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Modeling the Capacitated Multi-Level Lot-Sizing Problem under Time-Varying Environments and a Fix-and-Optimize

Meng You1, Yiyong Xiao1, Siyue Zhang1

  • 1School of Reliability and System Engineering, Beihang University, Beijing 100191, China.

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Summary

This study addresses dynamic production challenges by introducing new models for time-varying capacitated lot-sizing problems. These models effectively manage fluctuating costs and capacities in agile manufacturing environments.

Keywords:
capacitated lot-sizing problementropymixed-integer linear programmingoptimizationtime-varying environment

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Area of Science:

  • Operations Research
  • Industrial Engineering
  • Supply Chain Management

Background:

  • Traditional lot-sizing models assume static production environments, which are inadequate for today's agile enterprises.
  • Rapid changes in setup costs, inventory-holding costs, production capacities, and material prices necessitate new approaches.
  • Existing algorithms fail to account for the dynamic nature of modern production factors.

Purpose of the Study:

  • To develop and analyze mathematical models for time-varying capacitated lot-sizing problems.
  • To address the limitations of traditional methods in fast-changing production settings.
  • To incorporate dynamic capacity constraints and fluctuating costs into lot-sizing optimization.

Main Methods:

  • Developed two mixed-integer linear programming (MILP) models: one for single-level and one for multi-level lot-sizing.
  • Analyzed new properties related to solution feasibility and optimality for the proposed MILP models.
  • Utilized AMPL/CPLEX for computational experiments on benchmark instances.

Main Results:

  • The proposed models effectively handle time-varying setup costs and production capacities.
  • Computational experiments demonstrated the applicability and efficiency of the new models in dynamic environments.
  • Solution quality was assessed using entropy, showing improvement in optimized systems.
  • New best-known solutions were established for two benchmark problems.

Conclusions:

  • The developed MILP models provide a robust framework for time-varying capacitated lot-sizing problems.
  • These models are suitable for agile manufacturing environments with dynamic production factors.
  • The research offers practical tools for optimizing production systems facing continuous change.