In 1980 Miyazaki considered the weight of a job in which weight shows the relative priority over some other job in a sequencing of different jobs. After that some researchers such as Ghanshiam Das, Singh and Singhal [1981], Panwalker [1991] Sotskov, Allahverdi and Lai [2000], Chandramouli (2005) and Belwal, Mittal (2008) had considered the idea of N-job 2 machine flow shop scheduling problem wi...

Planning and scheduling problems in various industrial environments are combinatorial and very difficult. Generally, it is extremely hard to solve these types of problems in their general form. Scheduling can be formulated as a problem of determining the best sequence to execute a set of tasks on a set of resources, respecting specific constraints like precedence or disjunctive constraints (Car...

In the classical job shop scheduling problem (JSSP), n jobs are processed to completion on m unrelated machines. Each job requires processing on each machine exactly once. For each job, technology constraints specify a complete, distinct routing which is fixed and known in advance. Processing times are sequence-independent, fixed, and known in advance. Each machine is continuously available fro...

The No-Wait Job Shop (NWJS) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is given. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The NWJS problem consists in finding a schedule that minimizes the makespan. We address here the so-called Opti...

This article addresses the job-shop problem of minimizing the schedule length (makespan) for processing n jobs on two machines with sequence-dependent setup times and removal times. The processing of each job includes at most two operations that have to be non-preemptive. Machine routes may differ from job to job. If all setup and removal times are equal to zero, this problem is polynomially s...

This is a summary of the journal article (Malapert et al. 2012) published by Journal on Computing entitled “An Optimal Constraint Programming Approach to the Open-Shop Problem”. The article presents an optimal constraint programming approach for the Open-Shop scheduling problem, which integrates recent constraint propagation and branching techniques with new upper bound heuristics. Randomized r...

Scheduling problems received substantial attention during the last decennia. The job-shop problem is a very important scheduling problem, which is NP-hard in the strong sense and with well-known benchmark instances of relatively small size which attest the practical difficulty in solving it. The literature on job-shop scheduling problem includes several approximation and optimal algorithms. So ...

In this paper we consider the problem of cyclic schedules such as arise in manufacturing. We introduce a new formulation of this problem that is a very simple modi cation of a standard job shop scheduling formulation, and which enables us to use existing constraint reasoning techniques to generate cyclic schedules. We present evidence for the e ectiveness of this formulation, and describe exten...