IQTISHADequity journal MANAGEMENT Vol.
No.
Desember 2025, pages 63 Ae69 Optimizing Vaccine Distribution Costs Using Transportation Models: North West Corner and MODI Approaches in the Healthcare Supply Chain of PT Silkargo Indonesia Rahmad Ali Umar Dalimunthe1 .
Melia Eka Lestiani2.
Saptono Kusdanu Waskito3 Universitas Logistik dan Bisnis Internasional Bandung.
Indonesia.
rahmadaliumar@gmail.
Universitas Logistik dan Bisnis Internasional Bandung.
Indonesia.
mlestiani@yahoo.
Universitas Logistik dan Bisnis Internasional Bandung.
Indonesia.
saptonokw@yahoo.
ARTICLE INFO
ABSTRACT
Article history:
Received 02/10/2025 Revised 18/11/2025 Accepted 28/12/2025 Vaccine distribution is a crucial aspect of public health logistics, particularly when time and cost efficiency are top priorities.
This study aims to examine the optimization of a transportation model in vaccine distribution by applying the North West Corner (NWC) method as the initial solution and the Modified Distribution Method (MODI) for cost refinement.
The approach used is quantitative, with a case study conducted at PT Silkargo Indonesia through simulated data representing real operational conditions.
The results of the analysis show that the NWC method produces a total distribution cost of Rp 331,000,000, while optimization using MODI reduces the cost to Rp 317,500,000, yielding a savings of approximately 4.
These findings confirm that a combination of classical transportation algorithms can significantly enhance the performance of pharmaceutical distribution logistics.
This research provides theoretical contributions to mathematical modeling in health logistics as well as practical implications for decision-makers in the vaccine distribution JEL Classification:
Key words:
Cost optimization.
Distribution model.
MODI.
North West Corner.
Vaccine ABSTRAK Distribusi vaksin merupakan aspek krusial dalam logistik kesehatan masyarakat, terutama ketika efisiensi waktu dan biaya menjadi prioritas utama.
Penelitian ini bertujuan untuk mengkaji optimasi model transportasi dalam distribusi vaksin dengan menerapkan metode North West Corner (NWC) sebagai solusi awal dan Modified Distribution Method (MODI) untuk penyempurnaan biaya.
Pendekatan yang digunakan adalah kuantitatif dengan studi kasus di PT Silkargo Indonesia, melalui simulasi data yang merepresentasikan kondisi operasional nyata.
Hasil analisis menunjukkan bahwa metode NWC menghasilkan total biaya distribusi sebesar Rp 000, sedangkan optimasi menggunakan MODI berhasil menurunkan biaya menjadi Rp 317.
000, atau menghemat sekitar 4,1%.
Temuan ini menegaskan bahwa kombinasi algoritma transportasi klasik dapat meningkatkan kinerja logistik distribusi farmasi secara signifikan.
Penelitian ini memberikan kontribusi teoritis dalam pemodelan matematika logistik kesehatan serta implikasi praktis bagi pengambil keputusan di sektor distribusi vaksin.
INTRODUCTION
Vaccine distribution is a critical component of the healthcare supply chain system, particularly in a global context that demands rapid, secure, and cost-effective delivery of pharmaceutical products.
The increasing frequency of disease outbreaks and the urgent need for crisis response have rendered conventional logistics methods insufficient for vaccine distribution.
According to the World Health Organization (WHO, 2.
, suboptimal distribution leads to delays or spoilage of up to 30% of vaccines during transit, especially in developing countries with limited infrastructure.
In Indonesia, geographical challenges and regional disparities in logistics infrastructure further exacerbate the risk of inefficient distribution costs, particularly when reaching remote areas.
This situation positions vaccine logistics as a strategic issue that requires systematic * Corresponding author, email address: 1 rahmadaliumar@gmail.
IQTISHADequity journal MANAGEMENT Vol.
No.
