On a Flow-Shop Scheduling Problem with Fuzzy Pentagonal Processing Time

Abstract

Scheduling involves planning and arranging jobs across a coordinated set of events to satisfy the customer’s demands. In this article, we present a simple approach for the flow-shop (FS) scheduling problem under fuzzy environment in which processing time of jobs are represented by pentagonal fuzzy numbers. This study is intended to reduce the rental cost of the machine in compliance with the rental policy. The fuzzy FS scheduling problem is solved without converting the processing time into its equivalent crisp numbers using a robust ranking technique and a fuzzy arithmetic pentagonal fuzzy numbers. A numerical illustration indicates that the approach is workable, accurate, and relevant.

Two‐Stage Hybrid Optimization Algorithm for Silicon Single Crystal Batch Scheduling Problem under Fuzzy Processing Time

“…Equations ( 6) and (7) represent the calculation of fuzzy completion time. Equations ( 8)-( 10) are equality constraints, where equation (8) indicates that each job can only be processed by one furnace, equation (9) indicates that each furnace can only process one job at the same time, and equation (10) indicates that the fuzzy starting time of the next batch is equal to the fuzzy completion time of the previous batch plus the time to replace the quartz crucible, and the replacement time is 2 h. Equations ( 11)-( 13) are inequality constraints, where equation (11) indicates that the actual production quantity must be greater than the order required quantity. Equation (12) indicates that the starting time variables and running time variables must be greater than or equal to 0.…”

“…However, the infuence of uncertain processing time will cause a huge social and economic impact on enterprise production, which has attracted more and more researchers' attention [8][9][10][11]. For example, Sakaw and Mori [8] frst proposed a triangular fuzzy number ranking criterion to compare the size of fuzzy numbers and applied this criterion to solve the fuzzy job shop scheduling problem.…”

“…Engin and Yilmaz [9] used a fuzzy processing time and a fuzzy due date to formulate the multiobjective hybrid fow-shop scheduling with multiprocessor tasks problem. Alharbi and El-Wahed Khalifa [10] adopted pentagonal fuzzy numbers to represent the processing time to solve the fow-shop scheduling problem under fuzzy environment. Chen [11] used triangular fuzzy number to represent the uncertainty of job processing time to minimize the maximum fuzzy completion time for the fuzzy distributed fexible job shop scheduling problem.…”

Towards a Fuzzy Approach for Optimizing Single Machine Common Due Date Scheduling Problem under Uncertainty

“…Bicakci et al [25] examined the relationship between setup time and release dates, considering the overall scheduling literature, and also proposed a new mixed-integer linear programming formulation with O(n 2 ) binary decision variables and O(n 2 ) constraints for obtaining the optimal solution. Alharbi and El-Wahed Khalifa [26] introduced a flow shop scheduling problem with a pentagonal processing time of jobs to minimize the rental cost of the machine in compliance with the rental policy. Recently, an enormous number of researchers studied scheduling problems in different environments [27][28][29][30][31][32].…”

Generalized Intuitionistic Fuzzy Flow Shop Scheduling Problem with Setup Time and Single Transport Facility

“…Uthra et al [22] discussed n-job 3-machine generalized intuitionistic fuzzy flow shop scheduling problem with transportation facility, which transfers semi-processed goods from machine 1-2 and 2-3; however, return and setup times were not considered. Recently, Alharbi and Khalifa [23] proposed a novel approach to the flow shop scheduling problem concerning processing time as a pentagonal fuzzy number. Selvakumari and Santhi [24] proposed a novel division algorithm for the intuitionistic fuzzy flow shop scheduling problem and compared it with the existing Johnson algorithm.…”