1. Introduction
When carrying out repetitive works in building construction, workers are divided into several work teams; then, each team is allocated its individual works to proceed with a whole process relaying works to other teams. For example, one team transports a component from a stockyard to a place to be installed, then, another team receives and installs it. In this paper, the author proposes a model for representing worker allocation in a group work process and a mixed integer program model to optimize the resource allocation of a group work process, and verifies its validity using a case study.
2. Group work process
A group work process means a series of works in a specific work area, on a floor, or in a dwelling unit. To minimize the number of workers to be allocated to a group work process, workers should synchronize with their works by relaying their works to other works. In order to make works synchronize with other works, several alternatives are provided regarding the relationship between the number of workers and the duration.
3. Constraints of worker allocation planning in a group work process
For the optimization of worker allocation in a group work process, the following constraints must be taken into consideration:
(1) Precedences in a group work process
(2) Relayed works and collaborative works
(3) Assigned work process for free works
(4) Relationship between the number of workers and the duration in each work
(5) The maximum number of available work teams in an assigned work process
(6) The maximum period permitted
(7) The maximum number of workers allocated
(8) The number of iterations
The optimization has the following two objectives:
(1) To minimize the period by setting the upper limit of the number of workers
(2) To minimize the number of workers by setting the upper limit of the period.
4. Optimization of a group work process based on mixed integer programming
Here presents a modeling method using a mixed integer programming. To obtain the number of zero-one integer variables of a model, the number of works should be multiplied by the number of periods to be assigned. In order to reduce the number of variables, modeling is carried out only for the first iteration in a group work process. Then, based on the work model, the author presents constraints of mixed integer programming model.
5. Application for a case study
A case study is carried out on a group work process consisting of four assigned work processes to optimize the worker allocation planning. In a case study, the number of components is assumed to be 20, whereas the limit of the whole work period is set to be 350 minutes. As a result of modeling, the number of zero-one integer variables are 4,930, and the number of constraints are 13,934.
The mixed integer programming model was solved using SCIP. The optimization requires about 13 hours. Based on the results by mixed integer programming, resource allocation scheduling is carried out. Then, the author confirmed that it is possible to optimize the work process with the number of workers and the period in a group work process.
6. Conclusion
In a group work process, works deals with many components and usually iterates as many times as the number of the components. The method which the author presents would contribute to applying mixed integer programming to the optimization for planning of a group work process within available time range.
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