A Deterministic Matrix-Based Inventory-State Model for Multi-Product and Multi-Period Systems
Jellason Jerome Emmanuel *
Federal Polytechnic, Bali, Taraba State, Nigeria.
Abdullahi Alhassan
Modibbo Adama University, Yola, Adamawa State, Nigeria.
P. Nondika, Paul
Taraba State Polytechnic, Suntai, Jalingo Campus, Taraba State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
A deterministic matrix algebra approach for modelling inventory management in multi- product, multi-period systems has been developed, overcoming the limitations of existing inventory models which rely on conventional methods and computational software. The framework combines the initial inventory vector, replenishment matrix, demand matrix and a lower triangular accumulation matrix to calculate inventory levels with non-negativity and storage capacity constraints. The model is extended to evaluate procurement cost, sales revenue and profit in a single mathematical approach. The proposed model was tested on inventory data obtained from FAN-M Global Investment, Jalingo, Taraba State Nigeria with eighteen Fast-Moving Consumer Goods (FMCG) products observed for eighteen consecutive weeks. The results demonstrated that the matrix-based operations was able to track inventory movement across products and periods, calculate the cumulative inventory balances, identify inventory imbalances, maintain feasible stock levels, and provide a transparent assessment of financial performance using matrix operations alone. The study concludes that matrix algebra provides a simple, transparent and computationally efficient alternative for deterministic inventory management in organisations with limited computational resources and contributes a practical analytical approach for multi-product and multi-period inventory decision-making.
Keywords: Matrix, inventory, multi-product, fast moving consumer goods