Development of mathematical models and algorithms for optimizing the schedule of independent project activities

Planning is an important process for a project. The main planning processes include defining activities, planning resources, determining the duration of work, and developing a schedule. The paper examines projects with independent activities. The purpose of the study is to optimize project schedule by period. Three particular problems are considered. The first problem is to distribute activities over periods in order to achieve the maximum total effect of their implementation taking into account cost constraints in each period and the possibility of partial implementation of the activities in a given period. The solution algorithm is based on the Cost-Effect method. The validity of the proposed algorithm has been proved. The second problem deals with the distribution of work over periods with the prohibition of transferring part of the work to other periods and limitation of costs in each period. Based on the method of dichotomous programming, we propose an algorithm for solving the problem for two periods. For the number of periods greater than two, an approximate algorithm is suggested. For the case when information on unperformed activities in the course of project implementation changes, the problem of maximizing the total effect from the implementation of project activities in the current period is considered. Additionally, the effect from the implementation of a set of activities is visible after their completion and a certain effect manifests from the partial implementation of another set of activities. The effect obtained is proportional to the part of the amount of work performed. An algorithm for solving the problem based on obtaining parametric dependences of the total effect for each set of activities on the value of costs is proposed. The validity of the algorithm has been proved. Examples illustrating the application of the proposed algorithms are presented.

1. Azarnova T.V., Beloshitsky A.A. Analysis of Petri net based scheduling models. Vestnik Voronezhskogo gosudarstvennogo universiteta. Serija: Sistemnyj analiz i informacionnye tehnologii = Proceedings of Voronezh State University. Series: Systems analysis and information technologies. 2020;(3):32–42. (In Russ.).

2. Cristsbal J., Navamuel Е. An integer linear programming model including time, cost, quality, and safety. IEEE Access. 2019;7:168307–168315. DOI: 10.1109/ACCESS.2019.2953185.

3. Budiawati G., Sarno R. Time and cost optimization of business process RMA using PERT and goal programming. TELKOMNIKA (Telecommunication Computing Electronics and Control). 2019;17(2):781–787. DOI: 10.12928/telkomnika.v17i2.11792.

4. Barkalov S.A., Burkov V.N., Khodunov A.M. Maximization problems the volume of performed works in project management. Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya Kompjuternye tekhnologii, upravlenie, radioelektronika = Bulletin of the South Ural State University. Series Computer Technology, Aotimatic Control, Radio Electronics. 2019;19(2):66–76. (In Russ.).

5. Adamets D.Yu., Burkov V.N. Problems of independent work scheduling at limited time of project implementation and limited resources. Informatsionnye tekhnologii modelirovaniya i upravleniya = Information technologies of modeling and management. 2021;124(2):128–140. (In Russ.).

6. Bianco L., Caramia М., Giordani S. A chance constrained optimization approach for resource unconstrained project scheduling with uncertainty in activity execution intensity. Computers & Industrial Engineering. 2018;128:831–836. DOI: 10.1016/j.cie.2018.11.053.

7. Burkov V.N., Rossikhina L.V., Vyunov A.P., Rogovaya L.A. The optimal distribution problem for teams of specialists. Automation and Remote Control. 2019;80(1):93–101.

8. Chrusafi K., Basil K. Approaching activity duration in PERT by means of fuzzy sets theory and statistics. Journal of Intelligent & Fuzzy Systems. 2014;26:577–587. DOI: 10.3233/IFS-120751.

9. Harjanto R., Azis S., Hidayat S. The accelerating of duration and change of cost on construction project implementation. International Journal of Civil Engineering and Technology (UCIET). 2019;10(1):825–832.

10. Chu D. S., Vu Ho.N., Nguyen H.T. Management of interdependence projects portfolio. Vestnik nauki i obrazovaniya. 2020;95(17):25–36. (In Russ.).

11. Burkov V.N., Burkova I.V., Zaskanov V.G. The network programming method in calendar planning tasks. Automation and Remote Control. 2020;81(6):978–987.