MIXED-INTEGER QUADRATIC PROGRAMMING (MIQP) MODEL FOR THE OPTIMIZATION OF INTEGRATED FARMING SYSTEMS

  • Lasker Pangarapan Sinaga Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Medan, Indonesia https://orcid.org/0000-0002-5218-9082
  • Rizky Habibi Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Medan, Indonesia https://orcid.org/0009-0007-2026-7692
  • Suviardi Panggabean Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Medan, Indonesia https://orcid.org/0009-0009-9556-3984
DOI: https://doi.org/10.30598/barekengvol20iss4pp3197-3212
Keywords: Closed-loop Optimization, Integrated Farming System, Mixed-integer Quadratic Programming, Profit Maximization, Sensitivity Simulation

Abstract

This study develops a Mixed-Integer Quadratic Programming model to optimize resource allocation and profitability in integrated farming systems. The model links crop, livestock, and aquaculture components in a closed-loop framework that promotes internal resource use and reduces dependence on external inputs. Land productivity, labor, feed, fertilizer, and capital constraints are incorporated into a deterministic annual optimization model. A scenario-based case study for North Sumatra, Indonesia, is conducted using five commodities and three main resource categories. Sensitivity analysis across 243 scenarios varies price, productivity, input cost, feed cost, and capital parameters. The results show that the model identifies optimal land and labor allocations, improves permanent labor efficiency, and strengthens internal resource circulation. Profitability is most sensitive to commodity prices and productivity, while higher input and feed costs reduce system performance. Practically, the model can assist farmers, cooperatives, and local policymakers in evaluating allocation strategies and improving input efficiency. However, the study is limited by its deterministic structure, reliance on secondary data contextualized to North Sumatra, and single-year planning horizon, and it does not yet incorporate stochastic uncertainty or broader ecological and social objectives.

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Published
2026-08-24
How to Cite
[1]
L. P. Sinaga, R. Habibi, and S. Panggabean, “MIXED-INTEGER QUADRATIC PROGRAMMING (MIQP) MODEL FOR THE OPTIMIZATION OF INTEGRATED FARMING SYSTEMS”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 3197-3212, Aug. 2026.
Issue
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2026 Lasker Pangarapan Sinaga, Rizky Habibi, Suviardi Panggabean

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