توجه به استارت آپ و خاموش شدن ناگهانی سیستم با استفاده از یک ابزار بهینه سازی - شامل یک مطالعه موردی برنامه ریزی تولید لبنی

There are many different aspects a production-planning model has to be able to handle to make a model adequate for the purpose. One aspect is the handling of start-ups and shutdowns for different processes. The production plan is likely to be changed when considering, for example, a cost connected to the start-up and/or shutdown of processes. Besides costs associated with start-ups and shutdowns, waste may be produced during the start-up and shutdown. However, there is also the possibility of carrying out soft start-ups and shutdowns or limiting the number of start-ups and shutdowns. Thus, start-ups and shutdowns have to be handled in an adequate way in models to produce reliable and accurate results. In optimisation tools, this may be dealt with by introducing certain constraints, including integers. In this paper, the implementation of alternative ways to consider start-ups and shutdowns are presented. This is done in the energy system optimisation tool reMIND, which deals with Mixed Integer Linear Programming (MILP) problems. The purpose of this paper is to show four alternatives to consider start-ups and shutdowns in optimisation models. This involves, in total, almost 50 constraints. Also, a simple dairy case study is included in the paper to visualise the effect of implementing the different alternatives to shutdowns.

There are many different aspects to consider in the production-planning process, and there are different types of models that can be used to help with different situations. Simulation tools are widely used in industry as one part in the decision-making process. Decision support also includes risk management, economic calculations and optimisation. The decision support is a part of the decision-making process, which means helping people to make good decisions by understanding and analysing the effects of all of the alternatives [1]. Simulation modelling tools may be complemented by other modelling tools that enhance the support for decisions. Mardan and Klahr [2] have shown that an optimisation tool may be a very powerful complement to a simulation tool. By combining these tools this may increase the reliability of the results, but it also enhances the possibility of finding better solutions. An optimisation tool may be used to find the optimal result and a simulation tool may be used to find out whether it is possible to run the solution in reality [3]. To further increase the advantages of using a simulation tool and an optimisation tool in combination, it is necessary to consider start-ups and shutdowns in the optimisation tool. Many of the differences in the results from the two different tools occur because of a lack of modelling start-ups and shutdowns in the optimisation tool. Even without the use of both tools in combination there is a need for optimisation tools to consider start-ups and shutdowns, to make adequate production planning. Many articles have been published on the optimisation of systems, where the costs associated with the starting up and/or shutting down of processes are considered, see for example [4], [5], [6], [7] and [8]. However, appropriate or detailed information of the type of constraints that are needed to be included in the model for representing a start-up and/or a shutdown process are missing. Furthermore, the papers consider just a start-up and/or a shutdown that is associated with a cost, and do not take into consideration any other alternatives, such as the production of waste (called “waste” in the subsequent text) when shutting down or starting up a process or a restriction in processes requirements that force the processes to start or stop slowly. In addition, neither production planning nor manufacturing industries are used as case studies in published articles when considering start-ups or shutdowns. When looking at earlier systems that have been modelled using the energy systems optimisation tool reMIND [9], scrutinising other energy systems’ optimisation tools and conducting an additional survey between companies, four different alternatives on start-ups and shutdowns have been found to be most relevant involving e.g. costs and wastes associated with start-ups and shutdowns. The purpose of this paper is to show possible ways to model start-ups and shutdowns in optimisation models. Four alternatives have been included in this paper and the corresponding constraints for each alternative are presented. Also, a simple case study is included in the paper to show how important it is to consider start-ups and shutdowns in models for production planning in a dairy. To reduce the size of the paper, only shutdown examples are included, as both start-ups and shutdowns work in the same way.

By integrating the possibility of modelling start-ups and shutdowns in an optimisation tool, the results are more reliable and production planning is more likely to be more accurate. The complement of a simulation tool to an optimisation tool will be less important in this regards. However, other issues may motivate a use of the tools in combination, e.g. modelling of production interruptions and idling of production units. One drawback of including the functionality for start-ups and shutdowns is that large numbers of constraints are needed to illustrate the start-ups and shutdowns correctly. Integers are also needed for the functionality, which might lead to longer solution times. In this simple case study, additionally between 100 and 300 integers has been included, with the lowest value corresponding to Alternative 1 and the highest corresponding to Alternative 4. The problems have a solution time of less than 1 s for almost all models. Only Alternative 1 has longer solution times, up to 17 s. However, as Alternative 1 has less integers than the other alternatives, the amount of integers is not the issue which is increasing the solution times, instead, it is the complexity of the possible solutions for the model that are influencing the length of the solution times. In general, the solution times for the case study can be regarded as moderate. The case study has shown robust solutions, as the system costs when including the shutdown alternatives, do not increase by more than 0.6% in the worst-case scenario. Regarding Alternatives 1 and 3 (soft shutdowns and limited amounts of shutdowns), it is shown that it is possible to run the process continuously with only a minor increase in system costs (less than 0.014%). Alternative 4 (a waste associated with shutdowns) gives a higher cost compared with the other alternatives, as the waste also results in costs being produced in other parts of the process. Alternatives 2 and 4 (a cost associated with shutdowns and a waste associated with shutdowns) show the same tendency of trying to reduce the amount of shutdowns as much as possible. The peaks for steam and electricity are shown for each alternative. In some of the solutions the peaks increase considerably, and some alternatives increase by almost 60%. As no cost is associated with the peaks there is no incitement to keep them low. However, this has to be considered in future analyses, but as the focus of this paper has been start-ups and shutdowns of processes, this has not been considered here.