Neutrosophic Multi-Criteria Assignment Models for Industrial Decision-Making

Abstract

One of the most useful decision-making problems is known as Assignment Problem which used in different real-life situations. Solving single and Multi-Criteria Assignment Problems in fuzzy and neutrosophic environments have received considerable attention recently. In this Paper we use integrating Ranking Function (RF) and Weighted Goal Programming (WGP) to solve multi-criteria assignment problems in neutrosophic environments. Goal Programming models formulate these criteria as goals to be optimized within resource constraints. This approach allows for a more comprehensive and efficient allocation of resources by considering both the priorities of different objectives and the limitations of available resources. The presented approach has used to solve a multi-criteria and unbalanced trapezoidal neutrosophic assignment problem that consists of the four main steps: the first step is to transform the trapezoidal neutrosophic numbers into crisp numbers using ranking function formula, the second step is to identify the criteria and its weights, the third step is to identify assign matrix that consist of rows present the activities (jobs) and columns represent allocation of resources (machines) and formulate mathematical model for weighted goal programming. Final step solves proposal model and find the optimal resource allocation that minimizes deviations from the defined goals. This work has presented example of multi-criteria and unbalanced trapezoidal neutrosophic assignment problem which represents data for the Heavy Engineering Equipment State, which allows us to verify its effectiveness in a real industrial environment that has three criteria (rolling time, rolling cost, and number of rolling passes), three machines (allocation of resources) and eight job (activities). The results show that the presented approach is an efficient and easy to implement and can extend to other related problems.