A special class of scheduling problems is studied in this paper, named Hybrid Flowshop, n jobs have to be performedin a shop and each of them has the same routing (so this is a flowshop). A job consists in k different operations. A set of machines are able to perform each operation and thisset is called a stage. So when a job consists in two operations,there are two stages in the shop. After introducing the scheduling generalities, we define our preocupations and we propose a notationin order to identify precisely and rapidly a problem. Then a state of the art is proposed and presented in two parts. The first one is dedicated to the 2-stage hybrid flowshops and the second to thegeneral case of the k-stage. Then a summary puts to the fore that many problems remain unsolved.

We propose a temporal decomposition approach for the one-machine schedulingproblem with ready times and due dates. A set of feasible schedules ischaracterized by means of constraint-based analysis rules. They permit thedetermination of the feasible locations of each task in a sequence, representedby rank intervals. A decomposition procedure based on comparisons of rankintervals is developed in order to group tasks to be sequenced in theneighbourhood of each other in a feasible solution. Computational results are reported so that the capability of our approach to prepare the problem for a solution computation, achieved either by a human operator or by an automatic solving procedure, can be evaluated.

Constructive heuristics for shop scheduling problems are often based onpriority (or dispatching) rules. However, recent work has demonstratedthat insertion algorithms that step by step insert operations or jobs into partial schedules usually clearly outperform priority rules.In this paper, we consider various job shop scheduling problems withsetup times. For each job a specific technological route and a releasedate are given. Moreover, the jobs are partitioned into groups. Asequence independent setup time S rj is required on machine j when a job of the r-th group is processed after a job of another group. We consider different types of job availability, namely item and batch availability. As objective function we use both regular and nonregular criteria. For such problems we apply insertion techniquescombined with beam search. Especially we consider different insertion orders of the operations or jobs. A refined variant of the insertion algorithmis presented, where several operations are inserted in parallel. The proposed variants have been tested on a large collection of test problems and compared with other constructive algorithms based onpriority rules.