Management Span of Control Advisor

What is the best management structure for YOUR project?

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Abstract

Under certain conditions, a multi-level management hierarchy may allow very aggressive schedules to be satisfied. This Knol provides a scientific underpinning, derived from Information and Hierarchy Theory, that allows quantification of Brooks Law which states: “Adding manpower to a late software project makes it later.” It turns out that you CAN set up a multi-level structure for your project with additional personnel to speed project completion. This applies not only to software projects but to any complex engineering or business activity that requires coordination between multiple employees, managers, and departments.

Given this theoretical support, and a FREE Excel spreadsheet advisor, you can compare various management structures to determine how to set up your project to achieve the best combination of cost and schedule, considering the value of getting to market early or avoiding a late penalty.

An easy to use Excel-based tool helps you make the right decisions. It is available for FREE.

CLICK HERE for the FREE Management Span of Control Advisor Spreadsheet. 
 

Management Hierarchies and Span of Control

Management Span of Control is the number of workers reporting to their first-level manager, or the number of first-level managers reporting to their second-level, and so on up the chain of command.
 
The following figures indicate generic one-, two- and three-level structures. 
SINGLE-LEVEL Department – The manager (large square) has a number of workers (smiley faces :^) reporting to him or her. How many workers are too many in a single department? According to management experts, beyond a certain number, additional people will actually delay completion of your project.  What if there is a penalty for late delivery, or a bonus for completing early and being first to market? If you can’t simply add more people to a single department, what can you do to speed completion of your project?

TWO-LEVEL HIERARCHY – Second-level managers have several first-level managers reporting to them, plus a number of staff assistants, as indicated in the graphic. Could a two-level hierarchical structure allow you to add more people in a way that both speeds completion and reduces costs (compared to a single-level structure with too many people)? The answer is YES in many cases. How can you tell if your project is one of those cases?

THREE-LEVEL Hierarchy -  Above the second-level, the manager’s staff may include a chief of staff and several staff members. Can a three-level structure be better than a two-level one for your project? Well, as the wise person said, ”It depends!” 
 

The Management Span of Control Advisor

CLICK HERE for the FREE Management Span of Control Advisor Spreadsheet.
 
To use the spreadsheet (see screen capture below), you simply enter parameters describing your project and the Management Span of Control Advisor estimates the cost in Actual Person-Months (APM) as well as the number of months it will take to completion. It also consders the cost of a Person-Month, the desired completion time,  and the effect of a late penalty or a bonus for early completion to estimate the net cost in dollars (or other currency). This allows you to compare one-, two-, and three-level structures as well as different numbers of people per department and number of departments at each level, and pick the best structure to achieve your cost and schedule needs.
 
An example is worth a thousand words!
 

ENTER DATA FOR YOUR PROJECT 

 

Enter data on the first sheet (see screen capture above).

 

Enter Five Parameters for a One-Level Department 

  1. The size of your project in “Mythical Man-Months” (MMM). Think of MMM as the naive and idealistic estimate of the number of People-Months it would take to complete the work if you did not have to worry about the interaction between workers and management and the Law of Diminshing Returns. Your realistic project size, expressed in “Actual People-Months” (APM), will generally be several times larger than the MMM value. (The estimation of MMM is discussed in greater detail in a section below.) In this example, we have entered 200 MMM.
  2. The number of people on your project, including the manager. In this case we have entered 10 people (a manager plus nine workers.)
  3. The cost of one Person-Month in thousands of dollars, including overhead, etc. In this case we have entered $20K/month as the cost of a single worker. (We assume a Level-1 manager costs about the same as an average worker.)
  4. The value of saving one Schedule Month (for example to avoid a late penalty or to gain the advantage of being early to market). In this case we have entered $300K.
  5. Desired completion time, in Months. Generally your project needs to be completed by a given time in coordination with other projects and/or to meet market needs or avoid a late penalty. In this case we need the project to be completed within about 24 months.
     
