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A Pollution Sensitive Marxian Production Inventory Model with Deterioration Under Fuzzy System.

Sujit Kumar De1, Kousik Bhattacharya1

  • 1Department of Mathematics, Midnapore College (Autonomous), Midnapore, 721101 India.

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Summary
This summary is machine-generated.

This study introduces a new Marxian economic production quantity (M-EPQ) model integrating environmental pollution and fuzzy logic. It optimizes inventory management by considering pollution generation and Marxian economic principles for enhanced production strategies.

Keywords:
EPQ modelExploitationFuzzy systemMarxian theoryOptimizationPG model

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Area of Science:

  • Operations Research
  • Environmental Economics
  • Inventory Management

Background:

  • Traditional economic production quantity (EPQ) models often overlook environmental impacts and socio-economic factors.
  • Existing inventory models have not incorporated Marxian production theory, which offers unique insights into labor value and profit.

Purpose of the Study:

  • To develop a novel Marxian economic production quantity (M-EPQ) model that accounts for environmental pollution and fuzzy uncertainties.
  • To integrate Marxian principles, including manpower exploitation and surplus value, into inventory management for the first time.
  • To analyze the M-EPQ model under different selling price scenarios and validate its applicability through a case study.

Main Methods:

  • Development of a pollution generation (PG) model to constrain the M-EPQ model.
  • Application of fuzzy logic to handle uncertainties in production cost components.
  • Extension of foundational EPQ models by Harris and Taft to incorporate Marxian economic concepts.
  • Numerical illustration via a case study with a developed solution algorithm.

Main Results:

  • The proposed M-EPQ model successfully integrates environmental pollution and fuzzy logic into inventory management.
  • The study demonstrates the impact of Marxian economic concepts on profit functions within an inventory context.
  • Sensitivity analysis and graphical illustrations validate the robustness and applicability of the M-EPQ model.

Conclusions:

  • The M-EPQ model offers a novel framework for inventory management that considers environmental sustainability and socio-economic factors.
  • This research pioneers the application of Marxian production theory in operations research and inventory management.
  • The fuzzy M-EPQ model provides a more realistic approach to production planning under uncertainty and environmental concerns.