Desember 2025, pages 63 Ae69
LITERATURE REVIEW
Logistics distribution is a crucial component in the supply chain system, especially in the pharmaceutical sector, which heavily relies on temperature stability and timely delivery.
Vaccines, as sensitive biological products, require accurate and datadriven distribution planning.
Vaccine distribution demands the implementation of cold chain strategies and systematic route planning to ensure the product's effectiveness reaches its final destination.
Suboptimal distribution may increase the risk of product damage and lead to wasteful operational costs (Manupati et al.
, 2.
The transportation model in the context of operations research serves as a mathematical solution to allocate shipments from multiple warehouses to various destination points at the minimum possible The North West Corner (NWC) method is a simple technique used as an initial solution to determine distribution allocations.
Although not always optimal, this method provides a solid foundation for subsequent optimization stages, particularly in distribution systems involving numerous variables such as origin and destination locations (Arofah & Gesthantiara, 2.
To obtain a more efficient distribution solution, the Modified Distribution Method (MODI) is used to refine the results of the North West Corner (NWC) method.
MODI evaluates the initial solution by calculating the opportunity cost in the unallocated cells and then performs redistribution to reduce the total shipping cost.
The MODI method is capable of optimizing distribution routes and reducing logistics operational costs, particularly in the distribution of pharmaceutical commodities, which demand high efficiency (Marzuki et al.
In this study, the two main variables examined are distribution cost and delivery time.
Distribution cost is defined as the total expenditure per kilogram incurred during the shipping process from the warehouse to the destination, while delivery time refers to the total duration of distribution measured in hours.
According to Sachan & Kushwaha .
, the more efficient the selected distribution route, the lower the cost incurred and the faster the delivery time, thereby achieving logistics Based on theory and previous studies, the combination of the North West Corner (NWC) and Modified Distribution (MODI) methods provides a distribution modeling framework that is not only practical but also proven to enhance logistics efficiency.
In the context of Renogen vaccine distribu- mathematical solutions.
The operational logistics conditions in the private sector reflect an urgent need for improvement.
One such case is PT Silkargo Indonesia, a logistics provider for the pharmaceutical industry, which has experienced a surge in distribution demand in the post-pandemic period.
However, its operations are hindered by high shipping costs and inefficient distribution channels.
This complexity is further exacerbated by the absence of optimization algorithms in its decision-making systems.
Research by Manurung et al.
found that the use of traditional transportation methods can reduce logistics costs by up to 18% in a case study of a fast-moving consumer goods (FMCG) company.
Meanwhile, a study by Febriyanti et al.
revealed that the North West Corner method provides a quick initial solution, albeit not yet optimal.
These findings suggest that transportation model-based strategies could be more broadly applied, including in vaccine logistics.
Various approaches have been developed in the literature to address transportation and logistics allocation problems.
The North West Corner (NWC) method is utilized as an initial solution to determine distribution allocations using a simple algorithm, while the Modified Distribution Method (MODI) is applied to achieve an optimal solution based on opportunity cost evaluation (Taha, 2.
The integration of these two approaches promises greater efficiency in reducing vaccine distribution A study by Andini et al.
, which implemented the MODI method for the distribution of basic necessities, reported logistics cost savings of up to 23%.
However, studies that explore the combined application of NWC and MODI methods in the context of pharmaceutical vaccine logistics remain limited in practice.
Most research on distribution optimization remains at the simulation stage or is limited to mass consumer goods.
A knowledge gap arises when mathematical models are not directly connected to real-world case-based healthcare logistics Pujawana and Bah .
highlighted the limited integration of classical algorithms with healthcare logistics practices during global crises, which has led to a heavy reliance on operational intuition rather than data-driven approaches.
Empirical studies examining the application of the NWC and MODI methods within real-world vaccine distribution structures in Indonesia are virtually absent in recent scientific publications, despite the pressing and strategic nature of its logistics IQTISHADequity journal MANAGEMENT Vol.
No.
