Making investment decisions in an industrial enterprise under uncertainty

In the modern world, which is characterized by ultra-fast changes, as well as instability, complexity and ambiguity, the value of the ability to work effectively under conditions of high uncertainty is increasing. Such activity requires a step-by-step study of huge amounts of information and adjustments to work with it as new data becomes available in order to be able to accurately predict the future [1, 2]. The problem of working under conditions of uncertainty is extremely relevant at the level of large industrial enterprises. Especially in situations where it is necessary to quickly solve complex economic problems, incl. selection of investment projects. The existing toolkit is rather heterogeneous and represents a combination of quantitative and expert methods. As a result, testing of such approaches is required to minimize uncertainty in the process of making investment decisions at an industrial enterprise. In the future, this will improve the tools for dealing with uncertainty and speed up the process of making effective economic decisions. This issue is extremely important for both business owners and investors. Consequently, this problem is significant not only from a scientific, but also from a practical point of view.

• 1.    Methodology for the quantitative substantiation of investment decisions in conditions of uncertainty

The determining sign of uncertainty is the lack of sufficient information about the likelihood of future events. In particular, when making investment decisions under conditions of uncertainty, as a rule, there is not enough data on the likelihood of the implementation of investment project scenarios. In this case, the formation of the investor's personal attitude to probability is required based on a number of

Wald's criterion, based on careful decision making, is a pessimistic approach. The highest probability is assigned to the most unfavorable event among all considered projects and their corresponding scenarios, as shown in conditions:

W i = min ( X j ) , i = 1... n , j = 1... m

Wk = max ( Wi ) , i = 1... n         ,                              (1)

X opt im = X k , k g ( 1; n )

where W is Wald's criterion; n is the total number of i -th alternatives; j is the state (quantitative value) of the i -th alternative; X_ij is studied i -th alternative with state j ; W is the minimum value of the state of each i -th alternative; W_k is the maximum value of the alternative state among all the minimums; X_optim = X_k is the optimal alternative according to the criterion.

According to the optimistic “maximax” criterion, the highest probability is given to the best event in each alternative in accordance with:

M i = max ( X ij ) , i = 1... n , j = 1... m

< M_k = max ( M i ) , i = 1... n          ,                               (2)

X opt im = X k , k g ( 1; n )

where M is the “maximax” criterion; M_i is maximum value of the state of each i -th alternative; M_k is the maximum value of the alternative state among all the maximums; X_optim = X_k is the optimal alternative according to the criterion.

Laplace's criterion is based on the principle of insufficient justification and assumes that the probabilities of all alternatives should be equal to each other, and the priority is the project with the maximum average effect according to the conditions:

m

? X j

L - j -i----, i - 1... n , j - 1... m ,

<        m

L k - max ( L i ) , i - 1 _ n ,                                         (3)

, Xopt im - Xk, k g(1; n ), where L is the Laplace criterion; Li – average result of each i -th alternative; Lk – the maximum value of the alternative state among all averages; Xoptim = Xk is the optimal alternative according to the crite- rion.

The Savage criterion transforms the initial data into a “regret matrix” that takes into account the lost effect and gives preference to the project with a minimum loss in (4) and (5):

y i - max ( X jj ) , i - 1 _ n , j - 1 _ m r ij ^- y ^- X jj

,

where y is the maximum value of the state for each j -th case; r_ij – lost effect in the form of the difference between the maximum gain and the actual value for each state.

S i - max ( r ij ) , i - 1 _ n , j - 1 _ m ,

< S k - min ( S i ) , i - 1 _ n ,          ,                                  (5)

X opt im - X k , k g ( 1; n ) ,

Математика

where S is the Savage criterion; S – the maximum lost payoff of each i -th alternative; S – the minimum lost gain among all the maximums; X_optim = X_k is the optimal alternative according to the criterion.

The Hurwitz criterion is based on an expert's intuitive assessment of the likelihood of scenarios - the “optimism coefficient” ( α ). The choice of projects involves the study of only extreme scenarios according to (6) and (7):

X i max = ^max ( X j ) , i = ¹ - n , j = 1 - m

,

_ Xi min = min ( Xij ), i = 1-n, j = 1-m where X     is the maximum state value for each i -th alternative; X is the minimum state value i max for each i -th alternative.

H i = « • X im ax + ( 1 - ^а ) ' X im in , i = 1 - n , ^j = 1 - m ,

< Hk = max (Hi), i = 1-n,(7)

. Xopt im = Xk, k ^(1; n), where H is the Hurwitz criterion; Hi - the value of the gain, taking into account the “optimism coefficient” α for each i -th alternative; H – the maximum payout among all alternatives; Xoptim = Xk is the optimal alternative according to the criterion.

2.    Practical choice of investment projects in conditions of uncertainty.

The scenario conditions of investment projects for the modernization of an industrial enterprise are presented in Table 1, and the results of the assessment of the criteria are in Table 2.

Table 1

Brief description of projects

Alternative projects	Profit / Loss Scenarios (RUB thousand)
	Pessimistic	Neutral	Optimistic
Project 1	–1 000	–100	3 000
Project 2	0	10	2 000
Project 3	100	300	1 000
Project 4	–500	0	2 500
Project 5	0	200	1 500

Table 2

Criterion values for projects

Alternative projects	Selection of projects (criteria)	Criterion value, thousand rubles
Project 1	“Maximax” / Hurwitz	M 1 = max (–1000; –100; 3000) = 3000 At α = 0,8 H 1 = 0,8·3000 + 0,2·(–1000) = 2200
Project 2	Laplace / Hurwitz	T   0 + 10 + 2000 L =---------= 670 23 At α = 0,3 H 2= 0,3·2000 + 0,7·0 = 600
Project 3	Wald	W 3 = min (100; 300; 1000) = 100
Project 4	Savage	S 4 = max (600; 300; 500) = 600
Project 5	–

Mokhov V.G.,                                                         Making Investment Decisions

Chebotareva G.S.                                          in an Industrial Enterprise under Uncertainty

Calculations showed that the opinions of the most objective indicators (with the exception of the intuitive Hurwitz criterion) were divided between the first, second, third and fourth projects. When taking into account the expert assessment according to the Hurwitz criterion, the first and second projects become priority. The fifth project was not selected by any of the criteria, although it is among the breakeven ones.

Conclusions

• 1.    A method is proposed for solving the urgent problem of selecting investment projects in conditions of complete uncertainty.

• 2.    A comparative analysis of alternative projects and their scenarios was carried out according to five criteria for reducing uncertainty.

• 3.    The obtained results are recommended to be used when developing an approach to reducing uncertainty and making investment decisions at industrial enterprises.

The work was supported by grant of the President of the Russian Federation (МК-4549.2021.2).