The assignment problem is the core concept of fundamental optimization problem in the field of engineering and management sciences. In some situations, decision maker needs to optimize the assignment cost, assignment time, deterioration rate, profit and so on simultaneously which gives way to multi-objective assignment problem. In practical problems, there are some unpredictable conditions due to time constraints, limitations in data, inaccuracy in measurements and so on. So, the single valued trapezoidal neutrosophic numbers is considered here to handle this fact. The objective of this paper is to determine the optimal compromise solution for the neutrosophic bi-objective assignment problem by considering all the parameters as single valued trapezoidal neutrosophic number. Initially using score function, we convert the neutrosophic problem into its deterministic problem. Transformation techniques can assist the decision makers to present their neutral views and manage uncertainties efficiently in the decision-making situations. So, we have developed the transformation techniques for assignment problem such as linear, hyperbolic, exponential membership function, fuzzy programming approach, neutrosophic compromise programming approach, global criteria method and weighted sum method to transform the deterministic bi-objective assignment problem into its single objective assignment problem under neutrosophic environment. The reduced problem is then solved by LINGO to find the optimal compromise solution and it lets the decision maker to specify the targets. To evaluate the viability and accuracy of our study, numerical illustrations have been conducted and comparisons have been made. Sensitivity analysis have been performed in this study. Finally, conclusions and future explorations are depicted.
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