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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.20 No.4 pp.672-677

Financial Resource Multi Project Scheduling using Evolutionary Algorithm

Budovich Lidia Sergeevna, KulikovaNatalia Nikolaevna, Varfalovskaya Victoria Viktorovna*
Department of Economics and Innovative Entrepreneurship, Faculty of Economics and Law, MIREA - Russian Technological University (RTU MIREA), Moscow, Russian Federation
*Corresponding Author, E-mail:
September 10, 2021 September 12, 2021 September 27, 2021


Financial resource supplying and its management is considered a main issue in the project management by considering the optimization process. Organization of the formation and management of financial resources is necessary for the effective operation of enterprises. Measures to improve the management of the financial system should be carried out continuously. This will contribute to the achievement of the priority goals of the enterprise. This requires an assessment of the current state of the issue in question. Various sources of formation of financial resources of the enterprise are considered. The authors pay special attention to their own and borrowed funds. The ways of increasing the use of own and borrowed funds are considered. The article has developed a methodology for choosing financing methods. A correctly chosen financing policy contributes to an increase in the efficiency of all enterprise activities. Due to the application of evolutionary algorithms in solving complex problems, this algorithm has been used to solve the proposed mathematical model in financial resource multi project scheduling. The results show that the proposed algorithms are able to solve the existing complex integer linear programming model with a high number of nodes and different complexity coefficients in a short time.



    The making of managerial decisions aimed at improving the efficiency of using financial resources is the result of a step-by-step analysis followed by the identification of problems that reduce the effectiveness of financial management. There is no doubt that, for the particular enterprise, these decisions can be completely different, aimed at a qualitative change in the particular sphere of financial resource management that needs changes (Chen et al., 2019).

    Resource-constrained multi-project planning can be defined as the scheduling of project activities with attention to resource limitations and precedence relationships between those activities in such a way as to reach the best possible outcome in terms of an objective function (e.g. minimizing project completion time, delay, and execution costs) (He et al., 2021). Finance resource in the development strategy and the application of the optimization has been reviewed in the literature review (Liu et al., 2021). Resource-constrained multi-project scheduling problem is an extension of finance resource multi project planning for the simultaneous scheduling of multiple projects. It is useful for those businesses and organizations that have multiple projects in their portfolio and need to make scheduling decisions for all of them simultaneously.

    The critical route method is mainly used to schedule projects. This method helps the project executives in managing the execution time and the amount of budget required for the project. The critical path method provides useful information such as critical path (s), buoyancy time for non-critical activities, and total flow that are necessary for project planning (Munawir et al., 2021;Nisztuk and Myszkowski, 2019). Đumić et al. (2018) have provided a category for the finance resource planning in multiproject management. Wang et al. (2019) claimed that resource leveling issues are exacerbated to minimize fluctuations in resource consumption over time. In a study by Sergeevna and Yurievna (2021), they have discussed minimizing resource consumption fluctuations plays a major role in reducing the additional costs of repeated resource allocation. To level the resources, the actual start time for each non-critical activity and the amount of consumption of each resource in the whole network structure is determined. Teylo et al. (2017) have studied and compared the variety of optimization models that can be used for finance resource planning.

    A hybrid method based on genetic algorithm and ant colony optimization has been used to level multiple sources. The proposed method is then compared with some traditional resource leveling methods based on standard data series (Zhang et al., 2021;Ershov, 2018;Roozitalab and Majidi, 2018). In traditional planning, it was customary to treat project scheduling and resource procurement as separate issues, first schedule the activities, and then make ordering and procurement decisions accordingly. However, this approach overlooks the potential interactions between these decisions.

    The integration of resource-constrained project scheduling and resource ordering is especially useful for construction projects, where activities require labor resources as well as materials. In cases where materials are produced in a factory and need to be collected at the project site, coordinating project schedules with material production plans can lead to reduced costs, better access to resources, and shorter execution time. In this regard, El-Abbasy et al. (2017) present a fuzzy model and an exact solution method for scheduling and resource leveling. The exact solution provided by them has significantly reduced the solution time.

    The proposed method, in addition to solving the common challenges arising from the normalization and weighting of objective functions, using quasi-criteria instead of criteria, provides the possibility of considering ambiguity or uncertainty in resource consumption. The structure of the proposed model is designed to fit the actual conditions of the projects.


    The goal is to minimize the costs of simultaneous project scheduling and equipment scheduling by determining the optimal amount of activity time, activity completion time, and equipment scheduling. Considering the limitations.


    • Project activity index J = 1, .., N

    • Index of equipment used in the project i = 1, .., M

    • Time indicator t = 0, …, H

    • The earliest time to complete the activity, e

    • Overtime cost of employees, COi

    • The cost of transporting equipment, Sijk

    • Project delivery date, d


    Evolutionary algorithms is a method introduced in 1970 for solving complex problems, which has also been extended for integer problems. A detailed description of the basic concepts and principles of this method can be found in (Chaleshtarti et al., 2020;Mandych and Bykova, 2019.). This method has also been used to solve project scheduling problems. For example, Chaleshtarti et al. (2020) have used this method in combination with a genetic algorithm to solve a resource-constrained project scheduling problem with nonrenewable resources

    In this method, complex constraints (i.e. constraints that increase the complexity of the problem) are removed from the original problem and transferred to the objective function with the help of weighting coefficients (u). This process produces a relaxed problem that is simpler than the original problem. In the minimization (maximization) problems, the optimal solution of the relaxed problem is the lower bound (upper bound) of the solution of the original problem. In the evolutionary algorithms of this study, the constraints related to work resources are relaxed. To obtain multiobjective by weighted summation approach the function is considered as equation 1.

