A Greedy Approach for a Time-Dependent Scheduling Problem
The main aim of the paper is to construct a greedy algorithm for an approximate polynomial-time solution of a single machine time-dependent scheduling problem. In the problem the processing time pj of each job is described by a function of the starting time t of the job, pj = 1+αjt, where αj > 0 for j = 0,1, 2,..., n. Jobs are non-preemptable and independent, there are neither ready times nor deadlines, and the criterion of optimality is the total completion time.
There are two contributions of the paper. Firstly, some theoretical background for proposed algorithm is presented. In this setting useful notions of signatures for a given sequence of coefficients of the problem are introduced and their properties are considered. Secondly, these general results are applied to the case of the problem when its coefficients are consecutive natural numbers.
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