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Optimization of Fuel Inventory Management at A Retail Petrol Pump Using Linear Programming
Subject area: Management and Commerce · Area of research: Operations Research & Inventory Management
Abstract
Background: Retail fuel stations must balance stock availability with the cost of carrying fuel inventory. Methods: This study uses a 61-day daily inventory register (1 June–31 July 2026) for Motor Spirit (MS) and High-Speed Diesel (HSD) at a selected retail petrol pump. A two-stage approach was used: a data-quality audit followed by two independent Linear Programming (LP) models. Each model minimizes holding cost subject to daily inventory balance, a safety-stock floor, an assumed tank-capacity ceiling, and non-negative replenishment. Safety stock was set at twice average monthly demand and rounded upward to the nearest 10 L. The LPs were solved with scipy.optimize.linprog using HiGHS and independently validated for 122 fuel-day rows. Results: The audit identified 19 negative-inventory observations (15.6% of 122 rows) and only two deliveries per fuel during the study period. Total demand was 33,362 L for MS and 31,033 L for HSD. Historical combined holding cost was Rs. 23,794.86, compared with Rs. 6,074.13 under the LP benchmark, a model-based potential reduction of Rs. 17,720.74 (74.47%). Historical stockout days fell from 15 to zero and average combined inventory from 6,251.19 L to 1,637.62 L. All 122 optimized rows satisfied the model constraints, and all nine sensitivity scenarios remained feasible. Conclusion: The LP provides a transparent benchmark for demand-linked replenishment, but the reported savings are not a guaranteed operational forecast. Supplier lead time, minimum order quantity, delivery schedules, ordering cost, verified tank capacity, and longer demand histories are required for an implementable procurement model.
Keywords
Fuel inventory management; Linear programming; retail petrol pump; safety stock; holding-cost minimization; replenishment optimization.
References
[1] B. Amirjabbari and N. Bhuiyan, “Determining supply chain safety stock level and location,” Journal of Industrial Engineering and Management, vol. 7, no. 1, pp. 42–71, 2014. Journal of Industrial Engineering and Management
[2] A. Benantar, R. Ouafi, and J. Boukachour, “A petrol station replenishment problem: New variant and formulation,” Logistics Research, vol. 9, Art. no. 6, 2016. Springer
[3] S. E. Dınçer and E. Ekin, “Solution approach with linear programming to spare parts inventory management problems in aviation sector,” Journal of Life Economics, vol. 4, no. 2, pp. 77–102, 2017. Journal of Life Economics
[4] S. N. Emenike, A. Ioannou, and G. Falcone, “An integrated mixed integer linear programming model for resilient and sustainable natural gas supply chain,” Energy Sources, Part B: Economics, Planning, and Policy, vol. 17, no. 1, Art. no. 2118901, 2022. Taylor & Francis
[5] A. Fatima and M. Tufail, “Improving productivity through linear programming: A case of oil refinery industry,” SAE Technical Paper 2020-01-5128, 2020. SAE International
[6] Gurtu, “Optimization of inventory holding cost due to price, weight, and volume of items,” Journal of Risk and Financial Management, vol. 14, no. 2, Art. no. 65, 2021. MDPI
[7] F. W. Harris, “How many parts to make at once,” Operations Research, vol. 38, no. 6, pp. 947–950, 1990. INFORMS
[8] A. H. I. Lee and H. Kang, “A mixed 0-1 integer programming for inventory model: A case study of TFT-LCD manufacturing company in Taiwan,” Kybernetes, vol. 37, no. 1, pp. 66–82, 2008. Emerald
[9] Y. Liu, D. Kalaitzi, M. Wang, and C. Papanagnou, “A machine learning approach to inventory stockout prediction,” Journal of Digital Economy, vol. 4, pp. 144–155, 2025. ScienceDirect
[10] S. C. Nwanya, “Inventory cost framework for managing the petroleum product reorder point and order quantity policies,” Cogent Business & Management, vol. 6, no. 1, Art. no. 1558475, 2019.
[11] M. Schmidt, W. Hartmann, and P. Nyhuis, “Simulation based comparison of safety-stock calculation methods,” CIRP Annals, vol. 61, no. 1, pp. 403–406, 2012. ScienceDirect
[12] J. J. Vicente, “Optimizing supply chain inventory: A mixed integer linear programming approach,” Systems, vol. 13, no. 1, Art. no. 33, 2025. MDPI
[13] H. M. Wagner and T. M. Whitin, “Dynamic version of the economic lot size model,” Management Science, vol. 5, no. 1, pp. 89–96, 1958. INFORMS
How to cite this paper
@article{1723370,
author = {Hriday Das},
title = {Optimization of Fuel Inventory Management at A Retail Petrol Pump Using Linear Programming},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {3},
pages = {3041-3048},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1723370.pdf},
abstract = {Background: Retail fuel stations must balance stock availability with the cost of carrying fuel inventory. Methods: This study uses a 61-day daily inventory register (1 June–31 July 2026) for Motor Spirit (MS) and High-Speed Diesel (HSD) at a selected retail petrol pump. A two-stage approach was used: a data-quality audit followed by two independent Linear Programming (LP) models. Each model minimizes holding cost subject to daily inventory balance, a safety-stock floor, an assumed tank-capacity ceiling, and non-negative replenishment. Safety stock was set at twice average monthly demand and rounded upward to the nearest 10 L. The LPs were solved with scipy.optimize.linprog using HiGHS and independently validated for 122 fuel-day rows. Results: The audit identified 19 negative-inventory observations (15.6% of 122 rows) and only two deliveries per fuel during the study period. Total demand was 33,362 L for MS and 31,033 L for HSD. Historical combined holding cost was Rs. 23,794.86, compared with Rs. 6,074.13 under the LP benchmark, a model-based potential reduction of Rs. 17,720.74 (74.47%). Historical stockout days fell from 15 to zero and average combined inventory from 6,251.19 L to 1,637.62 L. All 122 optimized rows satisfied the model constraints, and all nine sensitivity scenarios remained feasible. Conclusion: The LP provides a transparent benchmark for demand-linked replenishment, but the reported savings are not a guaranteed operational forecast. Supplier lead time, minimum order quantity, delivery schedules, ordering cost, verified tank capacity, and longer demand histories are required for an implementable procurement model.},
keywords = {Fuel inventory management; Linear programming; retail petrol pump; safety stock; holding-cost minimization; replenishment optimization.},
month = {September},
}