As shown in the above screen capture, the Management Span of Control Advisor immediately estimates the completion time for a single department with the number of people you specified. In the example above, the Advisor estimates it will take about 71 months which is about 47 months too late! The Advisor also provides more detailed advice about how you might increase (or decrease) the number of people to improve the situation. (That detailed information is discussed in the following section.)
 
You can try adding people to this department but you will find, In this case, that a single department, no matter how many people you populate it with, cannot meet your aggressive 24 month schedule. You could make your schedule less aggressive or change the scope of your project and the Advisor will make the requisite estimates.
 
Let us assume your project scope is fixed in concrete and you cannot get any relief for the 24 month schedule. The only solution is to break the project up into pieces that are relatively independent of each other and assign each piece to a separate department. 
 

Enter One Parameter for a Two-Level Hierarchy of Departments

  1. The number of Level-1 departments in your Level-2 department. (All other parameters are carried forward from the above data entry items.) In this case, we have entered 7 as the number of Level-1 departments.
 
As shown in the above screen capture, the Management Span of Control Advisor immediately estimates the completion time for a two-level hierarchy with the number of Level-1 departments you specified. In the example above, the Advisor estimates it will take about 20 months which is about 4 months early! The Advisor also provides more detailed advice about how you might increase (or decrease) the number of people to improve the situation. (That detailed information is discussed in the following section.)
 
You can try reducing the number of departments or reducing the number of people per department to lengthen the estimated time to completion to 24 months, which will generally save you money. Or, you could just accept the early completion as a management reserve buffer against unforseen happenstance. This is your choice because the Advisor obviously does not know  the political and economic factors in your domain of expertise!
 
What if your project was larger than 200 MMM? What if it was so large that a Two-Level hierarchy could not complete it in the desired time period? In that case you would need a Three-Level hierarchy! You would have to further sub-divide the project into pieces that are relatively independent of each other and assign each piece to a separate Two-Level department. 
 

Enter One Parameter for a Three-Level Hierarchy of Departments

  1. The number of Level-2 departments in your Level-3 department. (All other parameters are carried forward from the above data entry items.) In this case, we have entered 4 Level-1 departments.
As shown in the above screen capture, the Management Span of Control Advisor immediately estimates the completion time for a Three-Level hierarchy with the number of Level-1 and Level-2 departments you specified. In the example above, the Advisor estimates it will take only about 7 months which is about 17 months early! We already knew that our 200 MMM was too small to require a Three-Level hierarchy but the Advisor brings that point forward by noting, in red, “Estimate may be unreliable due to very short duration.“  The Advisor, like any Excel spreadsheet, will crank the equations for any so data you provide, even if they do not apply exactly in a given case. However you, if you are an experienced manager, know that it will take at least a few months to get a large project properly staffed and organized and so on. That is why the Advisor alerts the user whenever a given management structure calculates out to less than a 12 month schedule.
 
On the other hand, if you had a project that was considerably larger than 200 MMM, or if the value of early completion was greater than $300K/month, a Three-Level approach might be the best. In those cases, the Advisor will do the calculations and the results will be reliable.
 

What About Cost vs Schedule Tradeoffs?

 

Glad you asked! The above screen capture provides more detailed estimates and suggestions about your project to help you trade COST and NET COST against TIME.

 
If you utilize a One-Level Department with 10 people, the Advisor estimates it will take about 710 APM (Actual People-Months) at a cost of about $14000K ($14M).
 
The Advisor separately calculates the NET, COST, and TIME savings you may achieve by increasing or decreasing the number of people on your project.
 
TIME savings: You may generally reduce the TIME to completion by increasing the number of people. However, after about 15 people in a department, you will actually increase the TIME! The Advisor knows where that point is and will let you know when decreasing people will actually save you TIME.
 
