Application of Linear Programming in Optimizing Resource Allocation in Small-Scale Industries: A Conceptual Review with an Illustrative Production-Mix Model

Abstract

Small-scale industries operate with tight limits on raw material, working capital, skilled labour and machine time, yet most allocation decisions in these units are still made through experience, habit or simple rules of thumb. Linear programming (LP), one of the oldest and best-understood techniques of operations research, offers a structured way of deciding how scarce inputs should be divided among competing products or activities. This paper examines the relevance of LP to resource allocation in small-scale industrial units. The study is conceptual and review-based: it traces the theoretical development of LP and its extensions, synthesises published work on production planning under constraints, and demonstrates the logic of the method through a hypothetical production-mix problem for a small coir products unit. The illustrative model shows that an LP-based plan yields a higher weekly contribution than a plan that simply favours the product with the highest unit margin, and that the shadow prices generated by the model give owners a practical guide to which resources are worth expanding. The review also finds that the main barriers to adoption in small firms are not mathematical but organisational, namely poor cost records, limited managerial time and a perception that optimisation tools belong to large enterprises. The paper argues that free spreadsheet solvers and open-source libraries have largely removed the cost barrier, and that capacity building through industry associations and MSME support institutions can make LP a routine planning aid. Implications for owners, trainers and policymakers are discussed