Integer Linear Programming for Patchwork Production Planning Optimization with Demand Uncertainty

Authors

  • Afnaria Afnaria University of Islam Sumatera Utara
  • Rina Filia Sari Universitas Islam Negeri Sumatera Utara
  • Dhia Octariani University of Islam Sumatera Utara
  • Isnaini Halimah Rambe University of Islam Sumatera Utara

DOI:

https://doi.org/10.30829/zero.v9i1.24349

Keywords:

Mathematical Modelling, Demand Uncertainty, Patchwork Products, Linear Programming, Production planning

Abstract

This study develops an Integer Linear Programming (ILP) model to optimize monthly production planning for handcrafted patchwork MSMEs in Medan, Indonesia. The model incorporates key operational constraints, including production time, material and handling costs, labor, electricity, capital limits, and uncertain demand. Demand uncertainty is modeled deterministically using upper and lower bounds derived from historical field data. The objective function maximizes total profit while ensuring resource feasibility. A real-world case study involving five products across five artisans is presented, resulting in a maximum profit of IDR 12,469,900. The model is implemented using LINGO 18.0 and validated through sensitivity analyses. Results show that a 50% reduction in demand may reduce profit by up to 33.8%, while an increase in lead time can lower profit by 17.1%. These findings demonstrate the model's robustness and its potential to serve as a decision-support tool for MSMEs facing volatile market conditions and operational constraints.

Author Biographies

Afnaria Afnaria, University of Islam Sumatera Utara

Departement of Mathematics Education, Faculty of Teacher Training and Education, University of Islam Sumatera Utara, Indonesia

Rina Filia Sari, Universitas Islam Negeri Sumatera Utara

Department of Mathematics, Universitas Islam Negeri Sumatera Utara, Medan, Indonesia

Dhia Octariani, University of Islam Sumatera Utara

Departement of Mathematics Education, Faculty of Teacher Training and Education, University of Islam Sumatera Utara, Indonesia

Isnaini Halimah Rambe, University of Islam Sumatera Utara

Departement of Mathematics Education, Faculty of Teacher Training and Education, University of Islam Sumatera Utara, Indonesia

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Published

2025-07-03

Issue

Vol. 9 No. 1 (2025): Zero: Jurnal Sains Matematika dan Terapan

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Articles

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