Desember 2025, pages 63 Ae69 tion at PT Silkargo Indonesia, this approach is expected to serve as a strategic solution to reduce costs and maintain delivery reliability in accordance with pharmaceutical standards.
yaycnyc : transportation cost from source i to destination yc ycUycnyc : number of units shipped from ycn to yc The total distribution cost is calculated by :
METHODS
This study employs a descriptive quantitative approach using a case study method, aiming to optimize vaccine distribution costs at PT Silkargo Indonesia.
The methodology applied in this research aligns with previous studies that utilized the Northwest Corner Method and Modified Distribution Method for transportation cost optimization (Enayati et al.
, 2.
yco ycu ycs = Oc Oc yaycnyc .
ycUycnyc ycn=1 yc=1 Where Xij is the allocation result obtained from the North West Corner (NWC) method.
3 Metode MODI (Modified Distribution Metho.
Step of the MODI Method :
Calculate the dual variables :
Determine ycOycn for each row and ycOyc for each column Data Sources and Unit of Analysis using the condition :
The data used in this study are simulated yaycnyc = ycOycn ycOyc secondary data, designed based on the actual disFor each allocated cell.
tribution structure of the company, which consists Compute the opportunity cost for each unalloof a central warehouse located in Bandung and five cated cell using :
destination cities: Balikpapan.
Surabaya.
Medan.
OIycnyc = ycOycn ycOyc Makassar, and Jayapura.
The variables examined Check for optimality :
include supply capacity, demand, and the distribuC If all OIycnyc > 0 , the current solution is optition cost matrix between locations.
The unit of analysis in this study is the vacC If any OIycnyc < 0 ,identify the cell with the cine distribution routes from the source .
aremost negative opportunity cost and prohous.
to each destination.
As this research inceed to the next step.
volves numerical simulation, it does not involve Contruct closed loop starting and ending at the human respondents and therefore does not apply selected unallocated cell.
sampling techniques (Sinnei et al.
, 2.
C Allocate the minimum value from the cells marked with a minus (A.
Metode North West Corner (NWC) C Then update the allocations by alternately The North West Corner (NWC) method is adding and subtracting along the loop.
used to obtain an initial feasible solution.
This algo5.
Refeat the process until all opportunity costs rithm operates by allocating supply from the topOI Ou 0, indicating that the optima solution has left cell .
orth-wes.
of the cost matrix and moves been reached.
horizontally or vertically until all supply and demand requirements are fulfilled (Huo et al.
, 2.
RESULT AND DISCUSSION
Steps of the NWC method:
The vaccine demand data based on delivery Start from the first cell in the first row .
op-left regions is presented in table 1.
corner of the cost matri.
Table 1.
Vaccine Demand Data Allocate the minimum value between supply Demand and demand.
Subtract the allocated value from both supply Destination City Demand ( k.
and demand.
Balikpapan 2,000 Move right if the demand is fulfilled, or down
Surabaya
3,000
if the supply is exhausted.
Medan
2,000
Repeat the process until all supply and demand
Makassar
2,500
have been allocated.
Jayapura Total Notation and Formula :
Let :
2,500
12,000
The vaccine delivry cost data by destination regions shown in table 2.
Table 2.
Vaccine Delivery Cost Data ycIycn : Supply capacity from source ycn yayc : demand at destination yc IQTISHADequity journal MANAGEMENT Vol.
No.
Desember 2025, pages 63 Ae69 Destination City Balikpapan Surabaya Medan Makassar Jayapura Pick up Shipping Cost per kg (R.
Air Freight Dooring 5,000 22,930 5,000 12,940 5,000 22,930 5,000 25,150 5,000 60,670 6,500 6,500 5,500 5,000 5,500 Destination City Balikpapan Surabaya Medan Makassar Jayapura Total Cost / Kg (R.
34,430 24,440 33,430 35,150 71,170 Biaya (Rp/k.
