Revised Kuhn-Munkres Algorithm for Dynamic Job Allocation Using Dummy Decider Technique

Generally, static job arrivals are assigned to resources by using the classical Kuhn-Munkres (KM) algorithm. However, in many real-world scenarios, job arrivals are dynamic, leading to changes in the number of nodes. This leads to dynamic node numbers in the left partition of the bipartite graph over time. Consequently, for such unbalanced dynamic workload-based problems, the initial assignment becomes invalid. This paper tackles the issue of dynamic job arrivals and proposes a revised assignment algorithm. It models both partial and complete reassignments in response to dynamic job arrivals. Numerical results demonstrate effective assignments for unbalanced problems with dynamic workload arrivals.