# Minimum-Energy Scheduling of Flexible Job-Shop Through Optimization and Comprehensive Heuristic
## 1 Introduction
### The Adopted Approach to Tackle a New Instance of a Job-Shop Scheduling Problem  
Considering this literature review and the adopted assumptions of the current study in Section 2, the scheduling problem treated in this study characterizes a sub-class of minimum-energy flexible job-shop scheduling problems for which, to our knowledge, until today, no specific study has been published. The specific characteristics of this problem include the following:* Release and due time constraints are considered for each job instead of the make-span, which is an objective to be minimized. This differentiates the current problem from, for example, [3; 22; 23; 24; 25; 26; 27; 28].
* Contrary to all the references consulted, the structures of the jobs are not limited to a mere sequence of activities and allow us to consider complex assembly and de-assembly operations.
* The delays and energy consumption resulting from product transfers between machines are considered. The only reference that considers transfer delays is [26]. However, transfer energy is not considered there.
* The adopted mono-criterion objective function. All the references cited in our literature review for flexible job shop scheduling consider the energy issue, except [3; 28], which formulate a multi-criteria optimization problem.  
The field of scheduling in industrial production workshops is all the more varied as numerous constraints specific to each realistic situation lead to problems for which different and often new resolution methods and associated algorithms must be developed. The philosophy adopted in this study to deal with a new scheduling problem, as is the case here, is the following:  
* First, precisely mathematically formulate the optimization problem and analyze the feasibility of its resolution as a MILP problem using exact standard methods.
* Second, analyze the conditions for implementing a scheduling solution in a dynamic environment. This generally leads to considering the use of approximate resolution methods. At this stage, the generation of a heuristic appears interesting for several reasons: it allows us to obtain, at reduced computational cost, a feasible solution, and it supposes the identification and understanding of relatively simple decision-making mechanisms that can produce acceptable solutions. Heuristics that have been developed for scheduling problems with some common characteristics can be a source of inspiration for its design, and the resolution of their blocking points can be a start for the new heuristic. Once the heuristic has been developed, its performance must be compared with those obtained using exact methods and basic scheduling rules such as priority rules.
* Finally, in the case where it looks interesting to go beyond the performance of the solutions provided by the heuristic, in general by considering the use of metaheuristics (which are much more computation intensive in time and memory than heuristics), the generated heuristic method can be useful. It can provide a starting solution for an available metaheuristic. When a new metaheuristic has to be developed, the heuristic can also give directions for the design of new search mechanisms in the construction of more efficient solutions, or it can even be embedded in the metaheuristics.