Management with Measurement: Inputs

"Management by Numbers" is seriously deficient as it focuses on a single dimension of a very complex multi-dimensional task. "numbers" are a necessary but far from complete aspect of the job. Some might say skills in "handling people" are much higher priority.

This stems from the rule of management: we only have managers if there is too much work for a single person.

In 1916 Henri Fayol laid out the dimensions as he saw them:

To manage is to forecast and plan, to organize, to command, to coordinate and to control.

Max Wideman uses "Plan, Organize, Execute, Monitor and Control" for Project Management [uncertain of the source].

"Management with Measurement" seems a much closer fit to what I'm trying to describe.

Why start here?
There are a number of measures that require a common element, Inputs:

• Productivity: Output / Hours Input
• Efficiency: Outputs / Total Inputs
• Effectiveness: Realised Benefit / Total Inputs

I've not seen Management or Cost Accounting methods to determine the input overheads incurred with Management. The total cost to the organisation of all managers.

First-line staff productivity, without the overheads of the management process and costs, are more indicative of workplace improvements.

As an investor, I'd like to be able to compare across companies their efficiency and effectiveness of management.
In the Public Sector, outputs and realised benefits are more nebulous ("one good policy a year per department"?), but inputs can be accurately measured and reported. Differences can then be explored.
In the Not For Profit sector, all overheads are critical, none more so than paying non-productive free-riders, and of real interest to many stakeholders: financial supporters, volunteers and the Board.

What types of employees are there?

• First-line employees: No reports, directly contribute to goods/services produced. Notionally 100% of time is "direct production".
• Leading Hands, Team Leaders: Have reports, but limited authority to direct them. Directly contribute to goods/services produced. Notionally near 100% of time is "direct production", so are counted as "first-line" employees.
• Supervisors: Reports are First-line employees or Team Leaders. Less than 25% of time is "direct production".
• Managers: Reports are Supervisors or Managers. Less than 5% of time is "direct production".
• Top-line Manager: Those managers who do not report to another manager within the organisation or organisational-unit. This definition includes "co-owners" or "co-CEO's".
• Owners: When the owner works in the business above the first-line, they will be counted as a supervisor, manager, or when the entity is large enough, as the Top-line manager, unless organised otherwise.
• Boards: These are regarded as external to the entity. Directors, owners and managers (like the CEO), who sit on the board and work in the business are counted within the business.
• Double-counting: No individual can be counted more than once. Each must be categorised into exactly one category per report. Internal consistency requires that organisations define a single set of classification rules that can be applied across the whole organisation, and is very infrequently changed.
• Lowest-level Principle: Those who can be classified at multiple-levels, like an owner/manager, should be classified at the lowest level. An owner/manager with one employee might consider themselves Top-line Manager, Manager and Supervisor, but they can only count classify themselves at their lowest authority level: supervisor.

Figures of Merit:

• Definitions:
• W: Size of First-line workforce.
• S: Size of supervisory workforce.
• M: Size of managerial workforce, including supervisors.
• Fan-out: the mean number of reports. Three figures reported:
• F_S: Supervisors (a whole number, not fractional). Sum of all first-line employees / sum of all supervisors.
• F_M: Managers (fractional). Mean of reports per manager, for all managers.
• F_T: Top-line manager (whole number). number of managers irectly reporting to the top manager.
• Hierarchy Depth:
• D: The mean of 'Depth': For each First-line employee, the number of people above them in the management chain to the CEO. Only count one path in "matrix" style organisation.
• Management Burden:
• B: The percentage of salaries and staff benefits paid to management.

These metrics also usefully apply to each Organisational Unit within an Organisation.
ie. Reporting for each Division and every Department, down to work-group level, will be useful for Organisations. Both for comparing the effectiveness/efficiency of the Management Process, but also for highlighting differences in the underlying task difficulty across the Enterprise. For a mining company, digging operations will have a different 'fingerprint' than Commercial and Planning departments.

For Public Service and Not-for-Profit organisations, drilling down, and especially reporting Management Burden, will be very useful to stakeholders, internal and external, to assess the organisation and Management Processes.