COST Savings: You may generally reduce COST, the number of APM) consumed by your project, by decreasing the number of people. However, below about 6 people in a department, you will actually increase the APM for your project! The Advisor knows where that point is and will let you know when decreasing people will actually save you APM.
 
NET Savings: On the other hand, if there is a late penalty or a bonus for early delivery (in this case valued at $300K/month), you have to take that into account. If you can finish early enough it may be worth adding to the APM expended in order to get that early bonus or avoid that late penalty. The Advisor knows where that point is and will let you know when increasing or decreasing people will actually save you NET COST. 
 
As the above screen capture indicates, time vs cost considerations also apply to a Two-Level and Three-Level management hierarchy, and the Advisor provides estimates for those structures.
 

The Lazy (and Crazy as a Fox) Manager’s Helper

 

 

What if you do not want to mess with all the above considerations and just want the Management Span of Control Advisor to make the “bottom line” recommendations? It can do that too, as indicated in the above screen capture.
 
Just specify a time window around your Desired Completion time and the Advisor checks every reasonable combination of number of people, number of Level-1 and Level-2 departments, and calculates the NET COST for each. It then picks the best one that fits within your schedule window.
 
In the above case, the schedule window has been set to +/- 6 months of the Desired Completion period of 24 months (i.e., from 18 months to 30 months).  It turns out that a Two-Level hierarchy yields the Best NET COST, considering the late penalty (and the bonus for early delivery). If you have 7 people per Level-1 department, and 5 Level-1 departments, you will complete your 200 MMM project in about 27 months, about three months later than you desire, but at an overall NET COST that is more favorable to you.
 
According to the Advisor, in this Best Case NET COST, you will consume about 1064 APM at a cost of $21282K ($21.3M). Your NET COST, including the three-month late penalty, will be about $22268 ($22.3M). 
 
If being three months late is not acceptable, you could reduce the schedule window or reduce the Desired Completion period.  It turns out that you can hit the 24 month schedule if you add an additional Level-1 department. According to the Advisor, you will consume more APM but avoid the late penalty at a minimal additional NET COST of less than $100,000. This is your choice because the Advisor obviously does not know  the political and economic factors in your domain of expertise!
 

The Advisor Provides Graphical Output

If you are curious and want to “look under the hood” of the Advisor, there are six additional sheets with graphical output and descriptive material about the equations utilized and how they are based in Information and Hierarchy theory, etc. You may also ”fine tune” some of the Advisor’s parameters. Here are some of the graphics that are provided.
 
The Project Profile graphs TIME (Months) vs COST (APM) for a One-Level department with from 5-20 people, a Two-Level hierarchy with 4-17 Level-1 departments, and a Three-Level hierarchy with from 3-13 Level-2 departments.
 
The WIN-WIN Range: Note that TIME goes down sharply while COST (in APM) also decreases slightly as the number of people (or departments) is increased from the lowest value to some moderate level, such as 6 people, 5 Level-1 departments, or 4 Level-2 departments. In this range, it is a win-win situation for both TIME and COST!
 
The Good Value Range: TIME continues to go down as you increase the number of people (or departments) a bit, up to perhaps 8 people, 6 Level-1 departments, or 5 Level-2 departments. In this range TIME reduction comes at a considerable additional COST, but, depending upon the overall situation for your project, it may be a good deal.
 
The Poor Investment Range: Beyond some point, further increases in people (or departments) still yields some TIME reduction, but it comes at a very high COST. If meeting schedule is absolutely critical, that investment may be required, but prior planning should be done to avoid those types of situations.
 
The Negative Return Range: After about 15 people or 14 Level-1 departments or 13 Level-2 departments, further increases will actually make the project later! (Proving Frederick Brooks correct when he famously stated his Law: “Adding manpower to a late software project makes it later.”)
 

