On the Significance of the Critical Path in Network Graphs for Certain Types of Geological Exploration Work

P. I. Stepanov

(Presented by the Department of Industrial Economics and Enterprise Organization)

Network graphs are a further development of linear schedules and calendar plans. Network graphs are constructed taking into account, as a rule, the technological and logical dependencies between the elements of work, meaning that each subsequent operation may begin after the preceding one has been completed, while operations not in such a dependency may be performed in parallel.

One of the main advantages of network graphs over linear ones is that, in a network model constructed with allowance for logical connections, it is possible to find the chain of operations with the greatest expenditure of time and other resources, or the so-called critical path. Other paths, which require less time than the critical path, will have time reserves (1, 2).

This information makes it possible to determine, on a scientific basis, the time required to perform a job or a set of jobs; the permissible delay or suspension periods for individual operations in accordance with time reserves; to allocate resources correctly, etc.

Experimental work aimed at determining the areas of rational application of network graphs in geological exploration work has established that not every production situation offers the possibility or expediency of identifying critical paths and time reserves.

In a network model, one of the main parameters is time estimates. In the initial construction of a network graph, the duration of individual operations or jobs is shown according to total labor input, i.e., in man-hours, man-days, man-months, etc. If the model is evaluated only by total labor input, then it is always possible to identify the critical path and time reserves. However, when compiling network graphs for small systems for purposes of planning and especially management, what is required is not general time estimates by labor input, but estimates expressed through the number of performers together with the time required to carry out the work of the graph.

For this purpose, resources are allocated among the jobs of the graph. After the allocation of performers and other resources among the elements of the graph, it turns out that under some conditions one should identify

the critical path and time reserves, while in others this cannot be done, since all paths will be equal to one another; and even if they are not equal, the time required to carry out the work will not be equal to the critical path. The presence or absence of a critical path and time reserves is influenced by the state of the resources involved in carrying out the work modeled by the network schedule. Resources may be in two states: limited and unlimited.

By limited resources is meant a production situation in which a job or a set of jobs is performed by a definite, strictly constant number of workers, means of transport, etc. A job or a set of jobs is carried out by a group of workers united in an integrated crew. In integrated crews, as a rule, there is no very strict specialization; rather, there is a combination of trades and interchangeability.

By unlimited resources is meant a state in which individual elements of a job, or individual jobs within some set, are performed by narrowly specialized workers, or by a group of workers, or by individual specialized subdivisions of a geological organization. The number of specialists brought in to carry out the work may be unlimited, just as an unlimited number of specialized subdivisions may be brought in.

The identification of the critical path is important when carrying out work modeled in a network schedule with unlimited resources. In this case, the total duration of carrying out the job or set of jobs will depend on the duration of the individual elements located on the critical path. It is not possible to redistribute resources from noncritical paths that have time reserves to the execution of critical-path jobs, because of the narrow specialization of the workers.

With limited resources, the need to determine the critical path and time reserves disappears. Here all paths must be equal to one another; if this condition is not observed, then the resources have been incorrectly distributed among the elements of the schedule. With limited resources, the total time for carrying out the job or set of jobs will be equal to the quotient obtained by dividing the total labor requirement by the number of workers.

Let us explain these propositions with simple examples.

Suppose trenches and shafts are being driven on a site in order to solve some geological problem, using the same composition of driving crews.

Driving the trenches requires 1 month, while driving the shafts requires 2 months. First situation: the trenches and shafts are driven by specialized crews of miners. In this case, the final geological evaluation of the site will be made after 2 months, i.e., after completion of the shaft driving, and the time reserve of the trench-driving crews is 1 month. Second situation: after completing their work, the trench miners are transferred to shaft driving, i.e., to assist the shaft miners. Then all work on the site will be completed in 1.5 months.

In the production of particular types of geological exploration work, resources, as a rule, are in a limited state. Thus, for example, assembly and dismantling work is performed by an assembly-and-dismantling (construction-and-assembly) or drilling crew having a strictly definite number of workers. The preparation of a report is handled by an office group having a constant composition and a definite number of workers.

executors. The office group carries out all processing of materials on its own. The task of the head of the office group is to distribute all work evenly among the executors, taking into account that all the work must be completed by a single deadline. If this condition is not observed, then some of the executors will finish their work earlier than others and will not be engaged in performing work, while another part of the executors will be overloaded with work. If it is impossible to use the first group of executors on office work, then a decision is made to transfer them to other work, and, with this in mind, the deadline for completing the work is established.

Thus, when drawing up network schedules for operational-production planning and management, it is necessary to take into account the state of the resources involved in carrying out the work and, taking this into account, make decisions on the deadlines for completing the project.

LITERATURE

1. Basic Provisions for the Development and Application of Network Planning and Management Systems. Ekonomika, 1965.

2. Network Planning and Management. Ekonomika, 1967.