In the modern industry, production systems play a very important role. The world’s population increases rapidly, which causes a growing demand for products. In order to satisfy this demand and compete successfully with the providers of similar products, each industrial company should carefully design its production system. It is necessary to create such a system that will be effective from the following perspectives: investment cost, operational cost, quality of manufactured products, flexibility and productivity. A production line is one of the most frequently used types of production systems since the epoch of Henry Ford, especially in the field of mass production. A production line consists of (work)stations aligned sequentially. These stations are equipped with machines performing a given set of operations on a semi-product that moves from one station to another in one direction. Human operators can also be assigned to a workstation.
Here, we concentrate on the decisions about the number of stations and the assignment of operations to them. Having too many stations in a line usually increases its total cost. Therefore, in order to reduce the costs we should have as few stations as possible. The productivity of a line, or, in other words, the number of products manufactured per some period of time, depends on the assignment of operations to stations. Which operations are assigned to the first station? Which operations are assigned to the second and so on? What is the sequence of the assigned operations at each station? A good assignment allows not only to increase the line’s productivity or to reach its desired level, but also to reduce the costs. The research is motivated by the case of a machining line that has to be designed to produce parts of several types. Machining means a process of material removal from a semi-product. Each station of a machining line is equipped with a single multi-spindle head where rotating tools such as borers, milling cutters, grinding heads and chamfering mills are mounted to perform operations required for all part types. When a part of a certain type arrives at some station and there are operations to be performed at this station for this specific part type, the station is activated and the required operations start simultaneously.
The station activation includes cleaning the working zone, loading, positioning and unloading of the part. It induces a cost associated with energy, equipment maintenance and labor. Logically, the less times stations are activated the better. It leads to the idea that operations related to a specific part should all be assigned to the least possible number of stations. In reality, it is not that simple. We have a production line that at the same time manufactures several part types. Some operations are common for different part types, some are not. We have to assure that the technological sequence of operations is satisfied for a specific part type. We must verify that incompatible tools are not mounted at the same station. Finally, we must assure that operations which for some technical reasons have to be executed at the same station are indeed assigned to the same station. The problem studied has to objectives. The first one – minimize the number of stations. The second one – minimize the total activation cost. The two objectives are considered in a lexicographic order. It means that first of all we search for the minimal number of stations. Then, for this found number of stations, we minimize the total activation cost.
We developed a solution approach, which combines integer linear programming with heuristics algorithms. In other words, we used a mixture of methods that guarantee an optimal (the cheapest, the best) solution, but usually require a high computational time, with the methods that do not guarantee the optimality, but provide a good solution within a small computational time. Our experiments showed that this approach was able to solve instances of practical sizes of up to 80 operations per production line.