A Regularized Mixed Integer Linear Programming framework with penalties for integrated workforce, subcontracting and production optimization

P. K. Sudhakar; R. Muthucumaraswamy; P. Selvaraju; S. Rukmani Devi; P. K. Sudhakar; R. Muthucumaraswamy; P. Selvaraju; S. Rukmani Devi

doi:10.3934/jimo.2026074

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 4: 2014-2043. doi: 10.3934/jimo.2026074

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Research article

A Regularized Mixed Integer Linear Programming framework with penalties for integrated workforce, subcontracting and production optimization

1.
Department of Mathematics, Sri Venkateswara College of Engineering, (Autonomous), (Affiliated to Anna University), Sriperumbudur, Chennai – 602117, Tamil Nadu, India
2.
Department of Artificial Intelligence and Data Science, Jerusalem College of Engineering (Autonomous), Chennai -600100, India
3.
Department of Computer Science, Saveetha College of Arts and Sciences, SIMATS Deemed to be University, Chennai, India

Received: 05 September 2025 Revised: 27 January 2026 Accepted: 25 February 2026 Published: 23 March 2026
90B30, 90B35, 90B50, 90C11

In this study, we introduce a Regularized Mixed-Integer Linear Programming (MILP) framework aimed at optimizing workforce allocation, production scheduling, subcontracting, and energy management within the footwear manufacturing domain. The proposed model incorporates two regularization-based penalty components: An L₁ (lasso-type) penalty, which constrains abrupt fluctuations in workforce levels and job sequencing across planning horizons, and an L₂ (ridge-type) penalty, which penalizes deviations from target capacity and energy utilization levels. This hybrid formulation improves model robustness, mitigates overfitting, and ensures a balanced trade-off between operational efficiency and cost performance. Empirical evaluation conducted over a six-period planning horizon using representative production data demonstrated the model's effectiveness. With regularization coefficients calibrated at λ₁ = 0.1 and λ₂ = 0.05, the MILP solver produced an optimal integer solution, yielding a total operational cost of ₹738,792.7 while sustaining workforce stability across all periods and completely avoiding additional hiring or layoffs.
- flow shop scheduling,
- batch process,
- regularization Technique,
- mixed integer programming,
- subcontract,
- production optimization
Citation: P. K. Sudhakar, R. Muthucumaraswamy, P. Selvaraju, S. Rukmani Devi. A Regularized Mixed Integer Linear Programming framework with penalties for integrated workforce, subcontracting and production optimization[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 2014-2043. doi: 10.3934/jimo.2026074

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Abstract

In this study, we introduce a Regularized Mixed-Integer Linear Programming (MILP) framework aimed at optimizing workforce allocation, production scheduling, subcontracting, and energy management within the footwear manufacturing domain. The proposed model incorporates two regularization-based penalty components: An L₁ (lasso-type) penalty, which constrains abrupt fluctuations in workforce levels and job sequencing across planning horizons, and an L₂ (ridge-type) penalty, which penalizes deviations from target capacity and energy utilization levels. This hybrid formulation improves model robustness, mitigates overfitting, and ensures a balanced trade-off between operational efficiency and cost performance. Empirical evaluation conducted over a six-period planning horizon using representative production data demonstrated the model's effectiveness. With regularization coefficients calibrated at λ₁ = 0.1 and λ₂ = 0.05, the MILP solver produced an optimal integer solution, yielding a total operational cost of ₹738,792.7 while sustaining workforce stability across all periods and completely avoiding additional hiring or layoffs.

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