Optimization of implementation of strategic priorities of the organization by means of the network planning and management model

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Narxoz university the Republic of Kazakhstan, Almaty

Optimization of implementation of strategic priorities of the organization by means of the network planning and management model

Shoranova A.E., Doctoral student of DBA

Республика Казахстан, г. Алматы



Summary

Development of any business is impossible without strategic planning of activities and determination of strategic priorities for the development of an organization. Moreover, the process of determining strategic priorities is not so complicated compared to the process of their implementation. The implementation of strategic priorities requires a well-developed plan with a hierarchy of decisions and stages for the implementation of the plan. At the same time, important decisions on the implementation and implementation of strategic priorities are assigned to managers at various levels.

The paper shows the option of applying the network planning model to the issue of the implementation of strategic priorities to the organization. Using the model made it possible to estimate the maximum and minimum possible deadlines for the execution of tasks, the total time reserves, optimize the number of executors, determine the critical path and tension coefficient for the implementation of the priority under consideration when the layout of cases is formed: a certain number of executors for each task, the optimal deadline for implementation of tasks.

Keywords: network planning, strategic priorities, critical path, tension coefficient, performers optimization.



Аннотация

Оптимизация реализации стратегических приоритетов организации посредством модели сетевого планирования и управления

Шоранова А.Е., докторант DBA, АО «Университет Нархоз»

Развитие любого бизнеса невозможно без стратегического планирования деятельности и определения стратегических приоритетов развития организации. Более того, сам процесс определения стратегических приоритетов еще не настолько сложен по сравнению с процессом их реализации. Реализация стратегических приоритетов требует четко разработанного плана с составлением иерархии решений и этапов осуществления плана. При этом важные решения по осуществлению и претворению стратегических приоритетов в жизнь возлагаются на менеджеров различных уровней.

В статье показан вариант применения модели сетевого планирования к вопросу реализации стратегических приоритетов к организации. Использование модели позволило оценить максимально и минимально возможные сроки исполнения задач, полные резервы времени, оптимизировать число исполнителей, определить критический путь и коэффициент напряженности по реализации рассматриваемого приоритета при сформированной раскладке дел: определенном количестве исполнителей по каждой задаче, оптимальном сроке выполнения, установленном порядке выполнения задач.

Ключевые слова: сетевое планирование, стратегические приоритеты, критический путь, коэффициент напряженности, оптимизация исполнителей.



Formulation of the problem

Important tasks in the process of implementing strategic priorities are the identification of resources, stages and timelines for the implementation of relevant activities. The need for resources depends on the specifics of the implementation of strategic priority. In this case, a budget is drawn up in which all the necessary expenses for the implementation of each priority separately are recorded.

A significant role in the implementation of the strategic priorities of the organization's development is assigned to human resources. It is important for the manager to clearly know the abilities of each employee who is potentially capable of fulfilling the tasks of implementing the respective strategic priority. It is also necessary to clearly define the order of actions and stages of implementation of tasks. In addition, the timing of the implementation of various tasks on the implementation of development priorities is of great importance. As a rule, the deadlines for implementation will depend on both human resources (quality and timeliness of execution of orders), and the schedule of execution determined by the manager at the appropriate level.

Analysis of recent research and publications

In the contemporary practice of many large companies, network management models are used that imply a departure from the top-down hierarchical control system [1]. The peculiarity of the network model lies in the horizontal management structure, i.e., communication is actions (operations). At the same time, the link suggests that some operations cannot be carried out until the other tasks preceding them are performed.

Using of network models of planning and management allows you to optimize the process of implementing strategic priorities. Since the achievement of each strategic priority is possible only with the implementation of certain tasks that are carried out in a strictly defined sequence.

In management tasks, methods of generating columns, the use of the Lagrange function [3], linear programming, various regression models [4], the Hungarian assignment task method [5], the heuristic algorithm [6] and [7] are often used. Various variants of mathematical models are also widely used: the Pareto method and the hierarchical method [8], the technique for determining bottlenecks [9], multi-criteria linear programming [10], various optimization methods [11].

The effectiveness of the use of network planning models is considered in the works of A.E. Polichka, E.V. Simonova in mathematical modeling of building disciplines [12], E.V. Bucenko, A.F. Shorikov in optimizing business planning processes [13].

Unsolved part of the problem

In general, network planning uses a graphical display of the work plan in their logical sequence and interconnection and allows you to subsequently optimize the current management by adjusting the original plan [14]. The use of network modeling allows you to analyze all the work and make improvements to the structure of the model prior to its implementation [15].