 

The Tradeoff of Number of People graphs the $K SAVED (or lost) vs the Number of People on the Project, assuming it is done by a single department. Note that COST (in APM) often goes one way and the value of TIME (avoiding late penalty or gaining bonus for early completion) the other way as you add or remove people. The NET savings is the sum of the COST and TIME savings. For the above graph, NET savings (heavy black line yellow diamonds) is maximized with eight people on the project. 
 
Similar charts are provided for the tradeoff of number of Level-1 and Level-2 departments.
 
 
The Summary #1 graph shows how the “bathtub curve” of Brooks famous paper works (see Knol – Quantifying Brooks Mythical Man-Month). If you add too many people, the months to completion will actually go UP!

 
But, Brooks Law is valid only for a one-level department (BLUE curve). A multi-level hierarchy of two-levels (PINK curve) or three-levels (GREEN curve) effectively “drains Brooks “bathtub”.
 

 

The Summary #2 graph compares the raw COST (NOT considering the benefit of avoiding a late penalty or being early to market) for the different numbers of people in Level-1 departments and for different numbers of departments in two- and three-level hierarchies. It also shows how COST increases as TIME decreases for a one-level department (BLUE curve), vs a multi-level hierarchy of two-levels (PINK curve) or three-levels (GREEN curve).
 

The Summary #3 graph  compares the COST (CONSIDERING the benefit of avoiding a late penalty or being early to market) for the different numbers of people in Level-1 departments and for different numbers of departments in two- and three-level hierarchies. It also shows how COST increases as TIME decreases for a one-level department (BLUE curve), vs a multi-level hierarchy of two-levels (PINK curve) or three-levels (GREEN curve).
 
For this project situation, the Management Span of Control Advisor says the two-level hierarchy yields the BEST NET COST.
 
The BLUE disk furthest to the left represents the lowest NET COST for a one-level department, and that is for eight people (a manager and seven workers). Note that that data point corresponds to a TIME to completion of about 75 months.
 
The PINK square furthest to the left represents the lowest NET COST for a two-level hierarchy, and that is for six Level-1 departments. Note that that data point corresponds to a TIME to completion of about 25 months, and that both the COST and TIME are far better than for a one-level approach.
 
The GREEN triangle furthest to the left represents the lowest NET COST for a three-level hierarchy, and that is for four Level-2 departments. Note that that data point corresponds to a TIME to completion of less than 10 months, but the NET COST is greater than for a two-level hierarchy.
 

How Do I Know What Value to Specify for Mythical Man-Month?

A Mythical Man-Month (MMM) is, like a UNICORN, a mythical beast. However, when you read the word UNICORN, you probably got an image of one in your head. After a bit of experience using the Management Span of Control Advisor, your will probably get better at assigning the appropriate value (or range of values) to  MMM.
 
Here is how you might start. I assume you have recently completed a similar project in terms of size and complexity, or at least one that is within a factor of two of the size and complexity of the proposed project. You therefore know how many APM (Actual People-Months)  were expended on that similar project and also the management structure that was utilized (number of levels, how many people per Level-1 department, and, if you used two or three levels, how many Level-1 departments per Level-2 and how many Level-3 departments in the project). Start with the default MMM value of 200 and enter the other data parameters, then go to the appropriate sheet (One Level, Two Levels, or Three Levels) and check the APM estimate. If it is too low, go back to the first sheet and increase the MMM value a bit. If too high, decrease the MMM value a bit. Repeat until you get an approximate match.
 
If you are not sure of the MMM value, you might do multiple analyses with different values (MMM=50, MMM=100, MMM=200, MMM=500 … MMM=1000). 
 

How To Get Best Value from the Management Span of Control Advisor?

If you have used management and mathematical analysis tools you know that estimation is not an exact science. Perhaps the best way to use the Advisor is to compare a range of different numbers of people per department and different numbers of departments.  Thus, while the exact estimates may not be absolutely accurate, the differences between different alternative management structures, on a percentage basis, will most likely be far more precise and reliable. 

