A weighted neutrosophic fuzzy goal programming approach to optimise multi-objective assignment problem

Assignment problems (APs) hold significant in industrial organisation, resource allocation, developing service systems, etc. Assigning appropriate jobs to the right employees is crucial when aiming to achieve objectives like cost-saving, ensuring production quality, and estimating production time. Decision makers (DMs) face immense pressure to optimise all of the objectives simultaneously determined to thrive in today's rapidly evolving market. Therefore, here considers, multi-objective assignment problems (MOAPs) to optimise all the objectives comprehensively. Additionally, only a tiny portion of the literature concentrates on both the quality of the commodities and the consistency of the objective functions while solving MOAPs and the consistency of the objective functions. Thus, in the proposed study, each task's quality undergoes evolution using a neutrosophic linguistic scale. Weights are determined employing the neutrosophic analytic hierarchy process (NAHP) to avoid comparisons and ensure the consistency in the objective functions. The weighted single valued neutrosophic fuzzy goal programming (WSVNFGP) method is proposed to resolve the deterministic MOAP and find Pareto-optimal solutions by combining weights. The study is strengthened by a fair contrast of the proposed algorithm with other widely-used approaches, leading to approval of the reasonability of the proposed algorithm over other schemes.