All these features of the network model, in our opinion, allow it to be applied to the process of implementing strategic priorities in an organization.

The purpose of the paper is to study the possibility of using network planning in the tasks of determining the strategic priorities of the organization.

Methods

To assess the plan for the implementation of the strategic priority of the organization, we apply the network planning model. The network model is an economic-mathematical model, reflecting a set of operations related to the implementation of a project, in their logical and technological sequence and communication. The analysis of the network model presented in graphical or tabular form allows, first, to more clearly identify the interrelationships of the project implementation stages and, secondly, to determine the most optimal order of implementation of these stages in order, for example, to reduce the implementation time for the whole complex of works. Thus, network modeling methods can be attributed to the methods of making optimal decisions.

In our case, the project is the implementation of strategic priority. At the same time, the duration of the work is set by three estimates - the minimum, maximum and optimal. The minimum estimate tmin (i, j) characterizes the duration of the work under the most favorable circumstances, and the maximum ^tmax (i, j) - under the most adverse conditions.

Duration of work in this case is considered as a random variable, which as a result of the implementation can take any value in a given interval. The expected value of tex(i, j) is estimated by the formula:

(1)

m - optimal task execution time [16].,

To characterize the degree of variation of possible values around the expected level, the variance is used, which is estimated as follows:

(2)

To determine the time reserves for network events, the earliest tp and the latest tp deadlines for event completion are calculated. Any event cannot occur before all the events preceding it are completed and all previous works are not performed. Therefore, the early (or expected) time tp(i) of accomplishing the i-th event is determined by the duration of the maximum path preceding this event:

, (3)

Lni - any path preceding the i-th event, that is, the path from the source to the i-th event of the network.

The delay in the occurrence of event i in relation to its early date will not affect the period of accomplishment of the final event (and, therefore, the period of performance of the complex of works) until the sum of the period of accomplishment of this event and the length (length) of the maximum of the following exceed the lengths of the critical path. Therefore, the late (or deadline) term tn(i) of accomplishing the i-th event is:

(4)

Lci - any path following the i-th event, i.e. path from the i-th to the final network event.

The time reserve R(i) of the i-th event is defined as the difference between the late and early dates of its accomplishment:

(5)

To determine the maximum possible implementation time for the whole work package with a 95% reliability, we will use the following formula:

, (6)

Z - normative deviation of a random variable,

SKP - standard deviation, calculated as the square root of the variance of the duration of the critical path.

The complexity of the network schedule is estimated by the complexity factor, which is determined by the formula:

, (7)

nw - number of works, units; nev - number of events, units.

The coefficient of intensity K of work Pя is the ratio of the duration of non-coincident (prisoners between the same events) segments of the path, one of which is the path of maximum duration passing through this work, and the other is the critical path:

, (8)

t(Lmax) - the duration of the maximum path through Py, from the beginning to the end of the network schedule;

tcr - duration (length) of the critical path; tlcr - the length of the segment of the considered maximum path coinciding with the critical path.



Research results

Let us consider an example of using network planning for the implementation of the strategic priority “Increasing the company's market share”. As it was said, for the implementation of strategic priority it is necessary to determine the complex of operations (works) and the timing of their implementation (table l).

Table 1

Complex tasks within the framework of the implementation of strategic priority

Task name	Designation	Job Code	Deadline, days	Number of performers, people
			min	max	°p-tim
Evaluation of the company's position in the market	A	(0,1)	10	14	12	4
Environmental analysis	B	(1,2)	14	20	18	5
Analysis of internal factors	C	(1,3)	12	18	16	3
Competition evaluation	D	(1,4)	20	28	24	4
Market risk assessment	E	(2,5)	5	7	6	2
Internal risk assessment	F	(3,5)	8	12	10	3
Analysis of potential customers	G	(4,6)	12	16	14	4
Definition of marketing strategies	H	(5,6)	20	28	24	5
Determination of the optimal selling price of products	I	(6,7)	5	10	7	3
Budgeting	J	(6,8)	3	6	5	3
Develop a financial plan	K	(8,9)	7	14	10	5
Calculation of financial indicators	L	(7,9)	3	5	4	3

Calculate the expected value and indicators of variance. The results are presented in table 2. network planning strategic priority

Using the data obtained, it is possible to find the main characteristics of the network model by a tabular method, the critical path and its duration.

The most important indicator of the network schedule is the time reserves. The time reserves of each path show the extent to which the duration of a given path can be increased without prejudice to the onset of the final event. Since each non-critical network path has its full time reserve, each event on this way has its own time reserve.

