In this article, a new multiobjective optimization model, MUST, is proposed to facilitate the staff-to-job assignment in consulting engineering firms. In addition to the typical objective of maximizing profits, other human resource related objectives are also incorporated to balance workloads, avoid excessive overtime, and eliminate demoralizing idleness while giving preference to projects with specified priorities. The present optimization problem is of significant complexity (nonlinear, non-smooth, and combinatorial) and has been proved NP- and #P-complete. To handle all the difficulties, MUST incorporates a particle swarm optimization algorithm to approximate the tradeoff surface consisting of non-dominated solutions. The application of MUST is demonstrated through a numerical case of assigning six engineering teams to fifteen incoming projects. It has been shown that non-dominated solutions generated by MUST help decision makers choose the compromised assignment plan which is otherwise hard and time-consuming to obtain. The comparisons with SPEA2 and LINGO verify the effectiveness and efficiency of MUST.