Mathematical Modelling and Optimization of Inventory Control Through Linear Programming: A Case Study of Haske Modern Bakery in Bauchi State
Article Sidebar
Page Numbers:
125-145
Digital Object Identifier:
10.58578/mjms.v4i1.7793
Viewed: 307 times
Downloaded: 178 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:
Umar Mujahid Aliyu1*, David Opeoluwa Oyewola2, Joel John Taura3, Salisu Lukunti4 
Copyright :
Authors retain copyright and grant the journal right of first publication.
Main Article Content
Abstract
This study investigates the application of linear programming optimization, complemented by primal and dual linear programming, to improve raw material allocation and maximize profitability for the Haske Modern Bakery in Bauchi, Nigeria. A mathematical model was developed to optimize raw material usage, increase production efficiency, and enhance company returns. Linear programming was employed to identify the most profitable production strategy. Additionally, the Economic Order Quantity (EOQ) model was utilized to effectively manage inventory. EOQ calculations determined the optimal order quantities for flour, sugar, butter, milk, and yeast to be approximately 59 bags, 22 bags, 11 cartons, 12 bags, and 56 cartons, respectively. The total costs of ordering flour, sugar, butter, milk, and yeast are N19,349, N11,171, N5,586, N6,119, and N27,928, respectively. Reorder points were established with stock levels triggering reorders in 20 bags of flour, 4 bags of sugar, 2 cartons of butter, 2 bags of milk, and 30 cartons of yeast, assuming a constant lead time of seven days. The results showed that the optimal production strategy involved producing 319.8294 units of small-medium loaf (X₅) and 533.0490 units of another product (Y₃), with all other products (X₁, X₂, X₃, ..., X₁₃ and Y₁, Y₂, Y₃, ..., Y₉) being zeros units. This strategy is projected to yield a maximum profit of N15991.47. This study underscores the significance of utilizing linear programming and EOQ models to enhance operational efficiency and profitability in the bakery industry.
Citation Metrics:
Downloads
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Acquah, S. K. (2024). The role of effective inventory management practices on organizational performance: A case of Tarkwa municipal hospital, western region, Ghana. World Journal of Advanced Research and Reviews, 21(2), 1628-1638.
Adebiyi, S., Bilqis, A., & Soile, I. (2014). Linear optimization techniques for product-Mix of paints production in Nigeria. Ismail OladimejiSoile ACTA Universitatis Danubius, 10(1), 181-190.
Alam, M. K., Thakur, O. A., & Islam, F. T. (2024). Inventory management systems of small and medium enterprises in Bangladesh. Rajagiri Management Journal, 18(1), 8-19.
Almrdof, F., & Attia, A. (2021). The effect of inventory management practices on productivity. PalArch's Journal of Archaeology of Egypt/Egyptology, 18(15), 256-265.
Alnaim, M., & Kouaib, A. (2023). Inventory turnover and firm profitability: A Saudi Arabian investigation. Processes, 11(3), 716.
Amit, A., Sharma, B., & Verma, C. (2020). A linear programming problem (LPP) with general form and constraints. Journal of Optimization Theory and Applications, 185 (2), 123-135.
Anantadjaya, S. P., Carmelita, P. W., Juhara, S., Irdiana, S., Moridu, I., Susanti, E., & Nawangwulan, I. M. (2023). Inventory and financial performance: Selected publicly listed manufacturing Indonesian and German companies. Финансы: теория и практика, 27(5), 76-89.
Baker, S. R., Johnson, S., & Kueng, L. (2024). Financial returns to household inventory management. Journal of Financial Economics, 151, 103758.
Chan, S. W., Tasmin, R., Aziati, A. N., Rasi, R. Z., Ismail, F. B., & Yaw, L. P. (2023, August). Factors influencing the effectiveness of inventory management in manufacturing SMEs. IOP Conference Series: Materials Science and Engineering, 226(1), 012024.
Chaudhary, S., & Giri, S. R. (2024). Enhancing production efficiency through integer linear programming-based production planning. Journal of Engineering Issues and Solutions, 3(1), 63-75.
Dey, B. K., & Seok, H. (2024). Intelligent inventory management with autonomation and service strategy. Journal of Intelligent Manufacturing, 35(1), 307-330.
Egharevba, A. J., & Ojekudo, N. A. (2021). Optimal raw materials mix through linear programming in Tehinnah Cakes and Craft. International Journal of Applied Science and Mathematical Theory, 7(2), 36-43.
Eze, A. N., & Uchenu, C. A. (2021). Inventory management techniques of small and medium scale enterprises in Anambra state. UNIZIK Journal of Educational Research and Policy Studies, 3, 295-307.
Gołaś, Z. (2020). The effect of inventory management on profitability: Evidence from the Polish food industry: Case study. Agricultural Economics/Zemědělská Ekonomika, 66(5).
Jain, A. K., Chouhan, S., Mishra, R. K., Choudhry, P. R. S., Saxena, H., & Bhardwaj, R. (2021). Application of linear programming in small mechanical based industry for profit maximization. Materials Today: Proceedings, 47, 6701-6703.
Jonsson, P., & Mattsson, S. A. (2021). Inventory management practices and their implications on perceived planning performance. International Journal of Production Research, 46(7), 1787-1812.
Kehinde Busola, E., Ogunnaike Olaleke, O., & Adegbuyi, O. (2020). Analysis of inventory management practices for optimal economic performance using ABC and EOQ models. International Journal of Management (IJM), 11(7).
Oluwaseyi, K. O., Elizabeth, A., & Olaoluwa, O. E. (2020). Profit maximization in a product mix bakery using linear programming technique. Journal of investment and Management, 9(1), 27-30.
Ozokeraha, C. F. (2020). Application of linear programming in profit maximization at glad tidings (Gt) foods, Benin City, Edo State, Nigeria. Innovative Journal of Science (ISSN: 2714-3309), 1(1), 26-38.
Zakariyya, A., Mashina, M. S., & Lawal, Z. (2022). Application of linear programming for profit maximization in Shukura Bakery, Zaria, Kaduna State, Nigeria.