The harmonogram

an overlooked method of scheduling work

One of the earliest known methods of scheduling work was invented in Poland by an engineer named Karol Adamiecki (1866-1933). His invention — the harmonogram — led to increases in output between 100% and 400% in metal rolling mills, in machine shops, in chemical plants, in agriculture, and in mining. The harmonogram is known to have made a sensation in 1903 when Adamiecki first described it and the results of its application before the Society of Russian Engineers in Ekaterinoslaw. (5, p. 108)

In essence, the harmonograms of Adamiecki were various work-flow network diagrams which resulted in graphical solutions to production problems. The fact that a work-flow network concept was being used in Poland as early as 1896 is significant. Today workflow networks are associated with the family of methods that began to be developed around 1957 in the United States (2). Probably the best known of these if Program Evaluation and Review Technique, or PERT. What is particularly interesting about Adamiecki’s earlier work-flow network concept is that it incorporated the best features of the Gantt charts (3) together with the network concept. Thus harmonograms have advantages over both PERT and Gantt charts as well as certain disadvantages.

The primary advantages of the Gantt charts lie in their straightforward simplicty. Although Henry. L. Gantt invented a variety of charts which are collectively known as the “Gantt charts,” they all employ a bar-graph presentation. Gantt’s various bar-graph configurations are based on the production time and production quantity for each oepration in the production process. (See Figure 1.)

Figure 1

In general, the Gantt charts cannot be regarded as utilizing the work-flow concept for the following reasons:

1) Gantt charts do not reveal the critical path. (The critical path consists of those critical operations which will delay completion of the entire project.) Moreover, the Gantt charts do not indicate how much slack time exists in non-critical operations.

2) Gantt charts yeild a rigid solution which soon becomes obsolete as a result of uncertainties in machine maintenance, labor efficiency, and materials supplies.

3) The Gantt charts become increasingly complicated and difficult to construct as the number of operations increases. If the number of operations exceeds several dozen, construction of a Gantt chart can become so difficult as to be not worth the effort.

The PERT approach consists of a system of arrows and circles to represent a production process (4). (See Figure 2.)

In a PERT diagram, circles represent events or the beginning and ending of activities. Arrows represent activities identified by their beginning and ending events. Numbers alongside the arrows designate activity times. Thus PERT utilizes the work-flow concept for the following reasons:

1) The PERT method reveals the critical path after arithmetic summation of all possible paths has been calculated. In simple problems the human eye in conjunction with a desk calculator can locate the critical path. However, for complicated projects involving many operations a computer program is necessary.

2) The PERT method can be updated by changing operation times and quantities as the work progresses. However, a change requires that the entire problem be re-solved in order to be certain of the solution. For complicated projects the use of a computer program will again be necessary each time changes occur.

3) Provided that computer facilities are available, the PERT method can deal with even the most complicated projects having many thousands of operations. Because of the cost and complexity of computer programming, the PERT method is best for extremely large and extremely complicated projects where construction time is critical.

Adamiecki’s harmonogram consists of a tableau of detachable paper strips, each held in place with clamps at both ends. There is one strip for each operation in the production process. Each strip is labeled according to the operation it represents. (See Figure 3.) The harmonogram is best described in Adamiecki’s own words which follow. This passage, translated by this author from the original Polish, is from a 1931 article entitled “Harmonograf” published in Przeglad Organizacji (Organizational Review) (1).

   The central principal behind the construction of a harmonogram is that the surface on which the harmonogram is illustrated does not consist of one fixed piece of paper, but consists of a series of paper strips each arranged vertically one alongside the other. These strips are fastened to a board with clamps so that each strip can be arranged or removed independently of the others. On the left edge of each strip is attached a narrow tab of thin metal plate metal or of colored celuloid which designates a segment of time. In drawing 2 one of these tabs is shown in a perspective view. The tab is made in the shape of a channel so that both of its sides are bent inward so as to compress the edge of a piece of paper. The compression is light enough that one can easily slide the tab along the piece of paper.

   On each vertical strip is drawn a linear time scale. One unit can represent an hour, a day, a week, etc., depending on how much accuracy is required in the particular problem.

   From the preceeding description it should be obvious how construction of a harmonogram involves cutting off a series of tabs each to a length representing the time required for a particular operation, placing the tabs on the corresponding strips of paper, and shifting the tabs to the optimal place as the succession and flow of activities requires. Thus with a little effort, the drawing complexity of constructing a harmonogram is reduced to the shifting of tabs. This greatly facilitates the many steps required in the construction of a harmonogram, since optimizing the location of a segment of time may be accomplished quickly and without difficulty. (1, pp. 275-277)

Figure 3
Adamiecki’s Harmonogram

Adamiecki’s Harmonogram

The harmonogram measures time from zero (at the top line of the paper strips) downward to as many units as required. (See Figure 4.) Each strip is labeled to indicate which are the immediately adjacent operations in the production process. In the example shown in Figure 4, the drill press operation 2-5 requires two units of time. It has to be preceded by another operation 1-2, and has to be followed by another operation 5—7.

