ON THE LIMITS OF THE RATIONAL USE OF LINEAR AND NETWORK SCHEDULES IN GEOLOGICAL WORK

P. I. STEPANOV

(Presented by the scientific seminar of the departments of political economy, industrial economics, and enterprise organization)

At the present time, in order to increase the productivity of managerial labor, and also to create conditions for rhythmic work by performers at workplaces, transport facilities, fixed assets, etc., effective methods of planning and management are being sought. One of the directions for improving planning and management is graphical methods.

Until recently, linear (bar) charts were widely used. In the last decade, instead of linear charts, charts of network planning and management, or network schedules, have begun to be used. Network schedules are a further development of linear charts. As a rule, both reflect the same information; the difference lies only in the method of representing it, as well as in the methods of analysis. When network schedules are analyzed, it becomes possible to obtain significantly more information, which is necessary for making optimal and objective decisions in planning, organization, and management.

Linear charts are a graphical representation of work being performed in calendar or working time by means of a straight line, the beginning of which reflects the start of the work, and the end—the completion of the work. In network schedules, what is taken into account is not the temporal dependence of the performance of work, but the logical dependence, meaning that any subsequent work cannot begin until the preceding work has been completed. If there is no such dependence, then the works may be performed in parallel.

The model has the form of a network—hence this method received the name of network schedules, or network planning and management.

A network schedule, being a model, makes it possible to study the logical regularities inherent in the production process, in a job or a complex of jobs, and on this basis to make objective decisions in planning and organizing these jobs, as well as in the process of managing their execution.

As the number of jobs combined by the schedule increases and the interrelations among the elements of the system become more complex, the effectiveness of using network schedules increases. This is due to the fact that, knowing the regularities of the system, it is possible to determine more correctly the sequence of performing the work and, taking this into account, to distribute human and material resources among the elements of the work. In addition,

...this property makes it possible to use mathematical apparatus and electronic computing machines (ECMs) to analyze the state of the laws governing the system.

The workers of the country’s geological service, just like the workers of the entire national economy, have been given the task of introducing network schedules into the practice of geological exploration work. Much theoretical and experimental work is being carried out in this direction. The Department of Industrial Economics and Enterprise Organization of the Tomsk Polytechnic Institute has conducted studies on the possibility and limits of the rational application of network schedules under the conditions of the West Siberian Geological Administration.

The studies have shown that in carrying out geological exploration work, both linear and network schedules should be used. Below, a justification is given for the effectiveness of applying one or another type of schedule.

Studies show that in geological work it is impractical to use ECMs for the analysis of network schedules. It is known that the use of ECMs is most effective when the network model contains more than 200–300 constituent elements \[1, 2\]. Up to this limit, it is more effective to calculate the parameters of network schedules manually. In this case, the calculation of the network schedule takes less time than the preparation of a program for an ECM.

In the production of geological work there are no systems in which more than 200–300 elements in logical dependence would be counted. At first glance it may seem that the complexes of geological work performed on the scale of a territorial geological administration, by expeditions and parties, can be classified as large and complex systems. A network schedule for this work can be drawn up by stitching together the network schedules of individual expeditions, and the latter by stitching together the network schedules of parties.

In reality, such a schedule cannot be drawn up. Here is why.

One of the features of network schedules is the presence of an initial event—the start of work—and a final event—the end of work. When there is one final event, the schedule is called single-objective; when there are several, it is called multi-objective; in this case there are interconnections among the events of the schedule.

Network schedules drawn up for geological work are, as a rule, single-objective. This is due to the fact that for each object of geological investigations an independent work project is drawn up. The types of work and their volumes are determined by the work methodology, proceeding from the aims and tasks of the geological study of only the given object. There are usually no interconnections whatsoever between work on the study of separate objects. The work is performed by a separate geological organization that is an independent cost-accounting subdivision with its own human and material resources.

A network schedule drawn up for work on an object is autonomous and is not stitched together with network schedules for other objects. In order to stitch together, i.e., to reduce network schedules for separate objects to a single network schedule, there must be some interconnections between the works reflected in the autonomous schedules. But, as shown above, there are no such connections between work on different objects.

