Markov Theory-based Methods For Monitoring Mold Projects

Mold is the basic process equipment of industrial production, and the level of mold production has become an important indicator which measure the level of a country’s manufacturing. Since the features of mold production is very consistent with the project, the vast majority of mold companies have adopted the way of project management for the mold production management. However, different from most of classic project formed single project management under deterministic environment, mold manufacturing projects are featured with high randomness, multi-project compete for shared resources and so on. These features make the existing project management methods are difficult to apply to the mold manufacturing project management. In addition, most of mold companies in our country are still stuck in the level of experience based subjective decision-making, which can easily lead to confusion production management, serious project tardiness and some other problems. Therefore, to improve the technical and management level of mold manufacturing enterprises, as well as the competitiveness of China’s mold manufacturing is an essential issue placed in front of us.Project management includes project planning and project monitoring two modules. Both of them are important to guarantee the successful implementation of the project. However, on the one hand, in the past few decades the research scholars are focused on the problems relevant to project planning, and lack of sufficient attention for project monitoring. On the other hand, the existing project monitoring studies were oriented to construction engineering and software development etc. classic project types, while lack of the researches oriented to mold manufacturing project. To address this problem, we mainly consider the randomness and other features of the mold manufacturing process, and to further explore the application of theory of Markov in the mold manufacturing project monitoring problems based on the existing researches. The specific research works are as follows:(1) For the problems that mold completion time is difficult to be accurately estimated due to the random reworks frequently occur during mold manufacturing, we abstract the critical path of the mold manufacturing project network as the research object, which described by a multi-stage multi-service queuing system with reworks under certain assumptions, and modeled and analyzed by using continuous-time Markov chain theory. A queue length estimation method considering the dynamic service rates was proposed, and the specified mold order’s completion time calculation formula was deduced. We also give a detailed description of four methods that used to calculate the approximate probability distributions of mold completion time.(2) For the three types of stochastic problems under the discrete time which including resources available amount uncertain, activity duration uncertain and both of them uncertain, we build a mold projects state evolution model by using discrete time Markov chain theory. Several priority rules has been input into the evolution model as projects production control strategies, which merits were judged by comparing the evolution results. Studied the curse of dimensionality problem of state space that the evolutionary model may be encountered, and proposed a filtering method based on the state transition probability threshold and duration cumulate probability threshold.(3) For the problem that the mold manufacturing projects queuing analysis model and state evolution model cannot optimize the production control strategy, we modeled the general mold manufacturing project monitoring problem by using the theory of discrete time Markov decision process. We described the optimal criterion of the proposed model and the dynamic programming value iteration algorithm to obtain optimal strategy. Then, we mainly analyze the curse of dimensionality problem of action space, and propose to dealing with it through limiting the feasible actions. On this basis, we study the project monitoring problems that do not consider activity outsourcing, and proposed an algorithm MRC based on multi-rule combinations.(4) For the problem that the constructed mold manufacturing project monitoring model is difficult to be solved, we proposed a solution based on the principle of space approximation. This solution separating the project group by using the method of resources decoupling, which greatly reducing the scale of the problem. On the basis of the construction and verification of project approximate load model, we studied the mold manufacturing project monitoring problem consider activity outsourcing, and proposed a heuristic algorithm H-SA based on activity importance indicator and outsourcing heuristic strategy.(5) For the problem that the results obtained based on the principle of space approximation may be a waste of resources, we proposed an improved solution based on the principle of space combined approximation. The basic idea of this solution is to coordinate the resources for projects might be outsourced which reduce the total project cost by reducing the unnecessary outsourcing. On the basis of this solution, we proposed an improved algorithm H-SCA. (6) The mold manufacturing project monitoring system based on Markov theory was developed, which not only can automatically generate a project group instance data or import data from benchmark instances and served as a research experiment platform, but also can communicate with the enterprise information management system and become the practical application system.In addition, we also designed corresponding computational experiments to verify the reliability of each model and algorithm proposed in this study. Through the above research and application, on the one hand a more comprehensive solution to the practical mold project monitoring problems were proposed. On the other hand the scope of application of the Markov theory had been extended. The conclusions of researches and applications related to this study can provide effective decision support for mold manufacturing projects management.