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Scheduling deteriorating jobs to minimize makespan. (English) Zbl 0936.90026
Summary: We consider a single-machine problem of scheduling n independent jobs to minimize makespan, in which the processing time of job J j grows by w j with each time unit its start is delayed beyond a given common critical date d. This processing time is p j if J j starts by d. We show that this problem is NP-hard, give a pseudopolynomial algorithm that runs in O(nd j=1 n p i ) time and O(nd) space, and develop a branch-and-bound algorithm that solves instances with up to 100 jobs in a reasonable amount of time. We also introduce the case of bounded deterioration, where the processing time of a job grows no further if the job starts after a common maximum deterioration date D>d. For this case, we give two pseudopolynomial time algorithms: one runs in O(n 2 d(D-d) j=1 n p j ) time and O(nd(D-d)) space, the other runs in O(nd j=1 n w j ( j=1 n p j ) 2 ) time and O(nd j=1 n w j j=1 n p j ) space.
MSC:
90B35Scheduling theory, deterministic
90C39Dynamic programming
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut