## 2 Materials and Methods
### Project Scheduling Problems--The Overview
#### 2.1.2 Schedule Optimization for Multi-Unit Construction Projects  
The problems of planning the execution of construction works are analyzed using various theoretical models. These models are usually of a deterministic or random approach. The most common methods of planning construction work (scheduling projects) are, e.g., CPM/PERT network planning (Critical Path Method/Program Evaluation and Review Technique) [37], Line of Balance (LOB) [1], methods based on LOB, such as the LSM (Linear Scheduling Model) or RSM (Repetitive Scheduling Method) [2], and Time Couplings Methods TCM [38]. Network planning is usually used to schedule construction projects that are unique, for example large-scale buildings (residential, service, or industrial). The second group of methods based on LOB is intended for scheduling repetitive projects. Repetitive projects are characterized by the possibility of their clear division into parts (units), which may be individual working plots of the building (work zones), individual floors, entire building structures or sections of buildings with specific lengths, e.g., linear construction projects. Examples of such projects are multi-story buildings, estates consisting of single or multi-family houses, pipelines, and roads. In each part of a given repetitive project, specialized work crews carry out dedicated activities as they move from one part of the previous venture to the next [39]. Among the repetitive projects, a special group can be distinguished, which consists in the implementation of many similar buildings. Such projects are referred to in the literature as multi-unit projects. The flow shop theory of scheduling is used in order to describe and solve such problems [40]. Flow shop scheduling is a special case of job-shop scheduling in theory of scheduling where there is strict order of all operations to be performed on all jobs. Flow shop scheduling may apply as well to production facilities as to computing designs. The current research on multi-unit projects focuses on the continuous improvement of the theoretical models. In article [41], a model of scheduling a multi-unit undertaking consisting in the implementation of many production halls was presented. The costs of works and directive deadlines for completion of works have been established for each unit. Penalties were charged for exceeding these deadlines. The task was to find the optimal order of execution of the halls, which would minimize the total cost of the project, including penalties for exceeding the directive deadlines. This task was solved using the metaheuristic scatter search algorithm. In [42], the NP-difficult problem of scheduling a construction project was considered with the criterion of the sum of penalties for exceeding the deadline for building construction. The parameters of this project were represented by fuzzy numbers or random variables with a normal distribution or the Erlang distribution. In [43], a scheduling model was presented with the possibility of performing one type of work by more than one working group and with sequence relationships given by any graph. The optimization task in this model was solved using the tabu search algorithm. In [44], the scheduling model for a multi-unit project assumes a linear relationship between the time and the cost of carrying out the activity. The criterion of minimizing the total value of the project cost determined on the basis of the mathematical programming model, taking into account direct and indirect costs, costs of missing deadlines and costs of workgroup discontinuities. The optimization task in this model was solved using the modified simulated annealing algorithm. In the paper [45] the author presents a model of a multi-site enterprise, in which he minimizes downtime during work to maintain the continuity of work of working groups. Additionally, he minimizes both the time and penalties for exceeding the deadlines for completion of works in the facilities.