<p>Optimal workforce allocation assigning, the right individual to the right task at the right time, remains a central challenge in operational management. This study presents a novel multi-objective assignment model that incorporates performance-based incentives under an uncertain decision-making environment, while simultaneously addressing budgetary and time constraints. The model is designed to align with contemporary corporate strategies that prioritize variable, performance-linked compensation structures over fixed salaries to enhance productivity and profitability. The proposed model considers three conflicting objectives: (i) minimizing total assignment cost, (ii) minimizing total performance time, and (iii) maximizing overall product/service quality. Uncertainty in model parameters is captured using single-valued trapezoidal neutrosophic numbers (SVTNNs), and a neutrosophic compromise programming approach (NCPA), along with an interactive fuzzy satisficing method, is used to derive a balanced solution. Ranking of neutrosophic values is performed using appropriate score and accuracy functions. A real-world case study based on the Tripura handicrafts industry is conducted to demonstrate the practical applicability of the model. The model is implemented and solved using the LINGO optimization platform. The results reveal that at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$q_{\alpha } = 75$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>q</mi> <mi>α</mi> </msub> <mo>=</mo> <mn>75</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$T_s = 50$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>50</mn> </mrow> </math></EquationSource> </InlineEquation> h, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$Q_s = 60$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>Q</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>60</mn> </mrow> </math></EquationSource> </InlineEquation> units, the optimal configuration yields a minimum assignment cost of 243.60, performance time of 106.83 h, and quality score of 204.625. Further sensitivity analysis demonstrates the responsiveness of the solution to variations in the critical quality threshold, time allocation, and quality targets, providing strategic insights for managerial decision-making. This work offers a rigorous mathematical framework and actionable managerial insights, contributing to the literature on assignment problems, incentive structures, and decision-making under uncertainty.</p>

A multi-objective assignment model incorporating incentives under uncertain environment with budgetary and time constraints

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发表日期：

2026年6月25日

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Jayanta Saha,
Amrit Das,
Saptadeep Biswas,
Uttam Kumar Bera

摘要

Optimal workforce allocation assigning, the right individual to the right task at the right time, remains a central challenge in operational management. This study presents a novel multi-objective assignment model that incorporates performance-based incentives under an uncertain decision-making environment, while simultaneously addressing budgetary and time constraints. The model is designed to align with contemporary corporate strategies that prioritize variable, performance-linked compensation structures over fixed salaries to enhance productivity and profitability. The proposed model considers three conflicting objectives: (i) minimizing total assignment cost, (ii) minimizing total performance time, and (iii) maximizing overall product/service quality. Uncertainty in model parameters is captured using single-valued trapezoidal neutrosophic numbers (SVTNNs), and a neutrosophic compromise programming approach (NCPA), along with an interactive fuzzy satisficing method, is used to derive a balanced solution. Ranking of neutrosophic values is performed using appropriate score and accuracy functions. A real-world case study based on the Tripura handicrafts industry is conducted to demonstrate the practical applicability of the model. The model is implemented and solved using the LINGO optimization platform. The results reveal that at $q_{\alpha } = 75$ $q_{α} = 75$ , $T_s = 50$ $T_{s} = 50$ h, and $Q_s = 60$ $Q_{s} = 60$ units, the optimal configuration yields a minimum assignment cost of 243.60, performance time of 106.83 h, and quality score of 204.625. Further sensitivity analysis demonstrates the responsiveness of the solution to variations in the critical quality threshold, time allocation, and quality targets, providing strategic insights for managerial decision-making. This work offers a rigorous mathematical framework and actionable managerial insights, contributing to the literature on assignment problems, incentive structures, and decision-making under uncertainty.