 

Theoretical Basis for the Advisor Methodology

 

Brief Description of Brooks Law

 

 

Theory and Equations Relating to Mythical Man-Month Analysis

A Mythical Man-Month is Brooks term for the idea that if a super programmer (I call him or her “Geek Zipperhead”) can complete a given project in nine years, then a department consisting of a manager and nine programmers can do the same job in one year! Of course it ain’t true. That is the point of Brooks influential Law “Adding more men can lengthen, rather than shorten, the schedule.”
 
Brooks presents the three figures shown above and verbally “waves his arms” to justify his Law. However, he provides asolutely no quantification! It is amazing to have a Law that all experienced Information Technology and Management experts agree is true, yet it has no real science or theory behind it! That is the point of my Knol on Quantifying Brooks Mythical Man-Month and this Knol and Management Span of Control Advisor Excel spreadsheet.
 
NOTE: One size does not fit all! This analysis is based on my PhD work that is founded on Shannon’s Information Theory and Smith and Morowitz’s work on the Intricacy of graphical stuctures. Therefore, like all models, it is somewhat simplified and idealized. It might best be used to compare and choose between two or more different management structures rather than as an absolute estimation tool.
 

Application of this Theory to a One-Level Department

a) For purposes of simplification, we assume a flat 10% Administrative Tax to cover the administrative work of the manager. Thus, for a small team of five People, we assume the Manager spends about half his of her time doing direct productive work on the Project. As the team grows larger, and administrative duties increase, we assume the Manager does less and less direct productive work. If the team grows over about ten People, we assume the Manager is fully involved in administrative tasks and probably passes some over to an assistant. We also assume the Level-1 Manager and the workers have about the same salaries and overhead costs.
 
The Equation for Administrative Efficiency is:
EA = 90 (%)
 
b) The Law of Diminishing Returns (LDR) says that if one Worker does 1 unit of work in a given period of time (say a Month), then W Workers will be less Efficient and produce fewer than W units of work in that given period of time. The LDR factor specified by Brooks is 1.5 but my analysis recommends the more common factor of 2. The “0.5” in the equation below is one divided by the LDR factor. (Had we used Brooks 1.5, it would have been 1/1.5 = 0.667.) Note that the effective number of People is reduced by the Administrative Tax.
 
The equation for LDR Efficiency is:
ELDR = 100 (0.9P)0.5 / (0.9P) (%)
 
b) The Optimal Span Hypothesis (OSH), developed in my 1996 PhD Dissertation says that, under certain assumptions, the Intricacy of a system, such as a Management Hierarchy, will be maximized when the Span is 6.4, at which point Intricacy = 0.53 bits. (The “0.53” in the equation below represents maximum Intricacy.) Any Span less than or greater than 6.4 will have less Intricacy. A Management Span of Control of six or seven will be very close to optimal. If we consider Intricacy to be proportional to Efficiency, then P people, consisting of a manager and P-1 workers who directly contribute to the work effort, will be less Efficient, and will produce fewer than P units of work in the given period of time.
 
The equation for OSH Efficiency used here for a One Level Department is:
EOSH = -100 ((2/(0.9P-1)) Log2 (2/(0.9P-1)) / 0.53   (%)
c) The overall Efficiency is the product of the three Efficiency factors (divided by 100 x 100 to account for the fact we are working with percentages) according to this equation:
EC  = EA ELDR EOSH  / 10000  (%)
 
Fine Tuning
For users who wish to experiment, the spreadsheet provides the ability to vary the value of the Administrative Tax (between 0 and 30%)  and the LDR Factor (between 1.0 and 3.0).
 
Nominal Values are: Administrative Tax = 10%    and   LDR factor = 2.0.

 

Application of this Theory to a Two-Level Department

In general, once individual Level-1 Departments are optimized (with five to fifteen people each, depending on the relative importance of COST and TIME to completion), the delivery TIME can be improved by adding from four to fourteen Level-1 departments.
 
