## 1 Introduction  
Industry is changing rapidly and is facing the fourth industrial revolution. In this new context, industrial systems need to be more flexible and intelligent to deal with an ever-growing data availability, real time decisions and increasing customization. With Internet of Things, which allows various objects in the company or on the shop-floor to communicate with each other, industrial systems will become more intelligent and able to anticipate shortage of materials, the need for maintenance operations or to respond to urgent commands. This will imply the use of more efficient tools for planning and re-planning shop-floor operations. Such decision support tools will be important at all decision levels: For example, at a strategic level, they can be used to decide which activities must be performed during a given planning horizon and to estimate the resources needed. At this level they can also be useful to model and test new shop-floor configurations and anticipate the impact of these changes on the system performance. Considering the tactical level, decision tools will allow to allocate resources to each activity planned to occur during a given time horizon. Finally, at the operational level they can be used to schedule the activities, determining the time allocation of each resource and to re-schedule them to respond to emergencies (new activities that have to be done as soon as possible). Table 1 summarizes the problems encountered at the different levels. In this paper, we present a hybrid optimization method to solve a lot sizing and scheduling problem encountered in a plastic injection facility that produces components for electronic products. The proposed method was first introduced in [1] and concisely used to solve optimization problems from different areas: healthcare systems, as well as textile and plastic injection industries, with promising preliminary results. In the current work, the method's application to plastic injection molding is further developed and its performance analyzed with a comparison to optimal and heuristic solutions. Injection molding can be considered as a single-stage manufacturing process where parts are produced by injecting a molten material, typically a thermoplastic polymer, like in our case study company, into a custom-made mold. In the injection machine, the material is molten, mixed and injected into the mold, acquiring, after cooling, the shape imposed by the configuration of the cavity and being then ejected. The obtained part usually have the finished shape, not requiring further operations. In general, the shop-floor is composed by several injection machines which are shared by different products necessitating different molds. A setup time occurs each time a new product has to be manufactured. This setup time consists in the time required to dismount the mold used for the previous part and to mount the new mold on the machine. Obtaining a good schedule for such a constrained problem can be a real challenge. The above described problem can be stated as follows: \(n\) jobs have to be processed on parallel machines, using their needed mold. These jobs have to be scheduled, considering their given processing time and due date before they have to be completed. When two jobs consecutively processed on one machine need two different molds, a sequence dependent setup time is recorded. Jobs have to be processed at once (non-preemptive constraint). To save setup costs, jobs using the same mold may be scheduled one after another. There are compatibility constraints between the molds and the machines: Each mold can only be assigned to some specific machines. Each mold exists in a single copy, thus the same mold cannot be used by more than one machine during the same time period. The objective is to find the suitable allocation of the jobs to the machines as well as the schedule of jobs on each machine so that minimizing the total tardiness.