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Optimization techniques for crisp and fuzzy multi-objective static inventory model with Pareto front

Author

Listed:
  • Anuradha Sahoo

    (Siksha ‘O’Anusandhan Deemed to Be University)

  • Minakshi Panda

    (Siksha ‘O’Anusandhan Deemed to Be University)

Abstract

Inventory management is an essential component of any business, but it can be difficult for businesses today to determine the ideal quantity level required to avoid shortages and to reduce waste. With the maximization of profit, if the backorder quantity is minimized, then this policy will be most preferred and economical. Likewise with the minimization of holding cost, the policy is such that the total order quantity is minimized. The model is formulated as a multi-objective linear programming problem with four objectives: maximizing profit, maximizing total ordering quantity, minimizing the holding cost in the system, minimizing total backorder quantity. The constraints are included with budget limitation, space restrictions and constraint on cost of ordering each item. When converting a fuzzy model to a crisp model, we employ the ranking function approach and graded mean integration method. In order to reduce stock out situations, the lowest optimal quantity level to place in the inventory is also determined using weighted sum and the $$\varepsilon$$ ε -constraint method. To prevent shortages, the ordering quantity is increased. Minimizing holding costs and back order quantity together enhance the model's profit. Budgetary restrictions, space limitations, and a pricing restriction on ordering each item are all included in the constraints. In a fuzzy context, the proposed inventory model turns into a difficulty of many criteria decision-making. To transform the data from the fuzzy model to the crisp model, the ranking function approach using the triangular fuzzy number, trapezoidal fuzzy number and triangular intuitionistic fuzzy number and graded mean integration methods are used. The optimal solution is obtained using numerical demonstration. Pareto optimal solutions using genetic algorithm for different objective functions are included. Sensitivity analysis of the model is carried out to discuss the effectiveness of the model.

Suggested Citation

  • Anuradha Sahoo & Minakshi Panda, 2024. "Optimization techniques for crisp and fuzzy multi-objective static inventory model with Pareto front," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 2242-2284, December.
  • Handle: RePEc:spr:opsear:v:61:y:2024:i:4:d:10.1007_s12597-023-00730-4
    DOI: 10.1007/s12597-023-00730-4
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    References listed on IDEAS

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    1. Arya, Rubi & Singh, Pitam, 2019. "Fuzzy efficient iterative method for multi-objective linear fractional programming problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 39-54.
    2. Pavan Kumar & Debashis Dutta, 2015. "Multi-objective linear fractional inventory model of multi-products with price-dependant demand rate in fuzzy environment," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(5), pages 547-565.
    3. D. Dutta & Pavan Kumar, 2015. "Application of fuzzy goal programming approach to multi-objective linear fractional inventory model," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2269-2278, September.
    4. Irfan Ali & Srikant Gupta & Aquil Ahmed, 2019. "Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(2), pages 173-189, April.
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