Abstract
AbstractThis paper considers a bi-criteria scheduling on parallel machines in fuzzy environment which optimizes the weighted flow time and maximum tardiness. The fuzziness, vagueness or uncertainty in processing time of jobs is represented by triangular fuzzy membership function. The bi-criteria problem with weighted flow time and maximum tardiness as primary and secondary criteria, respectively, for any number of parallel machines is NP-hard. So, a heuristic algorithm is proposed to find the optimal sequence of jobs processing on parallel machines so as to minimize the secondary criterion of maximum tardiness without violating the primary criterion of weighted flow time. A numerical illustration is also given in support of the algorithm proposed.
Highlights
Scheduling is concerned with the optimal allocation of scare resources with objective of optimizing one or several criteria’s (Baker, 1974)
We study the bi-objective scheduling on parallel machines in which the problem is divided into two steps: in the primary step, the weighted flow time of jobs is calculated and in the secondary step, the maximum tardiness is minimized with bi-objective function as Tmax/WFT
The problem is divided into two steps: one is primary in which weighted flow time of jobs is minimized and in secondary step, the maximum tardiness of jobs is minimized under the objective function value of primary criterion
Summary
Scheduling is concerned with the optimal allocation of scare resources with objective of optimizing one or several criteria’s (Baker, 1974). Sharma, Gupta, and Seema (2013) developed an algorithm to schedule jobs on parallel identical machines so as to minimize the secondary criteria of weighted flow time without violating the primary criteria of maximum tardiness in fuzzy environment. Sharma, Gupta, and Seema (2012) studied the bi-objective problem with total tardiness and number of tardy jobs as primary and secondary criteria, respectively, for any number of parallel machines in fuzzy environment. We study the bi-objective scheduling on parallel machines in which the problem is divided into two steps: in the primary step, the weighted flow time of jobs is calculated and in the secondary step, the maximum tardiness is minimized with bi-objective function as Tmax/WFT. Subject to the condition that all weights for jobs are non-negative, Here, S is the given sequence and WFT(S) is the corresponding objective function of weighted flow time
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