Vol. 25 No. 1 (2026): Mapana Journal of Sciences
Research Articles

Optimization of Single-Seller Multi-item in Multiple Outlets Distribution Network Fuzzy Inventory System with Lead Time and Carbon Emission Cost

  • R. Vithyadevi,
  • K. Annadurai
R. Vithyadevi
Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, Dindigul, Tamil Nadu, India
K. Annadurai
PG and Research Department of Mathematics, M.V. Muthiah Government Arts College for Women, Dindigul, Tamilnadu 624001, India.

Published 2026-02-14

Keywords

  • Fuzzy multi-object in multi-outlet inventory system;,
  • Alpha cut technique;,
  • Minimum integrated total cost;,
  • Optimal order quantity;,
  • Lagrangian process.

Copyright (c) 2026

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Abstract

Managing multiple products across various locations reduces total costs through consolidated replenishment.  This strategy reduces ordering costs because fewer transactions result in better pricing.  It also reduces shipping costs by using combined shipments to minimize transportation expenses.  The objective is currently inaccurate due to several variables that are not well-defined.  Hexagonal fuzzy numbers are utilized in this model to account for the uncertain nature of buyer and supplier parameters. Optimizing the fuzzy objective function is challenging because its output value remains uncertain.  The model is solved using the alpha cut technique combined with the Lagrangian method, while the fuzzy counterparts of the remaining constraints are available.  An algorithm is developed to determine the optimum order size for each item at every outlet. This approach simultaneously minimizes the joined entire price for the entire inventory system.  Evaluation of fuzzy multi-item in multi-outlet distribution network inventory system against crisp multi-item in multi-outlet distribution network inventory system is concluded with numerical illustrations.  Finally, graphical representations of the proposed system's performance are provided.  This fuzzy inventory framework is effective in optimizing results for multi-item across various outlets.

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