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

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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 \(\varepsilon\)-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.

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Abbreviations

MOLFIP:

Multi-objective linear fractional inventory problem

FPM:

Fuzzy programming method

FGP:

Fuzzy goal programming

MOLFPP:

Multi-objective linear fractional programming problem

FFLFPP:

Fuzzy fractional linear fractional programming problem

LFPP:

Linear fractional programming problem

HPM:

Homotopy Perturbation method

MONLFPP:

Multi-objective non linear fractional programming problem

FLFPP:

Fuzzy linear fractional programming problem

CLFPP:

Crisp linear fractional programming problem

LFP:

Linear fractional programming

LPPs:

Linear programming problems

MOPLFPP:

Multi-objective probabilistic linear fractional programming problem

MOLFIM:

Multi-objective linear fractional inventory model

GIFN:

Generalized intuitionistic fuzzy number

MOLFSTP:

Multi-objective linear fractional stochastic transportation problem

FCRA:

Fuzzy chance-constrained rough approximation

MOFTP:

Multi-objective fractional transportation problem

FRLMOFP:

Fuzzy random linear multi-objective fractional programming

FFPP:

Fuzzy fractional programming problem

TFN:

Triangular fuzzy number

TrFN:

Trapezoidal fuzzy number

MOFOP:

Multi-objective fractional optimization problem

IFMOLFPP:

Intuitionistic fuzzy multi-objective linear fractional programming problem

FPA:

Fuzzy programming approach

FGA:

Fuzzy goal programming approach

FIM:

Fuzzy interactive method

MOFPP:

Multi-objective fractional programming problem

HFE:

Hesitant fuzzy efficient

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Authors and Affiliations

  1. Department of Mathematics, Siksha ‘O’Anusandhan Deemed to Be University, Bhubaneswar, Odisha, 751030, India

    Anuradha Sahoo & Minakshi Panda

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  1. Anuradha Sahoo
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  2. Minakshi Panda
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Contributions

The problem was developed and the problem statement was validated by MP, the introduction portion was finished by AS, who also checked the grammar for similarities, and the draught of the results and discussion section was finished by AS and MP, who also checked the overall.

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Correspondence to Anuradha Sahoo.

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Sahoo, A., Panda, M. Optimization techniques for crisp and fuzzy multi-objective static inventory model with Pareto front. OPSEARCH (2024). https://doi.org/10.1007/s12597-023-00730-4

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