It all began with an idea from Torgny Almgren, Adjunct Professor at Mathematical Sciences. With one week left to deadline he contacted Michael Patriksson and Ann-Brith Strömberg and suggested that they should apply for an industrial doctoral student project grant from the Swedish Research Council, with the goal of scheduling multitask machines within reasonable time using mathematical modelling. He also had a suggestion of a possible person if the project would be granted: Karin Thörnblad, an engineer at the logistics function at GKN. Said and done, the application was written in record time, Karin was asked, and when the application was granted they went ahead.

The result was the PhD thesis Mathematical Optimization in Flexible Job Shop Scheduling: Modelling, Analysis, and Case Studies. In the thesis an iterative scheduling algorithm is launched, solving a time indexed optimization model with shorter time steps at each iteration, and where a new schedule may take at most 15 minutes to be produced. The most common goal of scheduling in academia is to “minimize makespan”, i.e., the time schedule from start to finish should be as short as possible. That does not work so well in a reality where the production is dynamic and continuous, in the way that new products are arriving all the time, so Karin’s goal function is instead a weighted sum of all the jobs’ finishing times and delays. In this way the overall goal to produce all the products in the right time is promoted.

The model was however not implemented in the production cell where Karin had made her case study. There would have to be design changes in the control system, and when it was decided that only one type of product would be produced in the cell in the future, the utility was considered to be not as great anymore. Instead, some months after the thesis defence the head of the heat treatment department contacted Karin. The prognosis for the department’s workload showed that they would have difficulties meeting their future production demand, despite the purchase of a new furnace. Maybe they could make better use of the furnaces?

Karin started with a pilot study. All sorts of products come to the heat treatment, both from the other departments and from external customers. It was a more complex case than the multitask cell, so she needed to develop her mathematical optimization model, which got the name SOLV (Schema Optimalt Lagt i Värmebehandlingen, or schedule optimally placed in the heat treatment). It did not only need to produce the desired results, but to do so within reasonable time. The first tests looked promising, whence the steering group decided to implement SOLV, and two IT engineers reinforced the project team in order to help automate the system. The hardest nut to crack was to find good sequences, as some operations demand a bake-out of the furnaces at high temperature during a long time. If the temperature of a brazing operation needs to go up, a bake-out is needed, otherwise not.

On November 3, 2015 the new scheduling model began to run at full speed. All operators have been trained, and a new schedule for the coming 24 hours is produced every morning before 9 o’clock. It takes between 3 and 15 minutes, depending on how many brazing operations (which may demand a bake-out) that are listed. During the first six months that SOLV was used the utilization of the furnaces increased by 7% on weekdays and 25% on Sundays, while queuing times and delays were reduced. But the effect is really much greater than that: is has enabled a product shift from short-term jobs to more complex and lengthy jobs. The effect can also be expressed as that the saved time for bake-outs and vacuum tests is 2300 hours, the capacity increase is 2700 hours, and the energy saving is 250 MWH, based on one year.

Next, it was the CMM (Coordinate Measuring Machine) centre of GKN who needed help. Their machines measure surfaces, evenness, length and thickness on products with the help of measurement probes. This was an easier problem from a mathematical point of view, but still more difficult to implement since it was not possible to obtain as much data for the computations. After having adapted the model for a few months the CMM centre could start for real at the turn of the year. And Karin continues: in March she begins a pilot study at the department of thermal spraying, where they mask, blast and spray a coat of heated or melted powder on product surfaces. For each product there is at least three moments and these take different time for different products. The introduction will take place during the autumn and the model has continued to be called SOLV, as it has now become an established concept.

– Common for all these three departments is that they are common resources – they serve the whole company and they also take external jobs. The planning situation is therefore rather messy. But I think we can benefit from the model and the algorithm on all bottleneck resources. It is also clear that success depends on many different things: the implemented algorithm is really good, but that would not have been sufficient. Now, managers and master planners were positive and understood what the work entailed, IT resources were available, good input data were secured, and there was a persistence in fixing flaws. That I was at the company both before and after the implementation and was able to speak the right language also played its part.

Eventually Karin hopes to be able to “productify SOLV” by cooperating with the IT department of GKN. Currently, each department needs a special mathematical model that is hard-coded for their particular planning case. If the optimization model instead is divided into several parts where some parts are common and some are department-specific, a programme can be created which for some parts is generic (for example input data interface) and for some parts specific, even if some manual work always will be required. Increased reliability, safer databases and faster interfaces are also on the wish list.

– You can also do more with the algorithm itself, if you have time to delve into the mathematics. Basically it is common plain integer linear optimization with an iterative solution procedure, the new about it is how you use it in practice and the integration of the model in an iterative solution procedure. Unfortunately, few people make use of mathematical optimization, instead genetic algorithms are spread – a kind of random process – just because it is easy to start such calculations. But these simplified methods often solve the wrong problem, and you have no idea how close or far from the optimal solution that you really get, Michael Patriksson concludes.**Text**: Setta Aspström**Photos**: Michael Patriksson, Karin Thörnblad and Ann-Brith Strömberg, Setta Aspström

Heat treatment furnace at GKN, Jukka Lamminuoto

Schedule produced by SOLV, Karin Thörnblad