A greedy heuristic for shift minimization personnel task scheduling problem

Shift Minimization Personnel Task Scheduling Problem (SMPTSP) is assigning a given set of predetermined tasks (with known start and finish times) to a minimum number of heterogeneous workers with predetermined shifts. Each task can be performed only by a specific subset of workers. Every task must be assigned to a worker. A worker cannot perform more than one task at a time, and tasks cannot be pre-empted. SMPTSP is NP-hard, but there is practical interest in solving very large instances of it in ground crew scheduling of a large airline in a large airport. Recently, there have been a few papers reporting various solution methods for large instances of SMPTSP. However, solving very large instances of SMPTSP remains a challenge. In this paper, we propose a novel greedy heuristic solution method for SMPTSP. A reduced problem is solved iteratively by selecting the best possible assignment of tasks to one worker. We have tested the Greedy heuristic method on 3 sets of available large test problems. The results show that the heuristic method performs well relative to the current solution methods, and has the added advantage of being able to solve very large instances fast.