Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences

Solving a permutation problem by a fully polynomial-time approximation scheme

“…Applying the matrix approach (Gawiejnowicz et al [2,3], Gawiejnowicz [1]), the problem (P ) can be formulated as follows: . .…”

“…We complete the section by a result that is an application of formula (1). 2,3]). Let a ↑ = (a 1 , a 2 , .…”

“…where S − (a) M (a) − M (a) denotes the so-called signature (we refer the reader to Gawiejnowicz et al [2,3] for details). We complete the section by a result that is an application of formula (1).…”

Structural properties of time-dependent scheduling problems with the l norm objective

“…Though such schemata have been proposed for single-or two-machine problems with p = 1 (see, e.g., Gawiejnowicz et al [14], Ocetkiewicz [25], Woeginger [32]) or for closely related problems with p = +∞ (see, e.g., Ji et al [18]), no such schemata are known for p > 1. Similarly, though there are known heuristic algorithms for single-machine problems with p = 1 (Gawiejnowicz et al [11], Mosheiov [24]), they were not proposed for p > 1.…”

“…Problem (P p ) can be concisely formulated using a matrix approach introduced and developed by Gawiejnowicz et al [10,11], in which schedules are expressed in terms of vectors and matrices. Let C(a) = (C 0 , C 1 , .…”