For example, a 500 MMM Project may take fourteen YEARS to be completed by a single department even if it is optimized for the shortest time! If the project can be divided up into sub-systems that are relatively independent of each other, and if each sub-system in assigned to a separate department, the TIME may be reduced from fourteen years to less than three! That sounds great until you look at the COST and find that is has ballooned to over $100M from the original $50M.
 
But, since “time is money” and being first to market with a given product may be the difference between winning and losing that segment, it may well be worth the extra $50M.
 
a) For purposes of simplification, we assume each Level-1 department has about the same number of people, as specified in the “One Level” area of the Excel sheet. We also assume Level-1 department managers and the workers have about the same salaries and overhead costs. We assume the Level-2 manager has a higher salary as well as a staff of assistants. 
 
b) Administrative Efficiency – On the “One Level” sheet we considered “Administrative Efficiency” and levied an “Administrative Tax” on workers and department managers. However, since the Level-2 manager and his or her assistants are not counted at all as sources of direct labor, the “Administrative Tax” does not apply to this “Two Levels” sheet except as a carryover from the “One Level” sheet.
 
c) The Law of Diminishing Returns (LDR) for interactions between people in individual departments, called ELDR-1 is carried over from the “One Level” sheet. An additional multiple department LDR efficiency is applied here to the interaction between each of the Level-1 departments. However, we assume each department is responsible for a sub-system that is more or less independent of the others, so the LDR factor may be lower. We use 1.5 rather than 2. The “0.67” in the equation below is one divided by the LDR factor. D is the number of level-1 departments.
 
The equation for LDR Efficiency is:
ELDR-2 = 100 D 0.67 / D (%)
 
d) The Optimal Span Hypothesis (OSH) for interactions between People in individual departments, called EOSH-1 is carried over from the “One Level” sheet. An additional multiple department OSH efficiency is applied here for the interaction between the Level-1 departments. If we consider Intricacy to be proportional to efficiency, and if a Level-1 department produces 1 unit of work in a given period of time, then a level-2 manager and D departments will be less Efficient, and will produce fewer than D units of work in the same given period of time. We also assume the staff of the Level-2 manager imposes a management burden roughly equivalent to having an additional Level-1 department
.
The equation for OSH Efficiency is:
EOSH-2 = -100 ((2/(D-1)) Log2 (2/(D-1)) / 0.53   (%)
 
e) The overall Efficiency in the product of the four Efficiency factors (divided by 100 x 100 x 100 to account for the fact we are working with percentages) according to this equation:
EC  = ELDR-1 ELDR-2 EOSH-1 EOSH-2  / 1000000  (%)
 
Fine Tuning
For users who wish to experiment, the spreadsheet provides the ability to vary the value of the Management Factor (between 1.0 and 5.0), which is how we account for the second-level manager’s higher salary plus staff salary and overhead. For example, M=4 would account for a Second-level Manager and three assistants. M=4.5 would account for a Second Level who earns 1.5 times as much as a First Level and has three assistants. The nominal value is Management Factor = 4.0.
 
You may also vary the LDR Factor (between 1.0 and 3.0) for the interaction of departments. Here we may assume that each department is working on a relatively independent portion of the overall project, thus, the LDR factor may be 1.5 or even less. (The LDR factor set on the “One Level” sheet, for the interaction of people within a department, is not affected by the value set here). The nominal value is LDR Factor = 1.5.
 

Application of this Theory to a Three-Level Department

In general, once individual Level-2 departments are optimized (with four to fourteen Level-1 departments each, depending on the relative importance of COST and TIME to completion), the delivery TIME can be improved by adding from three to thirteen Level-2 departments.
 
For example, a 500 MMM Project may take fourteen YEARS to be completed by a single Department even if it is optimized for the shortest time! Given certain assumptions, a two-level hierarchy may reduce that time to three years, and a three-level hierarchy may further reduce it to less than one year!
 
