Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines

Abstract

We give a polynomial approximation scheme for the problem of scheduling on uniformly related parallel machines for a large class of objective functions that depend only on the machine completion times, including minimizing the l p norm of the vector of completion times. This generalizes and simplifies many previous results in this area.

A unified view of parallel machine scheduling with interdependent processing rates

“…A variety of results have appeared in the literature for this special case (see, for example, Hochbaum and Shmoys 1988;Alon et al 1998;Liao and Lin 2003;Epstein and Sgall 2004). However, in the case of preemptive scheduling, several papers with fundamental results can be found (see, for example, Gorczyca et al 2011;Lawler and Labetoulle 1978;Gonzalez and Sahni 1978).…”

“…Different functions f, and thus function q, with real applications have been studied in the literature (see, for example, Alon et al 1998;Epstein and Sgall 2004;Chandra and Wong 1975;Woeginger 1997). Motivated by storage allocation problems and problems of placing records on a set of drums, objective (I) with q x i = x i p was introduced (Chandra and Wong 1975; Cody and Jr Coffman 1976).…”

“…Objective function (IV) with q x i = x i has applications in the sequencing of maintenance actions for modular gas turbine aircraft engines (Friesen and Deuermeyer 1981;Deuermeyer et al 1982). Objective function (III) with q x i = x i p and q x i = max 1, x i has been studied by several researchers (see, for example, Alon et al 1998;Epstein and Sgall 2004).…”

“…Note 3 Use of different function q in Eq. ( 16) in minimization or maximization of m ∑ i=1 q(D i ) can make the problem polynomial solvable or NP-hard (see Alon et al 1998;Epstein and Sgall 2004, for good discussions for special cases).…”