Earliness-Tardiness Scheduling Around Almost Equal Due Dates

Abstract

The just-in-time concept in manufacturing has aroused interest in machine scheduling problems with earliness-tardiness penalties. In particular, common due date problems, which are structurally less complicated than problems with general due dates, have emerged as an interesting and proli c eld of research. We prove that so-called almost common due date problems, in which the due date d j and processing time p j of each j o b J j (j = 1 : : : n ) are such that d j 2 D D+ p j ] for some constant D, are structurally less complicated also. Our main contribution is an O(n 2 ) t i m e dynamic programming algorithm for the almost common due date problem with large D. The dynamic programming algorithm is interesting in its own right, since the optimality principle behind it applies to other common due date and almost common due date problems as well. 1980 Mathematics Subject Classi cation (1991): 9 0 B 3 5 .

Minimizing Makespan on Identical Parallel Machines

“…Improvement heuristics have been proposed in Finn & Horowitz, 1979;Langston, 1982;Fatemi Ghomi & Jolai Ghazvini, 1998. In addition, metaheuristic procedures have been developed in Hübscher & Glover, 1994;Thesen, 1998;Dell'Amico et al, 2008;Paletta & Vocaturo, 2011. Many polynomial time constructive approaches, having a known worst-case performance ratio, have been developed to solve P||C max (for an overview, see Cheng & Sin, 1990;Lawler, Lenstra, Rinnooy Kan, & Shmoys, 1993;Hoogeveen, Lenstra, & Van de Velde, 1997;Chen, Potts, & Woeginger, 1998;Mokotoff, 2001). The most important constructive approaches to solve P||C max are:…”

A Particle Swarm Optimization Algorithm for Scheduling Against Restrictive Common Due Dates

“…De et al 8 , proposed a greedy randomized adaptive heuristic for the unrestricted problem with different penalties to find both the optimal due date and the optimal sequence of the jobs. Hoogeveen and van de Velde 9 addressed the unrestricted SMETSP with 'almost' CDD using a dynamic programming algorithm. More about algorithms on scheduling problems involving due dates can be found in two comprehensive reviews considered by Baker and Scudder 1 and Cheng and Gupta 10 respectively.…”

Hiking in the scheduling landscape

“…The special case of unit processing times was considered by Mosheiov and Yovel [123] who developed a polynomial time exact algorithm to minimize the total weighted absolute deviation on identical parallel machines. Beyond a common due date, Hoogeveen and van de Velde [83] consider the problem with almost equal due dates and present a pseudo polynomial time algorithm for minimizing the total weighted absolute deviation around almost equal due dates. Huynh and Tuong [157] generalize the setting to having k distinct due dates and introduce a polynomial time algorithm when k is a constant.…”