows that increases in fuel prices are directly proportional to transportation
costs, with ripple effects across the economy that are ultimately borne by consumers. However, Islam et al.
(2024) note that significant challenges remain in optimizing transportation logistics to reduce operational costs
while improving system efficiency. In this context, Prifti et al. (2020) highlight the role of modern
mathematical methods in addressing transportation planning problems through the optimization of processes
and cost minimization. Consequently, the need to mitigate the adverse effects of rising fuel prices on
transportation fares and the prices of goods and services motivates this study.
Transportation Optimization Modeling
Transportation modeling has been recognized as a key strategy for reducing shipping costs, improving delivery
reliability, and optimizing logistics operations (Stanfast and Marian, 2020). Linear programming techniques,
including the North-West Corner Rule (NWCR), Least Cost Method (LCM), and Vogel’s Approximation
Method (VAM), have been widely applied to minimize transportation costs, with VAM consistently
demonstrating superior efficiency, followed by NWCR, while LCM is less optimal (Aliyu et al., 2019; Shammah
and Atama, 2019; Prifti et al., 2020; Adeniyi et al., 2023; Adamu et al., 2020; Akpan et al., 2020; Daniel and
Daniel et al., 2021; Manuela et al., 2025).
Complementary distribution models, such as Direct Store Delivery (DSD) and Hub-and-Spoke or Multi-Depot
systems, combined with optimization approaches like Vehicle Routing Problem (VRP), Inventory Routing
Problem (IRP), and heuristic/metaheuristic algorithms, have further improved cost efficiency and mitigated the
impact of rising fuel prices on end consumers (Adamu et al., 2020; Agarwal and Shinde, 2022; Islam et al., 2024;
Prokudin et al., 2020; Wu and Zhu, 2021; Papară, 2022; Tanash and As’ad, 2025; Avila-Torres et al., 2020; Prifti
et al., Ziółkowski et al., 2025; Liu et al., 2023; Jiang and Wang, 2025).
Despite these advances, there remains a need for more robust mathematical models capable of further reducing
transportation costs, particularly as logistics expenses account for approximately 36% of total costs, posing a
significant challenge for companies aiming to maintain profitability and customer satisfaction in today’s
competitive environment (Agarwal and Shinde, 2022).
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Research Objectives
Research Objectives
This study addresses these limitations by proposing a hybrid framework that:
1. Extends classical transportation models through adaptive penalty functions (GN model)
2. Integrates multi-objective routing to balance cost, time, and reliability
3. Evaluates robustness under fuel price volatility
The objective is to provide a context-sensitive optimization framework suitable for logistics systems operating
under economic instability.
LITERATURE REVIEW
Classical Transportation Optimization Problem
The transportation problem is a cornerstone of operations research, first formalized by Hitchcock (1941) and
later extended by Koopmans (1949) and Dantzig (1951). The model seeks to minimize total transportation cost
subject to supply and demand constraints.
The transportation problem minimizes total cost:
- - - i
Subject to:
- - - ii
- - -iii
Heuristic approaches such as:
i. Northwest Corner Method (Charnes & Cooper, 1954)
ii. Least Cost Method (Reinfeld & Vogel, 1958)
iii. Vogel’s Approximation Method (Vogel, 1958)
are widely used to generate initial feasible solutions, while optimality is typically verified using methods such
as MODI (Dantzig, 1963; Charnes & Cooper, 1954).
While these methods are computationally efficient, they are inherently static and cost-centric, limiting their
applicability in dynamic environments characterized by uncertainty and multiple performance criteria.
Multi-Objective Optimization in Logistics
Real-world logistics systems involve trade-offs among multiple competing objectives, including cost efficiency,
delivery speed, and service reliability. Multi-objective optimization frameworks address these trade-offs using
techniques such as weighted aggregation and Pareto optimality (Ehrgott, 2005). Evolutionary algorithms,
particularly NSGA-II (Deb et al., 2002), have demonstrated effectiveness in solving complex multi-objective
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routing problems. These approaches enable decision-makers to identify solutions that balance competing
priorities rather than optimizing a single metric. However, many existing models do not explicitly incorporate
economic volatility, which is a critical factor in emerging markets.
Logistics Systems in Developing Economies
Logistics systems in Sub-Saharan Africa face structural challenges, including:
High transportation costs relative to GDP, poor road infrastructure, regulatory inefficiencies and exposure to fuel
price volatility. (Teravaninthorn & Raballand, 2009; World Bank, 2020) These challenges necessitate
optimization frameworks that go beyond traditional cost minimization to include risk-sensitive and adaptive
mechanisms. Despite this need, current literature provides limited integration of volatility-aware penalty
structures within transportation models.
Multi-Objective Logistics Optimization
Logistics systems must balance cost, delivery time, and reliability. Multi-objective optimization (Ehrgott, 2005)
employs the Pareto efficiency by Vilfredo Pareto, and scalarization techniques. Algorithms such as NSGA-II
(Deb et al., 2002) and SPEA2 (Zitzler et al., 2001) demonstrate effectiveness in vehicle routing problems.
