Correct formulation of the master production schedule is critically important for the optimization of the management ofa production planning and control system. Most of the models described in the literature solve the problem in two separate sequential stages: lot sizing and then sequencing. This often produces an MPS which is not optimized or even not feasible. On the other hand, when the problem is tackled with models based on mixed integer linear programming, then dimensional constraints have to be respected which can limit the field of applications of the model itself.A complete heuristic algorithm is presented in this paper which solves the problem oflot-sizingand sequencing in a single logic stage, together with the results of an extensive series oftests carried out to compare, in different types of production systems, the performances of the proposed heuristic and those of another algorithm taken from literature. The model concerns a single production line situation with relevant setup problems; on this production line component availability constraints are not considered (the model refers to mono-level bill of material products, but it can be applied also to the most critical level in multi-levels production systems). IntroductionMany industrial sectors attach great importance to (levels of) service, flexibility and elasticity as the company's basic competitive weapons. Phenomena which tend to create a market demand which is extremely variable in time, both in terms of quantity and type of products, are becoming increasingly frequent.Thus, there is a search for solutions in terms of production planning, programming and control models (PP&C) which are both as complete as possible in terms of ability to model the problem and, also, are capable of rapidly regenerating the production schedules which have been prepared when there are modifications or variations in the marketing input. In the case of process production, the basic problems which the PP&C system has to solve relate to the lot-sizing and sequencing stages, since the stage of requirement planning is simplified by the limited number oflevels involved in the bill of materials. Therefore, the primary objective of PP&C systems is the formulation of a master production schedule (MPS) in terms of:

In an effort to push for low-carbon transition, national governments and regulatory authorities are working to define market structures and legislative frameworks able to effectively support the spreading of electricity production from renewables. To this purpose, the opening of national Ancillary Services Markets (ASMs) to Distributed Energy Resources (DERs) plays a key role. However, pricing schemes and rules in place (e.g., incentives) can act as a barrier to the supply of regulation services by small-sized and renewable-based power plants. In this context, the present work evaluates the economic opportunities for DERs provided by the provision of tertiary reserve and balancing control in the Italian ASM. The research is carried out through the collection and processing of price data from the Italian electricity and gas markets over 4 years (2019-2022). Considering a reference architecture where DER units bid on the market through a Balancing Service Provider, the potential revenues on the ASM of a non-programmable or partially programmable DER unit are compared to the earnings expected of a conventional power plant in order to highlight whether unfair competition can represent a barrier. Then, possible evolutions in the current remuneration schemes are analyzed, to evaluate whether they can be able to support a better DER integration. From the analysis, it emerges that, even if negative prices could be useful to increase the competitiveness of RES-based power plants for downward regulation, the loss of the incentives can act as a deterrent to the offering of services on the market by DERs. Therefore, other regulatory options, such as the incentives retention in case of downward regulation, could also be needed.