A multiset-theoretic framework for inventory optimization in Motor garage systems

Abstract

Inventory system in motor garages involve repeated spare parts such as spark plugs, filters, and bolts, where multiplicity is essential for accurate representation. Classical set-theoretic model fails to capture repeated elements structurally, requiring external quantity variables. This paper develops a multiset-theoretic framework for motor garage inventory modelling, representing inventory as multiplicity functions over a finite universe of items. Algebraic operations, such as addition, difference, union, and intersection are formalized. Structural properties such as closure, commutativity, and stability are established. A dynamic inventory update model and demand-balancing optimization are proposed. Computational analysis demonstrates linear scalability. The framework provides a robust, computationally efficient method for small- and medium- scale inventory management.