Solving the problem of determining the time of work by a group of employees using fuzzy sets

Purpose of the research. The aim of the study is to develop algorithms for calculating the time to complete a task by a group of workers. The possibility of using fuzzy sets to set the time to complete the work by one employee, and the approach to setting fuzzy sets of the time to complete the work when communicating with the employee, based on optimistic and pessimistic times of work. At the same time, a new algorithm for summarizing fuzzy functions defined on different bearing sets is presented for calculating the resulting time to complete work by many workers.

Materials and research methods. The proposed algorithm is based on the idea of calculating the total task execution time for a certain value of the membership function. To calculate the time to complete the task, it is proposed to use the productivity of workers calculated from fuzzy functions of the time to complete the work. For the possibility of applying the generalization algorithm to the “clear" membership functions of the fuzzy function of the time the work is performed by a specific employee, restrictions are imposed. These functions must be continuous, monotonic and within the range take values 0 and 1. When the constraints are satisfied, the generalization procedure, defined as a search for the maximin of functions, can be represented as a search for arguments of membership functions for the same values of the functions themselves. In the case of specifying the membership unction of an individual employee in the form of a piecewise function, the generalization algorithm requires consideration only of the points at which the piecewise junctions have inflection points. After assigning a group of workers to the task, it is necessary to calculate all the inflection points of the resulting time to complete the work. For each obtained value of the membership function, it is necessary to calculate the total productivity of all employees. The result is a piecewise membership function of the fuzzy productivity function of all the workers assigned to the task, from which we can calculate the membership function of the fuzzy function of the task execution time.

Results. The procedure for setting fuzzy sets of task execution time for each individual employee is considered. A new algorithm for calculating the time to complete a task by a group of workers using fuzzy sets is proposed. For the proposed algorithm, a mathematical apparatus has been created for the procedure for generalizing fuzzy functions defined on various bearing sets. The paper provides a detailed analysis of the proposed generalization algorithm for two workers with different membership functions of the time of the work. In addition, with the help of software, the problem of determining the time to complete the work was solved when solving the problem of compiling teams of programmers (35 programmers) during the development of a software product (broken down into 15 tasks). At the same time, the assignment problem had to be solved manually.

Conclusion. The proposed approach makes it easy enough to calculate the generalized time to complete the work, but also requires further research. Basically, research is required that would allow for a defazification procedure or a decision support system based on fuzzy criteria. Studies related to the replacement of piecewise function by another monotonic, continuous function are also possible.

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