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March 21, 2026Mathematics0 citationsOpen Access

Population-Based Metaheuristic Algorithms for a Hybrid Batch-Continuous Production Scheduling Problem in a Distributed Pharmaceutical Supply Chain

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SLSeungjae LeeBKByung‐Soo Kim

Key Points

  • The aim is to optimize scheduling in a pharmaceutical production scenario that involves hybrid batch-continuous processes across multiple sites.
  • Formulation of a scheduling problem as a mathematical model.
  • Development of four metaheuristic variants using two population-based algorithms.
  • Application of two distinct solution structures for the scheduling model.
  • Performance comparison of proposed algorithms through numerical experiments.
  • Sensitivity analysis for managerial insights.
  • Successful minimization of makespan achieved with the proposed metaheuristic approaches.
  • Performance of different metaheuristic variants varies based on the scheduling scenario.
  • Managerial insights provided through sensitivity analysis help improve decision-making in supply chain management.

Abstract

We study a pharmaceutical scheduling problem with a hybrid batch-continuous manufacturing process in a distributed supply chain. The supply chain consists of heterogeneous plants and one distribution center. Each plant adopts an unrelated permutation flowshop layout consisting of a hybrid batch-continuous production line. Each pharmaceutical order is split and produced in multi-production sites located in various regions. The pharmaceutical medicines manufactured by the production sites are directly shipped to a distribution center. To minimize the makespan, we formulate the addressed scheduling problem as a mathematical model. To solve this model, we propose four metaheuristic variants by applying two population-based metaheuristics to two distinct solution structures. We compare the proposed metaheuristics to evaluate their performance in the numerical experiments. Additionally, we present managerial insights through sensitivity analysis.

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Cite This Study

Lee et al. (2026) studied this question.

synapsesocial.com/papers/69be36bf6e48c4981c675ebchttps://doi.org/10.3390/math14061044
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