Figure 4
Adamiecki’s Harmonogram Time and Sequence

Adamiecki’s Harmonogram Time and Sequence

Once the strips and tabs are prepared, optimizing the work-flow problem is simply a manual process of arranging the strips and sliding the tabs. Each strip is arranged according to the rule that all “from” operations must be to the left of the given strip. With the strips thus arranged, the tabs are slid into the time locations which the sequence of operations dictates. This reveals the events of the critical path and results in an exact estimate of the production time. If necessary, further refinements in the solution obtained can be made with the use of eyeball judgment and common sense. Thus the PERT approach shown in Figure 2 would result in the harmonogram solution of Figure 5.

To interpret this harmonogram solution, note that the sequence of tabs along the lower left of the tableau — 1-2, 2-6, 6-8, 8-10, and 10-11 — together occupy more time than does any other sequence of strips. This longest sequence constitutes the critical path. Between these critical operations occur several noncritical operations such as 3—8. Operation 3—8 can only be lengthened one unit before it will “push down” the tab on its right 8-10. Thus one unit of slack time exists for the operation 3—8.

The lines and symbols in Figure 5 are best explained in Adamiecki’s own words which follow. This passage is about one-third of Adamiecki’s 1931 article.

   As work reports concerning the progress of the operation arrive, they will indicate the amount of work remaining in relation to the amount completed; these percentages will indicate the level of time lost, and an angular line drawn with a thick pencil can indicate what has happened. For example, the diagram in drawing 4 shows that work was begun, that the required quantity was completed in the time allowed, that by time “D” was completed “DE” percent of the amount required, and that by time “B” was completed the entire amount required “BC.”

   In our second example (drawing 5), we can see that the work began on schedule, but was slow in being completed by the amount of time BB1.

   In drawing 6 is yet another example. The beginning of work was delayed by the amount of time AA1, then, after completion of an amount DE, the work was interrupted at time B1; finally, the work was completed at time B1 with a total delay in the schedule of BB1.

   The preceding examples suffice to illustrate the method of drawing the diagrams. If the process begins to get out of step with the forecast of the harmonogram, this can be indicated on the strips by signs or letters indicating the cause of the divergence; for example, R can indicate repairs in progress, M can indicate material shortage, etc.

Figure 5

If the planned time period is postponed because of such contingencies, it becomes necessary to shift the tab; for the sake of pictorial clarity this can be indicated in pencil using the symbols M and N on the strip before sliding the tab (drawing 7).

For easier interpretation, each type of activity can have a different color tab, and a pencil of a corresponding color can be used to indicate the progression of work.

After the project has been completed, the paper strips can be removed from the surface of the harmonogram, and we will be ready to begin planning our next flow of operations. However, before doing this we ought to photograph the final tableau. Such photographs can serve as suggestive material by associating completed jobs with future plans. Thanks to today’s advanced technology in photography, even the small businessman can easily take such photographs. It is best to photograph the final tableau with a small camera, such as a 6 cm by 9 cm, and to have the prints enlarged to the standard A-3 size of 420 mm by 594 mm.

From the preceding description, it should be obvious that the harmonogram has important advantages. In particular, the harmonogram is superior in the following respects:

1) The harmonogram method reveals the critical path without any arithmetic calculations. The mechanical shifting of strips and tabs is straightforward for projects having few or dozens of operations. Of course the harmonogram has limitations in that a project of a thousand operations would require an unrealistically large tableau and an unwieldy number of paper strips.

2) The harmonogram solution can be easily updated by sliding tabs and, if necessary, relocating the paper strips. In general, changes are simple to make.

3) While a harmonogram solution becomes increasingly complicated as the number of operations increases, this occurs to a lesser extent than with Gantt charts. In general, the harmonogram is ideal for projects too complicated for Gantt charts to solve, but too simple for PERT computer programs to be worth their expense.

Perhaps the reason Adamiecki’s invention was overlooked was his Polish article’s lack of emphasis on application. It also is possible that Adamiecki did not forsee the great potential of his own idea. In any case, perhaps this presentation will give some credit where it has been long overdue. Management practitioners should be aware of developments in other countries as well as their own. Additional creative thought and a variety of background environments may inspire new insights.


1. Adamiecki, Karol. 0 Nauce Organizacji (Warsaw:Panstwowe Wydawnictwo Ekonomicze, 1970).

2.Buffa, Elmwood S. Basic Production Management (New York: Wiley, 1971).

3.Gantt, Henry L. Organizing for Work (New York: Harcourt, Brace, and Howe, 1919).

4. Johnson, Robert. PERT for Managers (New York: Argyle, 1968).

5. Urwick, L. The Golden Book of Management (London: Newman Neame, 1956).

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