    M i n i m i z e [ J = 1 N [ b j c j ( Z j v j ) ] + i = 1 M G i ( j Y i N j 1 + j Y i N j 2 ) ] + i M j k S i j k . Y i j k + i M j k C I i . I M k + i = 1 M C o i . T o i + t i = 1 H 1 s W i t = e N d 1 r ( d t ) δ N t

    In this equation, δNt denotes the weighting coefficients of the corresponding constraints. One important challenge in this method is how to find the optimal value of weighting coefficients. One of the methods commonly used for this purpose is the Subgradient Optimization (SO) algorithm. The main problem with using this algorithm is how to find the step size (st) that guarantees the algorithm converges to the optimal solution. To overcome these challenges, this study uses a combination of evolutionary algorithms, which is henceforth called the LR algorithm.

    The research methodology involves several stages before the enterprise makes the final management decision on the rational type of financing.

    It is possible to can be guided by factors when choosing financing options:

    • - availability of financial resources;

    • - funding objectives;

    • - profitability of the project and payback period.

    In a quantitative analysis, it is necessary to calculate all the costs of the enterprise and draw up a schedule. All direct and indirect costs associated with cash flows for each financing option must be calculated. Commercial benefit is the basis when choosing a financing option Therefore, a qualitative analysis of the comparison of alternative financing options is the second step. Selection criteria need to be determined. The selection criteria must be meaningful and comparable. In order to evaluate the implementation of the proposed algorithms, the computer program was coded with MATLAB and then applied to 60 experimental problems as presented in Table 1.

    It is possible to can give non-price factors an assessment methodology for a comparative analysis between credit and leasing for the purchase of equipment: liquidity; obsolescence risk of equipment; need for collateral; sources of payment; the period of unprofitable work; payment option; forms of payments; impact on the balance; service maintenance of equipment; features of the contract. It is necessary to determine the significance of each factor.

    The previous stages will be intermediate. At the fourth stage, the manager conducts an analysis based on the table of expert assessments. Experts are employees of the enterprise (financial director, chief accountant, commercial director) or external experts. The table for drawing up expert assessments is shown in the Figure 3.

    Validation of model and solution method

    An enterprise needs financial resources for the development of production, consumption of a nonproduction nature, reservation, development and maintenance of the non-production sphere.

    An enterprise can allocate financial resources using its own (external and internal) and borrowed sources of financing (Chen et al., 2017).

    Types of enterprise financing policies:

    • - the self-financing policy is aimed at using the company's own external and internal funds (profit after tax, owners' funds, etc.) (Zyabkina et al., 2021);

    • - financing policy focused on borrowed resources. Such financing is typical for enterprises in which the return on assets significantly exceeds the interest rate on borrowed capital (Kuchinsky and Troshanina, 2014);

    • - mixed financing policy: own and borrowed financial resources are used.

    The financing policy is applied differently depending on the development of the enterprise

    Factors influence the choice of the type of financial policy (Figure 2).

    The growth of the company's profit is one of the main factors in increasing the efficiency of both the entire business activity and its various aspects, including the sphere of managing its own financial resources.

    This paper considers both project scheduling and equipment scheduling at the same time, in order to minimize the costs of activity compression, maintenance, rewards for delays, and fines for delays, transportation, equipment preparation, equipment unemployment costs, and operator overtime. For the first time, a multiobjective constrained algorithm was proposed. As shown in Figure 3, for all problem instances, the optimal solution of the mathematical model is has an acceptable level of accuracy. The numerical results obtained from the proposed algorithms also show acceptable optimality and feasibility distances and indicate that they can be applied to real-world issues.


    Project planning and scheduling is one of the most important issues faced by project managers and is one of the key factors in the success or failure of the project. Sources of financing for the enterprise activities can be own (profit) and borrowed. Each type of financing assumes: purpose of use, term (short-term, medium-term, long-term); quantity. In order to forecast the amount of own sources of financing, it is necessary to research the factors that can affect the growth of profits. Moreover, an important task is to attract sources of borrowed funds. Therefore, in the framework of the analysis aimed at assessing the effectiveness of using financial resources of a commercial enterprise, it is necessary:

    • - to study the composition, dynamics and structure of sources of refinancing and their use;

    • - to study the financial results and performance indicators of the enterprise;

    • - to study the financial stability and liquidity as key indicators of the financial condition of an enterprise that affect its performance and efficiency;

    • - to determine the type of financial policy of the enterprise.

    Based on the results of the analysis and identification of problems of financial management, the company should determine the possible ways to improve the efficiency of their use. These can be a wide variety of actions. In most cases, ways to improve efficiency depend on the financial policy chosen by the organization; it also determines the choice of financial instruments that, in one case or another, are acceptable and can be used correctly. The most effective ways to increase the efficiency of using own financial resources is the implementation of a complex of measures aimed at increasing income and reducing costs, and regarding attracting borrowed resources making the choice of affordable, available, sustainability, sufficiency, and easiness of receiving credit.



    Stages of selecting the type of financing.


    Factors influencing the choice of financing policy.


    Comparison of objective function optimization and the optimal value obtained from various algorithms and their convergence time.


    The evolutionary methods comparison tin time and solutions, based on size


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