Table 2

The results of the evaluation of the expected duration of time and variance

Task (i,j)	tmin(i,j)	tmax(i,j)	m(i,j)	Expected duration tex(i,j)	Dispersion S2(i,j)
0,1	10	14	12	12	0.44
1,2	14	20	18	17,67	1
1,3	12	18	16	15,67	1
1,4	20	28	24	24	1,78
2,5	5	7	6	6	0,11
3,5	8	12	10	10	0,44
4,6	12	16	14	14	0,44
5,6	20	28	24	24	1,78
6,7	5	10	7	7,17	0,69
6,8	3	6	5	4,83	0,25
8,9	7	14	10	10,17	1,36
7,9	3	5	4	4	0,11

Critical events of reserves of time do not have, since any delay in the accomplishment of an event lying on a critical path will cause the same delay in the accomplishment of the terminating event. Thus, by determining the early date of the onset of the terminating network event, one can determine the length of the critical path.

The results of the deadlines and time reserve are presented in table 3.

Table 3

Calculate the tjming and time reserve

Event number	Deadlines for the event: early tp(i)	Deadlines for the event: late tn(i)	Time reserve, R(i)
0		1,7763568394003E-15	1,7763568394003E-15
1	12	12	1,7763568394003E-15
2	29,67	31,67	2
3	27,67	27,67	0
4	36	47,67	11,67
5	37,67	37,67	0
6	61,67	61,67	0
7	68,84	72,67	3,83
8	66,5	66,5	0
9	76,67	76,67	0

In determining the early dates for completing the tp(i) events, we move along the network graph from left to right and use formula (3).

The length of the critical path is equal to the early completion date of the event 9: tkp = tp(9) = 76,67

When determining the late dates for accomplishing the events tn(i), we move along the network in the opposite direction, that is, from right to left and use formula (4).

The total reserve of the path shows how much the total duration of all the work belonging to the given path can be increased, provided that the duration of the whole complex of works does not change. It is formed when the previous work will end at its earliest date.

Rf(o,d = 12-12-0 = 1,7763568394003E-15	Rf(4,6) = 61,67-14-36 = 11,67
Rf (1,2) = 31,67-17,67-12 = 2	Rf(5,6) = 61,67-24-37,67 = 0
Rf(i,3) = 27,67-15,67-12 = 0	Rf(6,7) = 72,67-7,17-61,67 = 3,83
Rf(1,4) = 47,67-24-12 = 11,67	Rf(6,8) = 66,5-4,83-61,67 = 0
Rf(2,5) = 37,67-6-29,67 = 2	Rf(7,9) = 76,67-4-68,84 = 3,83
Rf(3,5) = 37,67-10-27,67 = 0	Rf(8,9) = 76,67-10,17-66,5 = 0

Определим свободный резерв времени:

Rf(0,1) = 12-12-0 = 0	Rf(4,6) = 61,67-14-36 = 11,67
Rf(1,2) = 29,67-17,67-12 = 0	Rf(5,6) = 61,67-24-37,67 = 0
Rf(1,3) = 27,67-15,67-12 = 0	Rf(6,7) = 68,84-7,17-61,67 = 0
Rf(1,4) = 36-24-12 = 0	Rf(6,8) = 66,5-4,83-61,67 = 0
Rf(2,5) = 37,67-6-29,67 = 2	Rf(7,9) = 76,67-4-68,84 = 3,83
Rf(3,5) = 37,67-10-27,67 = 0	Rf(8,9) = 76,67-10,17-66,5 = 0



Let us analyze the network model in terms of the implementation of tasks on the implementation of strategic priority (Table 4).

Table 4

Analysis of the network model by date

Task	Number of	Duration	Early dates:	Early deadline:	Late deadline:	Minimum
(i,j)	previous works	hi	start	ending	ending	cut
(0,1)	0	10	0	10	10	10
(1,2)	1	14	10	24	25	24
(1,3)	1	12	10	22	22	22
(1,4)	1	20	10	30	38	30
(2,5)	1	5	24	29	30	29
(3,5)	1	8	22	30	30	30
(4,6)	1	12	30	42	50	42
(5,6)	2	20	30	50	50	49
(6,7)	2	5	50	55	57	47
(6,8)	2	3	50	53	53	45
(7,9)	1	3	55	58	60	58
(8,9)	1	7	53	60	60	60

We choose the minimum value for all work ending in 9, which was 58. Therefore, the minimum time for completion of all tasks for the implementation of strategic priority will be 58 days.