The 3-part Fan-out should always be reported/written with Hierarchy Depth: [F_S/F_M/F_T/, D].

Eg: [12/3.5/6, 7.25]

Calculating Workforce size:

For the organisation, [12/3.5/6, 7.25]:

• total supervisory and management staff = management fan-out raised to the power of managerial hierarchy depth. (M = F_M^D-1 + F_T).
• M = 3.5^7.25-1 + 6 = 3.5^6.25 + 6 = 2514 + 6 = 2520.
• approximate supervisory staff = management staff divided by management fan-out. (S = M/F_M).
• S = 2520 / 3.5 = 720
• total first-line staff = supervisory staff times the supervisory fan-out. (W = S * F_S)
• W = 720 * 12 = 8640
• The first-line to management staff ratio ( 8640 to 2520, or 22.6% mgt of 11,160) can be calculated, but the management burden as a proportion of salaries/wages cannot be derived.

Note: Because summary statistics are reported and are all that is necessary for good comparisons, exact headcount/FTE's cannot be derived from the metric. In special circumstances, discussed below, exact numbers might be added to the metric.


FTE vs Headcount?

The Hierarchy Depth must be reported in Headcount, not FTE.
But both numbers are meaningful for Fan-out and I don't have a preference,

Presumably, nearly all managers and most supervisors will be permanent employees, so in the pyramid above the first-line, FTE and Headcount are identical.

In workforces with a high proportion of casual labour, like large retail operations, headcount must be reported not FTE, to get a true picture.

An 'F' could be added to the supervisory fan-out for clarification. eg: [5F/3.5/6, 7.25], For enterprises which feel both numbers are needed for a true picture, the supervisory fan-out in terms of Headcount should be written first. viz: [(12, 5F)/3.5/6, 7.25]

Smaller Enterprises, Depth less than 3

Why is a Depth of 3 interesting?
It is the first level at which managers report to managers and the top-line manager only has managers reporting to them.

• For an owner/operator enterprise, the depth, 'those above first-line', is zero. viz: [0/0/0, 0].
• When a business gets its first employee and the owner becomes a supervisor, the depth is 1. viz: [1/0/0, 1]
• As the business expands, leading hands or team leaders are hired. The owner is still a supervisor and the depth is 1. An owner with a staff of 15, including leading hands is: [15/0/0, 1]
• The next breakpoint, is the hiring of the first supervisor (as distinct from team leaders). The owner is now a manager. The depth is 2. At this point, good businesses will have appointed, even if not listed companies, a board to advise them and to provide some external review, feedback and accountability to the owners. Avoiding double-counting, a single-owner business with 4 supervisors and 32 staff would be: [8/4/0, 2]
• After the next step, managers reporting to managers, all business are equal under this model. viz [8/3.5/6, 4] and [(12, 5F)/3.5/6, 7.25] tell an investor, stakeholder or manager that both organisations have similar management processes and overheads but one has a much higher part-time casual workforce.

When a business has co-owners and no supervisors (and hence no managers), the fan-out for supervisors, managers and top-line manager should be written as 0.

Eg: [0/0/0, 0]

When a business has an owner(s), no employed supervisors and no managers, the fan-out for managers and top-line manager should be written as 0 due to the lowest-level principle. As discussed below, the first-line workforce size cannot be uniquely calculated, because the effective supervisory staff, the owners, isn't specified. The metric is ambiguous in these cases:

Eg: [(12, 5F)/0/0, 1] could describe an organisation with one owner and head-count 12, or two owners and head-count of 24.

Metric Deficiency: Workforce size for small organisations and exact Supervisor Count.

The proposed metric does not inform interested parties of the total headcount or FTE of first-line staff an organisation, only summary statistics of management. First-line staff numbers could be added as a preceding term when the organisation is small. For larger organisations, management and first-line staff numbers can be computed from the metric.

Eg: [(12, 5F), (12, 5F)/0/0, 1] or [(24, 10F), (12, 5F)/0/0, 1] to disambiguate the one or two owner example.

