Solving the Tree-Structured Task Allocation Problem via Group Multirole Assignment

Abstract

Task allocation is a critical phase of project management. Tree-type structures are frequently used constraints to obtain a pertinent task allocation. They can illustrate where one task may require numerous agents and when an agent can be assigned to different tasks (roles). The process of task allocation is made more complex when administrators need to satisfy sequential and fixed branch relationships between/among tasks (roles). This paper formalizes the tree-structured task allocation problem (TSTAP) with group multirole assignment (GMRA) and proves necessary conditions, the necessary and sufficient condition, as well as sufficient conditions, of TSTAP. The formalization makes it easy to find a solution with the IBM ILOG CPLEX optimization package (CPLEX). The necessary conditions improve the CPLEX solution by eliminating infeasible cases. The necessary and sufficient condition describes the solution space of TSTAP completely. Another exciting result is that the sufficient conditions can not only improve the CPLEX solution by describing a practical approximate solution space but also help decision-makers and human resource officers organize a team in order to successfully assign tasks. The proposed approach is verified by simulation experiments with respect to a real-world problem. The experimental results present the practicability of the proposed solutions in this paper. This paper was motivated by general cooperative projects whose tasks have tree-structured relationships. This can make the problem of successful multitask assignment extremely challenging. The traditional method of assignment such as the KM algorithm can no longer solve this problem. To solve the assignment problem with tree-structured relationships, an efficient many-to-many assignment with constraints is required. The proposed approach provides theoretical and technical foundations for efficient assignment of TSTA, which can not only provide a viable and effective assignment scheme for TSTA problems but also help human resource officers to formulate reasonable plans according to the relationships between/among tasks.