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Multi-item multiperiodic inventory control problem with variable demand and discounts: a particle swarm optimization

Seyed Mohsen Mousavi1, S T A Niaki2, Ardeshir Bahreininejad1

  • 1Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia.

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This study introduces a fuzzy multi-item inventory control model for variable demands and budget constraints. The multi-objective particle swarm optimization (MOPSO) approach efficiently minimizes costs and space, outperforming genetic algorithms.

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Area of Science:

  • Operations Research
  • Supply Chain Management
  • Optimization

Background:

  • Inventory control models are crucial for managing stock levels under variable demand and budget limitations.
  • Existing models often simplify demand patterns or discount structures, necessitating more comprehensive approaches.
  • Balancing inventory costs and storage space is a key challenge in multi-item, multi-period inventory systems.

Purpose of the Study:

  • To develop a fuzzy multi-item multi-period inventory control model for known-deterministic variable demands with budget constraints.
  • To incorporate backorder and lost sale considerations for shortages, alongside batch ordering and integer decision variables.
  • To address both unit and incremental quantity discounts for multiple products.

Main Methods:

  • Formulation of the inventory problem within a fuzzy multi-criteria decision-making (FMCDM) framework, resulting in a mixed-integer nonlinear programming model.
  • Application of a multi-objective particle swarm optimization (MOPSO) algorithm to find optimal and near-optimal solutions.
  • Comparison of MOPSO with a weighting approach and a multi-objective genetic algorithm (MOGA) for efficiency assessment.

Main Results:

  • The MOPSO approach successfully derived a set of compromise solutions, balancing total inventory cost and storage space.
  • Numerical illustrations demonstrated the effectiveness of MOPSO in solving the complex inventory control model.
  • Graphical and statistical analyses confirmed the superior efficiency of MOPSO compared to MOGA.

Conclusions:

  • The proposed fuzzy inventory control model effectively handles complex scenarios including variable demands, budget limits, and diverse discount structures.
  • MOPSO is a highly efficient metaheuristic for solving multi-objective inventory optimization problems, offering better performance than MOGA.
  • The model provides valuable insights for inventory managers seeking to minimize costs and space utilization simultaneously.