24,000 22,500 30,000 28,000 45,000 18,000 Ai Shipping Cost per kg (R.
Air Freight Dooring 22,930 12,940 22,930 25,150 60,670 6,500 6,500 5,500 5,000 5,500 Total Cost / Kg (R.
34,430 24,440 33,430 35,150 71,170 Table 5.
Initial Allocation Table (North West Corner Metho.
Table 3.
Allocation Data Using the North West Corner (NWC) Method Alokasi .
5,000
5,000
5,000
5,000
5,000
The initial distribution solution based on the North West Corner (NWC) method, with a total supply from Jakarta of 11,705 kg, yields the following allocation:
1 Allocation Steps Using the North West Corner (NWC) Method Are Shown in Table 3 :
Rute CGKAeBPN CGKAeSUB CGKAeKNO CGKAeUPG CGKAeDJJ UPGAeDJJ Total Biaya Awal Pick up Demand Destination City Demand ( k.
Balikpapan 2,350 Surabaya
2,545
Medan
1,520
Makassar
2,312
Jayapura
2,978
Total
11,705
Total Biaya (R.
Determining an initial feasible solution without considering costs is done solely based on allocations from the upper-left corner of the table .
Start from the top-left cell (Jakarta Ie Balikpapa.
Compare supply and demand, then allocate the smaller value of the two.
Subtract this allocation from both supply and demand.
If the supply becomes 0, move down to the next row.
If the demand becomes 0, move to the next column.
Repeat this process until all supply and demand values are The NWC method provides an initial solution with a total cost of Rp 331,000.
However, this result is not necessarily optimal Ai because some routes may have higher costs compared to alternative inter-hub combinations .
or example, the direct CGKAeDJJ route compared to CGKAeUPGAeDJJ).
MODI Step Ae Determining the Values of yc1 and ycyc Since there is only one source (Jakart.
, we set:
yc1 = 0 For the allocated cells, the following formula is ycaycnyc = ycycn ycyc Ne ycyc = ycaycnyc Thus, the values obtained are:
Table 6.
Table of yeyeU Values Destinasi City Balikpapan Surabaya Medan Makassar Jayapura 2 Steps of MODI Method (Modified Distribution Metho.
Ae Simple Optimization Scenario:
34,430
24,440
33,430
35,150
71,170
OIycnyc Opportunity Cos.
OIycnyc = yaycnyc Oe .
cycn ycyc ) Here is a detailed explanation of the optimization process using the Modified Distribution Method (MODI) applied in the vaccine distribution study from Jakarta to five destination The vaccine distribution costs were calculated based on three main components: pickup cost, air freight cost, and final delivery .
The total distribution cost per destination city is as follows:
Since all cells have been fully allocated, then:
OIycnyc = 0 For all cells that already contain allocations, the OIycnyc = 0 because we derive yc1 and ycyc from the same For the cells that do not contain allocations .
on-basi.
, we calculate OIycnyc the u and v values that have already been determined.
In this case, all relevant cells in the Jakarta row already contain allocations .
e have exactly 5 allo- Table 4.
Transportation Cost Table (CA) Ae in IDR per kg IQTISHADequity journal MANAGEMENT Vol.
No.
Desember 2025, pages 63 Ae69 cated cells that satisfy m n Oe 1 Therefore, for each non-existent/empty cell in the standard model Ai none are present Ai meaning the calculation of OIycnyc for empty cells is not available, and all allocated OI = 0 Delta OIycnyc < 0 .
Reallocation Ai mathematical formulation and selection of yuE 000 45.
000 = Rp 317.
Savings:
ycs0 Oe ycs1 = 331.
Oe 317.
Rp 13.
Table 9.
Strategi Efisien Metode NWC Total Biaya (R.
Efisiensi (%) Ai
MODI
Strategi Efisien Pengiriman langsung ke semua rute Redistribusi sebagian muatan CGKAeDJJ ke UPGAeDJJ By applying the MODI method to redistribute part of the allocation, a distribution cost saving of:
000 Oe 317.
000 = Rp 13.
