We study the two-machine flow shop problem with (minimum) delays.The current best approximation factor achieved for this problem is 11/6 ≈ 1.833 (due to Karuno and Nagamochi; their algorithm runs in time O(n log n)). Our main result is a 1.628-approximation algorithm for the case when processing times depend only on machines. This case is strongly NP-hard even when all processing times are equa...

this paper considers a two-stage assembly flow shop problem (tafsp) where m machines are in the first stage and an assembly machine is in the second stage. the objective is to minimize a weighted sum of earliness and tardiness time for n available jobs. jit seeks to identify and eliminate waste components including over production, waiting time, transportation, inventory, movement and defective...

With the popularization of multi-variety and small-batch production patterns, flexible job shop scheduling problem (FJSSP) has been widely studied. The sharing processing resources by multiple machines frequently occurs due to space constraints in a shop, which results resource preemption for workpieces. Resource complicates problems that are otherwise difficult solve. In this paper, under proc...

this study considers scheduling in hybrid flow shop environment with unrelated parallel machines for minimizing mean of job's tardiness and mean of job's completion times. this problem does not study in the literature, so far. flexible flow shop environment is applicable in various industries such as wire and spring manufacturing, electronic industries and production lines. after mode...

Genetic algorithms are a very popular heuristic which have been successfully applied to many optimization problems within the last 30 years. In this chapter, we give a survey on some genetic algorithms for shop scheduling problems. In a shop scheduling problem, a set of jobs has to be processed on a set of machines such that a specific optimization criterion is satisfied. According to the restr...

This is a summary of the PhD thesis defended by the author in September 2011 at thé Ecole des Mines de Nantes (EMNantes). The thesis was advised by Narendra Jussien (EMNantes) and co-advised by Louis-Martin Rousseau (´ Ecole Polytechnique de Montréal – Poly), Christelle Guéret (EMNantes) and André Langevin (Poly). The manuscript is written in French and can be obtained from The focus of the dis...

A two level branch and bound algorithm is developed to solve an altered form of the standard flow-shop scheduling problem modeled as a bilevel programming problem. The flow-shop scheduling problem considered here differs from the standard problem in that operators are assigned to the machines and each operator has a different time table for the jobs on each machine. The shop owner is considered...

A flexible flow shop problem can be considered as a generalization of a pure flow shop problem in which the jobs have to go through the stages in the same order. We consider a flexible flow shop problem with unrelated machines and setup times, where the processing times depend on the chosen machine and setup times are sequence-dependent. While for classical problems the processing times for eac...

In this paper, we address the problem of finding a permutation schedule of n jobs in an m machine flow-shop environment that minimizes the maximum completion time Cmax (Makespan) of all jobs. The jobs are available at time zero and have sequence-dependent setup times on each machine. All parameters, such as processing and setup times, are assumed to be known with certainty. This problem is clas...