The general assignment problem (GAP) involves allocating tasks to available agents to minimize the total cost of the assignment. GAP has applications in the various industrial and service fields due to its potential to enhance productivity and optimize the use of resources. Bin-packing is a basic optimization problem that aims to minimize the number of bins required to house inserts while at the same time preventing exceeding bin’s capacity. This study uses Excel to present a heuristic to solve the GAP by means of a modified first-fit-decreasing bin-packing heuristic. The proposed algorithm assigns N-heterogeneous jobs to M-heterogeneous machines, N> > M, to enhance fairness among machines. This heuristic sets the number of bins equal to the number of machines and the number of inserts equal to the number of jobs. The proposed heuristic accounts for single- and multiple-dimension bin-packing where each dimension is associated with a job/machine attribute of significance to the decision maker. Unlike bin-packing, the heuristic allows over capacitating bins while preserving fairness. The paper presents a case study of a two-dimensional nature where time and power limitations are key to the assignment. In this scenario, decision makers try to optimize over-time and over-power to get the job done while minimizing associated costs. Results obtained from the study illustrate the simplicity of the proposed algorithm while at the same time shows the significance of weights of the two attributes on the results.