Hence the conclusion follows that complexes of work performed by separate geological parties on specific objects are not interconnected with one another, do not constitute a single system, and, consequently, cannot be modeled as a single network schedule. This circumstance is the main limiting factor in terms of scale.

the use of network schedules, especially from the point of view of the possibility of using computers to analyze network schedules.

At the scale of territorial geological administrations, for the purpose of planning, organizing, and managing work carried out at individual sites, it is sufficient to have a linear work schedule. This conclusion is quite applicable also to the scale of an expedition.

The production situations discussed above very often do not make it possible to draw up a comprehensive network schedule even for a single party carrying out work at several sites. The only dependency between separate operations at different sites is the provision of materials and transport. But this dependency is purely organizational in nature, does not fit into a network schedule, and is easily resolved with the aid of a carefully prepared linear schedule reflecting the sequence of deliveries of materials and the allocation of transport means.

Experimental work has shown that network schedules are effective for planning, organizing, and managing a complex of works performed at a single work site, as well as individual types of geological exploration work that contain a large number of operations with complex interrelations among them. These include assembly and dismantling work, office-processing, thematic, and repair work, as well as the construction of major facilities, etc. Directly in the process of drilling exploratory boreholes, driving pits, ditches, and underground mine workings, a network schedule takes the form of parallel paths without interrelations with one another and differs almost not at all from a linear schedule, either in form or in the amount of information. The sequence of work is determined by the technological dependence of operations involved in deepening a borehole, ditch, or pit and in advancing the face of a mine working. The work is cyclically repetitive in character and is performed by specialized integrated crews.

In assembly and dismantling, office-processing, and thematic work, and in construction, network schedules also should not always be used exclusively. The boundary of the rational application of network and linear schedules is determined by the number of operations making up the work and by the complexity of their interrelations with one another, as well as by the work experience of the executors. When the number of operations is small and the links between them are simple, it is better to use linear schedules. As the number of operations and the complexity of the interrelations among them increase, network schedules produce a greater effect. This is explained by the fact that, as the number of operations increases and the links among them become more complex, the executors cannot mentally represent the model of the work; on this basis, errors are made in planning and in establishing the sequence of work performance, as a result of which losses of working time arise because the completion dates of some operations and the start dates of other operations do not match, the workload of the executors is uneven, etc.

On the basis of experimental work carried out on the use of network schedules in office-processing work, the following parameters may be recommended preliminarily. When the number of executors in office-processing work is up to 5–7 and the number of operations is up to 20–30, ordinary calendar plans may be used, of which linear schedules are the prototype. With a larger number of executors and operations, network schedules give the greatest effect. It should be noted, however, that the indicated boundary depends to a large extent on the experience of the work supervisor and the principal executors. The lower their qualifications, the greater the effect obtained from a network schedule with a smaller number of executors, and vice versa. The same approach should be taken

toward determining the limits of the rational use of network schedules for the planning, organization, and management of other types of work.

When network schedules are used for the planning, organization, and management of individual types of geological work, the method used for allocating resources among the elements of the schedule is of great importance. Resources may be allocated both on the schedule itself and on additionally constructed resource-loading charts (a chart of the loading of performers, a chart of transport loading, etc.). The latter take the form of a linear schedule.

Experimental work has established that the allocation of resources among the operations of a network schedule, and the determination of the sequence in which work is to be performed, are best carried out on additionally constructed loading charts for the various resources. In this case, clarity is significantly improved and the time spent on allocating resources among the operations of the schedule is reduced. The network schedule itself serves, as it were, as a visual aid that helps establish the sequence of performing the work and allocate it among the performers. In the course of work with the schedules, when the state of resources changes, only the loading charts are rebuilt and refined, while the network schedule remains unchanged. The network schedule is constructed with strict logical dependence taken into account, without scale; the loading charts, however, are constructed to a time scale, for which time in hours, working days, weeks, months, etc., is plotted along the abscissa axis.

The use of graphical methods for planning, organization, and management will make it possible to create conditions for the rhythmic work of individual teams of geological prospectors and, on this basis, to increase labor productivity and reduce the cost of geological prospecting work.

REFERENCES

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

2. V. E. Reksin. Methods of Network Analysis in Production Management. Ekonomika, 1966.