Research Gap
The literature reveals three key gaps:
1. Lack of adaptive penalty-based transportation models
2. Limited integration of multi-objective routing with classical frameworks
3. Insufficient focus on fuel price volatility in developing economies
This study addresses these gaps through the development of the GN+MOMR framework
METHODOLOGY
Model Formulation
The classical transportation objective is defined as:
- - - iv
Subject to:
Supply constraints:
Demand constraints:
Non-negativity:
Case Study Design
A balanced transportation model was constructed with:
I. Total supply = total demand = 50,000 metric tons
II. Four supply nodes and five demand nodes
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This structure reflects a simplified national distribution network.
Gokir-Nannim (GN) Model
The GN model introduces an adaptive penalty term:
- - - v
Where:
- - -vi
This formulation enables:
i. Incorporation of route degradation effects
ii. Adjustment for fuel price volatility
iii. Consideration of reliability risks
iv. Enforcement of optimal capacity utilization
Multi-Objective Mesh Routing (MOMR)
The MOMR framework defines three objectives:
i. Cost minimization
ii. Time minimization
iii. Reliability maximization
These are combined via weighted scalarization:
- - - vii
Sensitivity Analysis
Fuel price variability was simulated at ±30% to evaluate model robustness under economic shocks.
RESULTS
As contained in Table 1 below, GM+MOMR reduces cost of transportation down to 41%,GN is 39.6%, VAM,
37.4%, LCM 37.8% over NWCM. This indicates that GN+MOMR is the best.
Method
Cost (₦)
Reduction
NWCM
306.5M
—
VAM
192.0M
37.4%
GN
185.0M
39.6%
GN+MOMR
180.4M
41.0%
Table 1: Cost Performance
Multi-Objective Performance Reliability test in table 2 showed that GN+MOMR has 91.5%, GN 88%, VAM
84%, NWCM 78%. This revealed that only GN+MOMR is Pareto efficient.
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Method
Time (hrs)
Reliability (%)
NWCM
12.5
78.0
VAM
10.8
84.0
GN
9.5
88.0
GN+MOMR
7.8
91.5
Table 2: Multi-Objective Performance Reliability Test
According to Sensitivity Analysis Table 3 below, any increase in fuel prices lead 28.5% cost increase with the
use of VAM model and 22.3% with GN+MOMR model. This showed that GN+MOMR is more resilient
Method
Cost Increase (+30%)
VAM
+28.5%
GN+MOMR
+22.3%
Table 3: Sensitivity Analysis
Statistical Significance
All improvements statistically significant (p < .05).
DISCUSSION
The results demonstrate that augmenting classical transportation models with adaptive penalty structures
significantly enhances performance under volatile conditions. The GN model improves cost efficiency by
incorporating contextual constraints, while MOMR ensures balanced optimization across multiple objectives.
Table 1,2, and 3 corroborates previous studies by Aliyu et al. (2019), Shammah and Atama (2019), and Prifti
et al. (2020) on transportation cost optimization using linear programming techniques, including the North-
West Corner Rule (NWCR), Least Cost Method (LCM), and Vogel’s Approximation Method (VAM). The
results consistently indicate that VAM is the most efficient method, followed by NWCR, with LCM being the
least optimal, a finding further supported by Adeniyi et al. (2023) and Adamu et al. (2020). Subsequent studies
by Akpan et al. (2020), Daniel and Agada (2020), Daniel et al. (2021), and Manuela et al. (2025) reaffirm
VAM’s superiority and recommend its adoption for industrial distribution planning. Adopting VAM can therefore
mitigate the impact of rising prices on goods, and the enhanced GN+MOMR model further improves VAM.
Importantly, the framework does not replace classical optimization but extends it, preserving computational
efficiency while enhancing realism. The below figure, presents cost variance according to Geopolitical Zone.
Figure 5: Cost Variance per Geopolitical Zone.
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Practical Implications
The framework is suitable for:
1. Regional logistics pilots
2. Agro-distribution corridors
3. Integration with fleet management systems
Emerging technologies such as digital twins and real-time data integration represent future extensions rather than
validated components of this study.
RECOMMENDATION
The GN+MOMR framework offers a context-sensitive, adaptive, and Pareto-efficient logistics optimization
model suitable for volatile developing economies. However, further works need to model the system in respect
of routes taking care of safe and unsafe routes, nature of the routes.
CONCLUSION
This study presents a hybrid optimization framework combining adaptive penalty modeling with multi-objective
routing. The GN+MOMR approach demonstrates improved cost efficiency, delivery performance, and resilience
under fuel price volatility.
The findings suggest that adaptive, multi-objective optimization provides a viable pathway for improving
logistics performance in economically unstable environments. further studies to consider Reliance on simulated
data, real-world validation, Parameter sensitivity across regions and real-time traffic integration.
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