Mathematical Modelling and Optimization of Inventory Control Through Linear Programming: A Case Study of Haske Modern Bakery in Bauchi State - Aliyu, Umar Mujahid; Oyewola, David Opeoluwa; Taura, Joel John; Lukunti, Salisu (Darul Yasin Al Sys, 2026)
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.