A binary-rounding heuristic for multi-period variable-task-duration assignment problems

Multi-period assignment problems seek to allocate employees to tasks as required across multiple time periods. This type of problem is a subset of three-dimensional assignment problems and is NP-complete. A binary-rounding heuristic, which allows the determination of a feasible zero-one solution from a feasible continuous solution was developed and applied to 72 test problems. The heuristic found the optimal solution to 68 of the 72 problems and was within 95% of the continuous optimum in the other four cases. The CPU time and iterations required were significantly reduced over those required by a pure integer solution process.