We formulate an assignment problem-solving framework called singleobject resource allocation with preferential order (SORA/PO) to incorporate values of resources and individual preferences into assignment problems. We then devise methods to find semi-optimal solutions for SORA/PO problems. The assignment, or resource allocation, problem is a fundamental problem-solving framework used in a variety of recent network and distributed applications. However, it is a combinatorial problem and has a high computational cost to find the optimal solution. Furthermore, SORA/PO problems require solutions in which participating agents express no or few dissatisfactions on the basis of the relationship between relative values and the agents’ preference orders. The algorithms described herein can efficiently find a semi-optimal solution that is satisfactory to almost all agents even though its sum of values is close to that of the optimal solution. We experimentally evaluate our methods and the derived solutions by comparing them with tho optimal solutions calculated by CPLEX. We also compare the running times for the solution obtained by these methods.