Optimization of scheduling problems with deterioration effects and an optional maintenance activity

In this investigation, the single-machine scheduling problem with deterioration effects and an optional maintenance activity is explored. Deterioration effect means that the actual processing time of the job is a function of its normal processing time and its starting time. As an optional maintenance activity, the machine will perform a maintenance activity. After the maintenance activity is completed, the machine will return to the initial state, and the job deterioration will start again. The goal is to determine an optimal sequence and the location of the maintenance activity that minimizes some objective functions. We prove that the problem of minimizing the makespan, total completion time, and total absolute differences in completion (waiting) times can be solved in polynomial time \(O(n^4)\), where n is the number of jobs. For the total weighted completion time minimization, if the weights are positional-dependent weights, we prove that the problem can be solved in polynomial time; if the weights are job-dependent weights, this problem is NP-hard. To solve the problem with job-dependent weights, we present the heuristic, tabu search, and branch-and-bound algorithms.