An Improved Algorithm for Scheduling Jobs on Identical Machines

Decomposition and hybrid simulated annealing heuristics for the parallel-machine total tardiness problem

“…The generalized SPT sequence is uniquely optimal for P/ /C V ; therefore, it yields a sequence of job completion times that satisfy (1) and (2). Because SPT coincides with EDD, it also yields a sequence with ordered due dates; therefore it yields a minimal total tardiness sequence according to inequality (3).…”

“…The application of KPM to the 15-job problem of Ho and Chang [10] yields the job sequences (7,15,3,1,12,9) and (14,5,8,6,10,13,4,2,11), respectively, on the two machines with ͚ 15 iÅ1 T i Å 162, which is an improvement over the TPI solution of Ho and Chang. Koulamas [11] tested his KPM heuristic extensively against all other heuristics for P/ /T V available at that time (namely the WI, DS, and TPI heuristics) and concluded that KPM easily outperformed all other heuristics.…”

“…Elmaghraby and Park [8] developed a branchand-bound algorithm to minimize some penalty functions of tardiness, when processing times and due dates are the same for each job. An improved algorithm for this case was proposed by Barnes and Brennan [2].…”

Heuristics for Unrelated Parallel Machine Scheduling with Secondary Resource Constraints

“…Elmaghraby & Park (1974) proposed a branch-and-bound algorithm to minimize some penalty functions of tardiness. An improved algorithm for this case was proposed by Barnes & Brennan (1977). Dogramaci (1984) developed a dynamic programming procedure to minimize total weighted tardiness.…”

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

“…Interestingly, all exact algorithms for TWCT in the parallel machine environment are limited to identical machines up until 1999. These include the branch-and-bound (B&B) algorithms of Elmaghraby and Park (1974), Barnes and Brennan (1977), Sarin et al (1988), Belouadah and Potts (1994), and the dynamic programming techniques of Lawler and Moore (1969), Lee and Uzsoy (1992). Unsurprisingly, these papers have very limited success in solving instances of any meaningful size -clearly partly due to the lack of powerful computers back then.…”