Assignment Problem for Team Performance Promotion under Fuzzy Environment

This paper constructs a general fuzzy assignment problem (GFAP) based on a real-world scenario and proposes a solution procedure. Suppose a project team consists of workers and a manager. The workers are responsible for performing jobs and the manager for restraining the total cost. The corresponding cost for a worker to perform his assigned job is not defined deterministically but as a subnormal fuzzy interval with increasing linear membership function. Job quality is then linearly and positively related to the cost of the job and is taken as the performance of the worker. On the other hand, the performance of the manager is negatively related to the total cost and is defined as a fuzzy interval with a decreasing linear membership function. It is common practice for a company to regard the lowest performance among members as the team performance in order to increase overall team performance. Hence, using the max–min criterion, a mixed nonlinear programming model of the GFAP is constructed. The model can be transformed into a general 0-1 fractional programming problem with max–min objective function. An algorithm that combines simplex and trade-off approaches is proposed to solve the problem. A numerical example and the computational results show that the constructed model and the proposed algorithm are useful and efficient.