On Johnson's Two-Machine Flow Shop with Random Processing Times

Abstract

A set of n jobs is to be processed by two machines in series that are separated by an infinite waiting room; each job requires a (known) fixed amount of processing from each machine. In a classic paper, Johnson gave a simple rule for ordering of the set of jobs to minimize the time until the system becomes empty, i.e., the makespan. This paper studies a stochastic generalization of this problem in which job processing times are independent random variables. Our main result is a sufficient condition on the processing time distributions that implies that the makespan becomes stochastically smaller when two adjacent jobs in a given job sequence are interchanged. We also give an extension of the main result to job shops.

Minimize presentation lag by sequencing media objects for auto-assembled presentations from digital libraries

“…The objective is to find a schedule that minimizes the expected makespan E(C max ). Such a case with exponentially distributed process times has been shown to be in general tractable with a complexity O(n log n) [108,8,24,60]. However, in multimedia delivery applications over the Internet, a typical probability density function for the end-to-end bandwidth is in general inverse bell-shaped [47].…”

An aggregation procedure for simulating manufacturing flow line models

“…Systems of this type are widely used in industry to represent situations in which parts arrive at a service area, obtain the service they require, and then move on to the next service area or leave the system. Flow line manufacturing systems have been widely studied in operations research as serial, series or tandem queueing systems [see references [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

An Improved Harmony Search Algorithm for the Distributed Two Machine Flow-Shop Scheduling Problem

“…The two machine flow-shop scheduling problem has been widely studied during the past few decades [1][2][3][4][5][6][7][8][9][10]. Recently, the distributed shop scheduling has attracted more and more attention [11][12][13][14][15][16][17][18], which is considered under the globalization environment to improve the production efficiency and economic benefits in the multi-plant companies.…”