Scheduling independent jobs on uniform parallel machines to minimize tardiness criteria

Abstract

The problem of scheduling N jobs on M uniform parallel machines is studied. The objective is to minimize the mean tardiness or the weighted sum of tardiness with weights based on jobs, on periods or both. For the mean tardiness criteria in the preemptive case, this problem is NP-hard but good solutions can be calculated with a transportation problem algorithm. In the nonpreemptive case the problem is therefore NP-hard, except for the cases with equal job processing times or with job due dates equal to job processing times. No dominant heuristic is known in the general nonpreemptive case. The author has developed a heuristic to solve the nonpreemptive scheduling problem with unrelated job processing times. Initially, the algorithm calculates a basic solution. Next, it considers the interchanges of job subsets to equal processing time sum interchanging resources (i.e. a machine for a given period). This paper models the scheduling problem. It presents the heuristic and its result quality, solving 576 problems for 18 problem sizes. An application of school timetable scheduling illustrates the use of this heuristic.

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

“…In this work, a solution procedure is introduced beginning with the single machine problem and then extended to the general case of m machines. Alain Guinet [42] considered the problem of scheduling n jobs on m uniform parallel machines with the objective of minimizing the mean tardiness or the weighted sum of tardiness with weights based on jobs, periods or both. For the mean tardiness criterion in the non-preemptive case, the problem is NP-hard, except for the cases with equal job processing times or with job due dates equal to job processing times.…”

Hybrid Job Shop and Parallel Machine Scheduling Problems: Minimization of Total Tardiness Criterion

“…There is the work of Wilkerson & Irwin, (1979) and finally one must mention the Montagne's Ratio Method (Montagne, 1969). We can also quote works of: Eom et al, (2002), the tabu search based method of Armentano and Yamashita, (2000), the three phase method of , the neural network method of Park & Kim, (1997), the work of Radhawa and Kuo, (1997) and also Guinet, (1995). And the former work of Arkin & Roundy, (1991), Luh et al, (1990), Emmons &Pinedo, (1990) andEmmons, (1987).…”

Heuristics for Unrelated Parallel Machine Scheduling with Secondary Resource Constraints

“…Suresh & Chaudhuri (1994) presented a GAP-EDD algorithm to minimize maximum tardiness. Guinet (1995) employed a simulated annealing method to minimize mean tardiness. Randhawa & Kuo (1994) examined the factors that may have influence on the scheduling performance and proposed heuristics to minimize mean tardiness.…”