000 is achieved, which is approximately 4.
1% more efficient.
Suppose we shift yuE kg from the Jakarta Ie Jayapura route to the Jakarta Ie Makassar route yuE =478 k.
The change in total cost OI ycs resulting from this shift can be computed directly from the difference in cost per kg between the two routes:
OIZ = ( ycaycAycaycoycycycayc Oe ycayaycaycycaycyycycyca ) ycU 0 Numerical substitution:
ycaycAycaycoycycycayc Oe ycayaycaycycaycyycycyca = 35.
150 Oe 71.
= Oe36.
cIycy/ycoyc.
yuE = 478 ycoyci From the calculation results, the CGKAeDJJ cell shows a negative i .
ndicating the highest cos.
Appendix: Visualization of Distribution Cost Optimization Results Shifting part of the 500 kg allocation to the UPGAe DJJ route produces a cost saving:
000Oe18.
y500=13.
y 500 = 13.
000Oe18.
y500= 13.
Table 7.
Improvement Cycle Rute CGKAeBPN CGKAeSUB CGKAeKNO CGKAeUPG CGKAeDJJ UPGAeDJJ Total Biaya Optimal (MODI) Alokasi Baru .
Biaya (Rp/k.
2,000 24,000 3,000 22,500 2,000 30,000 2,500 28,000 1,500 45,000
1,000
18,000
Ai Ai Total Biaya (R.
Figure 1.
Comparison Chart of Total Distribution Costs Before and After MODI Optimization for Each Destination City.
Visualization of Distribution Cost Optimization Results Before and After the MODI Method The bar chart below illustrates the comparison of total vaccine distribution costs from Jakarta to five destination citiesAiBalikpapan.
Surabaya.
Medan.
Makassar, and JayapuraAiboth before and after the optimization using the Modified Distribution Method (MODI).
Key Insights:
C Overall, the application of the MODI method generates a distribution cost saving of Rp 13,500,000, equivalent to approximately 4.
efficiency compared to the initial condition.
This shows a cost reduction .
decrease in total Shifting the allocation from Makassar to Jayapura reduces the total cost by Rp 13,500,000.
Table 8 Comparison of Total Costs Before MODI
Metode NWC
MODI
Total Biaya (R.
Efisiensi Ai Ie 4,1% Here is the English translation:
After MODI .
fter shifting = 478 k.
C Balikpapan: Rp.
C Surabaya: Rp.
C Medan: Rp.
C Makassar: Rp.
C Jayapura: Rp.
C Makassar Ae Jayapura : Rp.
New total:
Z = 48.
CONCLUSION
The implementation of the transportation model for vaccine distribution from Jakarta to five destination regions at PT Silkargo Indonesia demonstrates a significant potential for cost savings.
In the initial condition, the total distribution cost amounted to Rp 331,000,000, calculated using IQTISHADequity journal MANAGEMENT Vol.
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the North West Corner initial solution.
After optimization using the Modified Distribution Method (MODI), the distribution cost was reduced to Rp 317,500,000 per distribution cycle, resulting in a savings of Rp 13,500,000, equivalent to 4.
1% of the initial total cost.
Based on these savings, the MODI method has proven effective in lowering transportation costs without compromising the fulfillment of demand in each destination area.
The optimization process successfully identified that reallocating part of the shipment from JakartaAeJayapura to MakassarAeJayapura contributed to achieving the cost reduction.
Acknowledgements The authors would like to express their sincere gratitude to PT Silkargo Indonesia for the valuable data and insights provided during the research process.
Appreciation is also extended to the academic supervisors at Universitas Logistik dan Bisnis Internasional, whose guidance and critical feedback significantly enhanced the quality of this Special thanks go to the editorial and review
team of the ICARS 2025 conference for their constructive comments and for providing a platform to disseminate this research
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