Parallel-machine scheduling with general positional deterioration and maintenance

We consider the parallel machine problem with generalized positional deterioration effects and multiple maintenance activities to minimize the total workload. The decision is to determine jointly the optimal assignment of jobs on each machine, the optimal maintenance frequencies, the optimal positions of the maintenance activities, and the optimal job sequences on each machine. The deterioration rates of job processing times on machines are represented by a general non-decreasing function and the maintenance activity is not necessarily perfect. The problem is modeled as a rectangular assignment problem and we show that the problem can be optimally solved at most in O(nm+4) time. An illustrative example is used to show the computational procedure.