Hybrid Job Shop and parallel machine scheduling problems: minimization of total tardiness criterion

Scheduling is a scientific domain concerning the allocation of limited tasks over time. The goal of scheduling is to maximize (or minimize) different criteria of a facility as makespan, occupation rate of a machine, total tardiness ... In this area, scientific community usually group the problem with, on one hand the system studied, defining the number of machines (one machine, parallel machine), the shop type (as Job shop, Open shop or Flow shop), the job characteristics (as pre-emption allowed or not, equal processing times or not) and so on. On the other hand scientists create these categories with the definition of objective function (it can be single criterion or multiple criteria). The main goal of this chapter is to present model and solution method for the total tardiness criterion concerning the Hybrid Job Shop (HJS) and Parallel Machine (PM) Scheduling Problem. The total tardiness criterion seems to be the crux of the piece in a society where service levels become the central interest. Indeed, nowadays a product often undergoes different steps and then traverses different structures along the supply chain, this involve in general a due date at each step. This can be minimized as a single objective or as a part of a multiobjective case. On the other hand, the structure of a hybrid job shop consists in two types of stages with single and parallel machines. That is why we propose to point out the parallel machine PM problem domain which can be used to solve the hybrid job shop scheduling system. This hybrid characteristic of a job shop is very common in industry because of two major factors: at first some operations are longer than other ones and secondly flexible factory. Indeed, if some operations too long; they can be accelerated by technical engineering but if it is not possible they must be parallelized to avoid bottlenecks. Another potential cause is the flexible factory: if a factory does many different jobs these jobs can perhaps pass through a central operation and so the latter must increase his efficiency. This work is organized as follow: firstly a state of the art concerning PM is realized. The latter leads us to a the HJS problem where we summarize a state of the art on the minimization of the total tardiness and in a second step we present several results concerning efficient heuristic methods to solve the Hybrid Job Shop problem such as Genetic Algorithm or Ant Colony System algorithm. We also deal with multi-objective