Mathematical Modeling of Manufacturing Lines with Distribution by Process: A Markov Chain Approach

Today, there are a wide variety of ways to produce goods in a manufacturing company. Among the most common are mass or line production and process production, both of which are antagonists. In an online production system, materials move from station to station, receiving added value on a well-defined layout. In a production line by process, the materials randomly visit a set of machines strategically located in order to receive a treatment, almost always through metalwork machines, according to the final product of which they will be part. In this case, there is not a predefined layout, as the incoming materials are sectioned and each piece forms a continuous flow through different workstations to receive some process. This activity depends on the function of the product and its final destination as a component of a finished product. In this proposal, Markov chain theory is used to model a manufacturing system by process in order to obtain the expected values of the average production per machine, the total expected production in all the facilities, the leisure per machine and the total productive efficiency of the system, among other indicators. In this research, we assume the existence of historical information about the use of the equipment, its failures, the causes of failure and their repair times; in any factory, this information is available in the area of manufacturing engineering and plant engineering. From this information, statistical frequency indicators are constructed to estimate transition probabilities, from which the results presented here are derived. The proposal is complemented with a numerical example of a real case obtained from a refrigerator factory established in Mexico in order to illustrate the results derived from this research. The results obtained show their feasibility when successfully implemented in the company.