Minimizing flowtime subject to optimal makespan on two identical parallel machines

Abstract

We consider the problem of scheduling jobs on two parallel identical machines where an optimal schedule is defined as one that gives the smallest total flowtime (the sum of the completion time of all jobs) among the set of schedules with optimal makespan (the completion time of the latest job). Utilizing an existing optimization algorithm for the minimization of makespan, we propose an algorithm to determine optimal schedules for this problem. We empirically show that the proposed algorithm can quickly find optimal schedules for problems containing a large number of jobs

Sheet-Metal Shop Scheduling Considering Makespan and Flow Time Criteria~!2009-06-01~!2010-05-12~!2010-06-22~!

“…Constraints (6) and (7) ensure that a sheet is only processed when its predecessor is finished. Constraint (8) calculates the makespan for the batch of sheets. Constraint (9) ensures that every workpiece is included on a sheet and hence produced.…”

“…Solution approaches for standard problems related to the problem considered in this article have already been suggested. Gupta and Ho [8] consider the parallel machines problem for finding an optimal schedule with the smallest total flow time among the schedules with optimal makespan. Bagga and Bhambani [9] propose a simple procedure for obtaining the sequence that minimises total flow time subject to minimum makespan in the flowshop problem.…”

Design of a Hyperheuristic for Production Scheduling in Job Shop Environments

“…Currently, the use of hyperheuristics in the processes of production scheduling and programming in Job Shop environments has not been widely spread [4]. However, there are some hyperheuristics based on methodologies such as heuristics [5], algorithms [6][7][8][9][10], genetic algorithms [11][12][13][14], intelligent particles [15][16][17][18][19], ant colonies [20], immune systems [21], and others [22][23][24][25][26][27][28].…”