We estimate the coefficients of complexity and intensity. Network models that have a complexity factor from 1.0 to 1.5 are simple, from 1.51 to 2.0 - medium complexity, more than 2.1 - complex. In our case, the complexity factor was:

Kd = 12 / 10 = 1,2

Since Kd <1.5, the network model is simple.

The coefficient of intensity K of work Py can vary from 0 (for work in which the maximum length of the paths that do not coincide with the critical path consists of fictitious works of zero duration) to 1 (for the work of the critical path). The closer to 1 coefficient of tension K of work Py, the more difficult it is to perform this work in a timely manner. The closer to the work of Py to zero, the greater the relative reserve has the maximum path that passes through this work. The results of the calculation of the coefficient of tension are presented in table 5.

Table 5

The coefficient of intensity

Task	Way	Maximum way, t(Lmax)	Matching works	t1cr	Calculation	K
(0,1)	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67
(1,2)	(0,1)(1,2) (2,5)(5,6) (6,8)(8,9)	74,67	(0,1)(5,6) (6,8)(8,9)	51	(74,67-51)/(76,67-51)	0,922
(1,3)	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67
(1,4)	(0,1)(1,4) (4,6)(6,8) (8,9)	65	(0,1)(6,8) (8,9)	27	(65-27)/(76,67-27)	0,765
(2,5)	(0,1)(1,2) (2,5)(5,6) (6,8)(8,9)	74,67	(0,1)(5,6) (6,8)(8,9)	51	(74,67-51)/(76,67-51)	0,922
(3,5)	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67
(4,6)	(0,1)(1,4) (4,6)(6,8) (8,9)	65	(0,1)(6,8) (8,9)	27	(65-27)/(76,67-27)	0,765
(5,6)	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67
(6,7)	(0,1)(1,3) (3,5)(5,6) (6,7)(7,9)	72,84	(0,1)(1,3) (3,5)(5,6)	61,67	(72,84-61,67) / (76,67-61,67)	0,745
(6,8)	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67
(7,9)	(0,1)(1,3) (3,5)(5,6) (6,7)(7,9)	72,84	(0,1)(1,3) (3,5)(5,6)	61,67	(72,84-61,67)/(76,67-61,67)	0,745
(8,9)	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67	(0,1)(1,3) (3,5)(5,6) (6,8)(8,9)	76,67

The calculated stress coefficients allow to further classify work by zones. Depending on the magnitude of the intensity factor K, there are three zones: critical (K > 0,8); subcritical (0,6 <K <0,8) and backup (K < 0,6).

The closer the tension coefficient to unity, the more difficult it is to perform this task in a timely manner; the closer to zero, the greater the relative reserve is the maximum path through this task.

To determine the maximum possible execution time of the whole complex of tasks, we find the value of the argument Z, which corresponds to a given probability of 95% (the value of the F (Z) column is 0,95 * 100% in the table corresponds to Z = 1,96):

T = 76,67+1,96*2 = 80,59

Consequently, the maximum completion time of the whole complex of works at a given 95% probability level is only 81 days.

Figure 1 - Network implementation schedule of strategic priority



Conclusion

The optimization of the deadlines due to the redistribution of resources is based on the fact that tasks that are not on the critical path have time reserves. For the transfer of resources, for example, people, tasks with a tension ratio in the range from 0 to 0,55 are used, which determines the belonging of the task to the reserve zone. Figure 1 shows the network schedule for accomplishing priority tasks and highlights the critical path, the duration of which was 76,67 days.

The figure shows the critical path (0,1) (1,3) (3,5) (5,6) (6,8) (8,9), which ensures the execution of tasks in 77 days. However, the manager should carefully consider the possibility of its implementation without performing other tasks.

The tension coefficients show that all the designated tasks for the implementation of priority fall into the subcritical or critical zone (tasks (1,2) and (2,5)). This means that there is no reserve both in terms of accomplishment of the tasks set and in the number of performers. It is even possible that for tasks falling into the critical zone, additional labor resources will be required. The duration of the minimum journey was 58 days. However, at the set intensity with a probability of 95%, the implementation of the strategic priority will be carried out within 81 days.

Thus, the application of the network planning and management method allows the following:

1) check the feasibility of planned tasks (works) and their structure;

2) identification of unnecessary tasks, for example, not mandatory due to changes in technology;

3) determining the possibility of parallel tasks;

4) the determination of the appropriateness of the level of detail obtained for the tasks, and, if necessary, the dismemberment of certain works in order to increase parallelism.



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