Linear Programming for Profit Optimization in Small-Scale Manufacturing: A Python-Based Simplex and Machine Learning Approach

Open Access

Year : 2026 | Volume : 15 | Issue : 02 | Page : 01 12
By

Shipra Aggarwal,

  1. Director of Finance, Pelham Community Pharmacy, Waltham, Massachusetts, USA

Abstract

Profit maximization under resource constraints is a classic challenge. Small manufacturers face tight margins and scarce capital every day. This paper tackles that problem using four Python-based methods. The case study is Bintang Bakery in Bandar Lampung, Indonesia. The bakery makes three bread types and faces 18 resource constraints. Data comes from Anggoro et al. Methods tested include LP revised simplex, Differential Evolution, PSO, and ANN Surrogate. General-purpose scipy minimizers fail when all 18 constraints are active. The linprog function with revised simplex converges in just two iterations. All three ML methods independently reach the same optimal solution. The optimal plan is 3,740 flavored, 1,300 mattress, and 520 bargain packs. Monthly profit reaches Rp. 19,750,000, which is Rp. 250,000 above current output. Beyond algorithm comparison, three financial planning bridges are developed. First, shadow price analysis quantifies each resource constraint’s marginal value. The labor constraint carries a dual value of Rp. 138,461 per labor-hour. This figure is the break-even ceiling for any overtime investment decision. Second, working capital analysis tracks the incremental inputs required. Moving to the optimal mix needs only 1.806 extra labor-hours. The monthly free cash flow gain is Rp. 250,000, or Rp. 3,000,000 annually. Third, sensitivity analysis identifies three actionable financial thresholds. Flour supply must fall more than 8.82% before it constrains the plan. The flavored bread price must drop below Rp. 1,867 before the mix shifts. Each extra labor-hour adds exactly Rp. 138,461 to monthly profit. DE and PSO serve as dynamic recalculation tools when these inputs change. All calculations are verified, with full Python code and nine figures.

Keywords: Linear programming for profit optimization in small-scale manufacturing: A python-based simplex and ML approach

[This article belongs to Research & Reviews : Journal of Statistics ]

How to cite this article:
Shipra Aggarwal. Linear Programming for Profit Optimization in Small-Scale Manufacturing: A Python-Based Simplex and Machine Learning Approach. Research & Reviews : Journal of Statistics. 2026; 15(02):01-12.
How to cite this URL:
Shipra Aggarwal. Linear Programming for Profit Optimization in Small-Scale Manufacturing: A Python-Based Simplex and Machine Learning Approach. Research & Reviews : Journal of Statistics. 2026; 15(02):01-12. Available from: https://journals.stmjournals.com/rrjost/article=2026/view=250345

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Regular Issue Open Access Original Research
Volume 15
Issue 02
Received 17/06/2026
Accepted 23/06/2026
Published 10/07/2026
Publication Time 23 Days

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