The assumptions are that the project can be divided up into sub-systems and sub-sub-systems that are relatively independent of each other, and, if each sub-system in assigned to a separate Level-2 department, and each sub-sub-system to a separtate Level-1 department, the TIME may be reduced from fourteen years to less than one! That sounds great until you look at the COST and find that is has ballooned to around $140M from the original $50M.
But, since “time is money” and being first to market with a given product may be the difference between winning and losing that segment, it may well be worth the extra $90M.
 
a) For purposes of simplification, we assume each Level-1 department has about the same number of people, as specified in the “One Department” area of the Excel workbook. We also assume each Level-2 department has about the same number of Level-1 departments, as specified in the “Two Levels” area of the Excel workbook. We also assume Level-1 department managers and the workers have about the same salaries and overhead costs. We assume the Level-2 and Level-3 managers have higher salaries as well as a staff of assistants.
 
b) Administrative Efficiency – On the “One Level” sheet we considered “Administrative Efficiency” and levied an “Administrative Tax” on workers and department managers. However, since the Level-2 and Level-3 managers and their staffs are not counted at all as sources of direct labor, the “Administrative Tax” does not apply to this “Three Levels” sheet except as a carryover from the “One Level” sheet.
 
c) The Law of Diminishing Returns (LDR) for interactions between people in individual departments, called ELDR-1 is carried over from the “One Level” sheet as is the ELDR-2, for interaction between Level-1 departments, carried over from the “Two Levels” sheet. An additional Level-3 LDR Efficiency is applied here to the interaction between each of the Level-2 departments. However, we assume each Level-2 department is responsible for a sub-system that is fairly independent of the others, so the LDR factor may be lower. We use 1.3 rather than the 2.0 that was used on the “One Level” sheet or the 1.5 used on the “Two Level” sheet. The “0.77” in the equation below is one divided by the LDR factor. D is the number of Level-2 departments.
 
The equation for LDR Efficiency is:
ELDR-2 = 100 D 0.77 / D (%)
 
d) The Optimal Span Hypothesis (OSH) for interactions between people in individual departments, called EOSH-1, is carried over from the “One Level” sheet as is the EOSH-2 , for interaction between Level-1 departmets, from the “Two Levels” sheet. An additional multiple Department OSH Efficiency is applied here for the interaction between the Level-2 departments.  If we consider Intricacy to be proportional to Efficiency, and if a Level-2 department produces 1 unit of work in a given period of time, then a Level-3 manager and D Level-2 departments will be less Efficient, and will produce less than D units of work in the same given period of time. We also assume the staff of the Level-3 manager imposes a management burden roughly equivalent to having two additional Level-2 departments.
 
The equation for OSH Efficiency is:
EOSH-2  = -100 ((2/(D)) Log2 (2/(D)) / 0.53   (%)
 
e) The overall Efficiency in the product of the four Efficiency factors (divided by 100 x 100 x 100 x 100 x 100 to account for the fact we are working with percentages) according to this equation:
EC  = ELDR-1 ELDR-2 ELDR-3 EOSH-1 EOSH-2 EOSH-3 / 10000000000  (%) 
 
Fine Tuning
For users who wish to experiment, the spreadsheet provides the ability to vary the value of the Management Factor (between 1.0 and 20.0), which is how we account for the third-level manager’s higher salary plus staff salary and overhead. For example, M=7 would account for a Third-level Manager and six assistants. M=9 would account for a Third Level who earns twice as much as a First Level and has seven assistants. The nominal value is Management Factor = 8.0.
 
You may also vary the LDR Factor (between 1.0 and 3.0) for the interaction of departments. Here we may assume that each department is working on a relatively independent portion of the overall project, thus, the LDR factor may be 1.3 or even less. (The LDR factor set on the “One Level” sheet, for the interaction of people within a department, andthe LDR factor set on the “Two Level” sheet are not affected by the value set here). The nominal value is LDR Factor = 1.3.