On A Scheduling Problem of Time Deteriorating Jobs

Abstract

We consider a scheduling problem with a single machine and a set of jobs which have to be processed sequentially. While waiting for processing, jobs may deteriorate, causing the processing requirement of each job to grow after a fixed waiting time t 0 . We prove that the problem of minimizing the makespan completion time for all jobs is NP-hard. Next we consider the problem for a natural special case where the job requirement grows linearly at a job-specific rate after t 0 . We develop a fully polynomial time approximation scheme for the problem in this case. We also give further NP-hardness results, and a polynomial time algorithm for the case where the job-specific rate is proportional to the initial processing requirement of each job.1998 Academic Press

Optimal Composition Ordering Problems for Piecewise Linear Functions

“…Then the problem can be reduced to the minimum total composition ordering problem ((f i ) i∈[n] , c = t 0 ). A number of restrictions on the processing time p i (t) has been studied in this literature (e.g., [3,6,16]).…”

“…and τ : [n] → [n] denote a permutation such that τ (j) (j ≤ k) is equal to the jth σ(i) that satisfies (3). Then (τ, k) is optimal for the maximum partial composition ordering problem ((f i ) i∈[n] , c).…”

Single-machine scheduling with deteriorating jobs

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A Proposed United States Grand Strategy for 2015-2030

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