Modeling of the Labour Force Redistribution in Investment Projects with Account of their Delay
I.D. Kolesin, O.A. Malafeyev, I.V. Zaitseva, A.N. Ermakova, D.V. Shlaev
MModeling of the Labour Force Redistribution in Investment Projects with Account of their Delay
I.D. Kolesin , O.A. Malafeyev , I.V. Zaitseva *1 , A.N. Ermakova , D.V. Shlaev Stavropol State Agrarian University, 12, Zootechnicheskiy Lane, Stavropol, Russia, 355017 Saint-Petersburg State University, 7-9, University Emb. , Saint-Petersburg, Russia, 199034 *1 [email protected], [email protected], [email protected], [email protected] September 19, 2017 Abstract.
The mathematical model of the labour force redistribution in investment projects is presented in the article. The redistribution mode of funds, labour force in particular, according to the equal risk approach applied to the loss of some assets due to delay in all the investment projects is provided in the model. The sample of the developed model for three investment projects with the specified labour force volumes and their defined unit costs at the particular moment is given.
Key words : model, modeling, investments, labour force
Mathematics Subject Classification (2010):
1. Introduction
The introduction of investment projects in volatile conditions is followed by the risk to lose the major part of the assets due to the investments delay. These losses are stipulated by, for instance, inflation. In this case, having received the initial sum of money, a company could pay for some equal (without priority) work or resources. As the inflation level varies for different resources, it is reasonable to follow the principle of equity and allot some assets for every investment projects with the equal loss risk due to delay. Since all the investment projects are equal, the terms of delay is also supposed to be equal [1-3]. It should be noted that the principle of equity allows the company avoiding the conflict with a customer if it hasnβt apply any other approach. Weβll define the problem of the specified assets redistribution per labour force following the risk equity [4-7].
2. The Mathematic Model of the Labour Force Redistribution in Investment Projects 2.1. Problem Setting n of investment projects are considered. It is required to allot the resources (as well as labour force) in volume V ,β¦Vn in n investment projects. Suppose, this ork requires π π = π π π π , π = 1, πΒ΄π , β¦ , π π ). But the assets at present (B) are not enough for the labour force payment in n all the investment projects, i.e. π + π + β― + π π > π΅ . If only a part of labour force is employed in an investment project, it could require more investing till the further funds are received because of inflation. Suppose, at present the labour resources are divided in volumes Ρ( |1π’ + β― + Ρ π π’ π = π΅)π’ , β¦ , π’ π . Then, the following investments are required to complete the balance: π πβ² = π πβ² (π π β π’ π ) , π πβ² > π π , π = 1, πΒ΄ , where, Ρ π β costs per unit at the time π‘ = 0 , π πβ² - costs per unit after the time t . Let us assume costs growth pro rata time t : π πβ² = π π + π π π‘ , π π > 1 , π = 1, πΒ΄ . We comprise the ratio: π πβ² π π β = π π ,
1, πΒ΄ . We call π π i- investment project failure risk. It is required to allot the assets (B) according to the equal risk approach in all the investment projects. π = β― = π π , i.e. to find such π’ , β¦ , π’ π , that the formula π πβ² (π π β π’ π )Ρ π π’ π = π is fulfilled and, where (r is unknown value) . Suppose, the terms of delay π , β¦ , π π .are set. Then, π πβ² = π π + π π π π , π = 1, πΒ΄ . Comprising the ratio π π (π π βπ’ π )π π π’ π = π π , π β 1, πΒ΄ . , we find the formula for π’ π out of every expression π’ π = π πβ² π π π πβ² +π π π π , π β 1, πΒ΄ . Let us substitute these formulas to the equation π π’ + β― + π π π’ π = π΅ and suppose π π = π, π β 1, πΒ΄ . We get the equation as to the unknown r. Suppose, its solution is π = π . Substituting the value found π to the expression for π’ π , we find all π’ π . Suppose, there are three investment projects (n) with labour force volumes: π = 100, π = 300, π = 250 and costs per unit at the time π‘ = 0 are π = 2, π = 3, π = 1 . Suppose, all the works are delayed at the time Π’ = Π’ = Π’ = 10 , the labour force inflation rises respectively to time, and the proportionality coefficients are defined: π = 0.1, π = 0.4, π = 0.2 . Then in time T=10, the new costs per unit are: π = 3 , π = 7 , π = 3 ( π πβ² = π π + π π π π , π = 1,2,3 ). uppose, the company obtains the assets in the amount of B=295 at the time π‘ = 0 , whereas, the projecting costs of assets is It is necessary to allot the assets B in three investment projects, so that the total cost of labour force in volumes π’ , π’ , π’ is equal to B=295 : π β π’ + π β π’ + π β π’ = 295. Then we comprise the expression based on the equal risk approach: Ρ (100 β π’ )π π’ = Ρ (300 β π’ )π π’ = Ρ (250 β π’ )π π’ = π. Having expressed each of π’ , π’ , π’ in r and substituted them in (*) , we receive: π Ρ + π π + π Ρ + π π + π Ρ + π π = 295. The only positive root r of this equation will be equal to r*=8.3 (residual 295-294.476=0.524). Substituting r* in the expression for π’ π π’ π = π πβ² π π π πβ² +π π π , π = 1,2,3 , we find the required volumes of labour force: π’ = 15.3, π’ = 65.8, π’ = 66.4 .
3. Results and Discussion
It should be mentions that theoretical and practical aspects of the sustainable growths of the economy, in general, and the economy of particular regions are not worked out sufficiently. At present, there is much concern about the labour force management. If the essence of the labour force management is clear enough, its basic principles are to be identified and studied. Thus, the topicality of labour force redistribution for providing the stability and balance of positive geographical shifts is stipulated by the necessity to study social and economic factors of labour force development in the current economic environment. The authors have studied the essence and performance of labour force in reasonable detail [15-16]. The problems concerning the labour force management on the basis of its structure were sufficiently considered, the main philosophy of formation management and major mathematical model-based methods were identified [17-18]. The economic methods of analysis, assessment and forecasting of the regional labour potential used to study the labour sector in agriculture Stavropol Territory were introduced [19-20].
4. Conclusion
In view of the above-mentioned, the research of the principles applied for the labour force alteration, the assessment of labour force planning and its impact on the regional economic development, the development and justification of methods and procedures used in the labour force management are turned out to be topical. The concept of economy development based on the analysis considering the assessment and forecasting the labour force level could be formed as the result of his research. The solution of the complex problems connected with the labour force management refers to the formulation of the new theoretical and methodological approach to the management system. Therefore, itβs required to create the corresponding economic and mathematic modeling apparatus, management and optimization procedures, to determine the quality criteria for transition processes and perspective management laws. The reference model differs by the ability to achieve the qualified take-off and immediate intellectual development of labour force at work getting more and more complex should be taken as a base.
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