Application of the Johnson Problem to Solve Applied Problems

This article discusses the application of Johnson’s algorithm to analyze the work of a volunteer help desk and the work of an online store if the initial data for the algorithm are random numbers from a given interval. For this purpose, a program has been developed for solving the Johnson problem for modeling work, i.e. simulating the processing of applications (orders, calls), written in the Python programming language using IDE – PyCharm 2021.1, Qt Designer and PyQt5, in which the processing time of applications is a random variable from a given interval. The analysis of the results obtained allows us to make recommendations on the number of applications that the service system can process if the processing time is random, but belongs to a given interval, as well as predict the waiting time for applications to arrive.

1. A. Korbut and Yu. Yu. Finkelstein “Discrete programming” Moscow: Nauka, 1969.
2. Kofman “Introduction to applied combinatorics” Moscow: Nauka, 1975.
3. Kormen, C. Leiserson, R. Rivest “Algorithms: construction and analysis 2nd ed.” Moscow: “Williams”, 2007.
4. M. Johnson. Optimal two – and three-stage production schedules with setup times included. P-402. Santa Monica, California, the RAND Corporation, 1953. – P. 10.