And for a large organisation with a large casual workforce:

[(12,500, 6150F), (12, 5F)/3.5/6, 7.25]

Application

The Fan-out and Depth figures can be used to accurately define "Small", "Medium" and "Large" enterprises. The ATO defines a small business as having an aggregate turnover of under $2million a year, and everything else by default, is "large". There is another break-point at $20million/year, where taxes must be paid monthly, suggesting that "medium" sized entities have turnover between $2- and $20-million/year.

At the average weekly wage and with 25% on-costs and staff costs of 50%, $2-million/year is currently 10-15 FTE's.

The US SBA (Small Business Administration) defines 'small' as under 500 (local) employees. Any entity larger is a "large" business.

Company size definitions:

• Micro-Business: less than [0.5F/0/0, 0]
• Small Business: up to [20F/0/0, 1] and for low-intentsity manufacturing [100/0/0, 1]
• Large Business: over [500F, s/x/y, z], where x and y greater 0, and z greater 4.
• Medium Business: [10-500F, s/x/y, z], where x greater than 0.

Examples of Management Burden

The cost of managers is related to two things:

• the "fan-out". The number of people that report to a manager.
• the hierarchical multiplier. For each level increase in the hierarchy, what's the percentage increase in salary, assuming a constant multiplier?

The fan-out cannot be under two.
For that to be true, at least one manager has a direct-report count of 1, which violates a basic rule:

We have managers because there is too much work for one person to do.

I expect fan-out and hierarchical multiplier to be related: a larger multiplier if there are more reports.

Using Telstra as a rough model:

• There are ~30,000 (2¹⁶) employees.
• Front-line staff are paid ~$40,000, and, in the days of Sol Trujillo, the CEO got ~$10M, or 256 (2⁸) times the average front-line staff wage.

If there was a fan-out of 2, there'd be 15 levels of hierarchy and 50% of the workforce would be first-line and 50% management and supervisors.

Lets say it was 16 levels, so for every two levels of hierarchy, pay is doubled.
Each level would have a 1.414 (square-root 2) multiplier.

The table below contains some examples of Management Burden, B. In a real organisation with access to the accounting system, B would be calculated, not estimated like this.

The assumptions made in this example:

• 'Fairness' and consistency in apportioning the wage differential between every level of management, from supervisors to Top-line manager.
• More realistically, the gap between first-level employees and supervisors will be smaller than the gaps between management levels, as well as the supervisory fan-out, F_S, will be larger.
• "the senior management team", the Top-line manager and their direct reports, are likely to be on their own payscale.
• The effects of F_T, and difference to, F_M are ignored.

Columns:

• W = first-line workforce
• M = managerial workforce
• W + M = total workforce
• F_M = Fan-out of management
• D = Hierarchical Depth, layers above first-line employees.
• Max Wage Ratio = ratio of highest wage (CEO) to average first-line wage
• Hierarchical wages multiplier = assumed fair multiplier between each level of management.
• Avg Wage mult = Average (mean) wage of enterprise, as a multiple of average first-line wage.
• Wages multiplier = Total wages as a number of multiples of first-line wages.
• Mgt Burden = Management Burden, management wages as a percentage of total staff costs.

Management Burden with varying Maximum Wage Ratios

W	W+M	FM	D	Max	Hierarchial	Avg	Wages	Mgt
				Wage	wages	Wage	multiplier	Burden
				Ratio	multiplier	mult
16,384	32,767	2.0	14	128	1.414	1.698	3.395	70.54 %
16,384	32,767	2.0	14	32	1.281	1.389	2.778	64.00 %
16,384	32,767	2.0	14	256	1.486	1.923	3.846	74.00 %
16,384	32,767	2.0	14	1024	1.641	2.640	5.281	81.06 %
16,384	21,845	4.0	7	32	1.641	1.271	1.694	40.96 %
16,384	21,845	4.0	7	256	2.208	1.666	2.213	54.81 %
16,384	21,845	4.0	7	1024	2.692	2.197	2.929	65.86 %
32,768	37,449	8.0	5	32	2	1.167	1.333	24.98 %
32,768	37,449	8.0	5	256	3.031	1.405	1.605	37.7 %
32,768	37,449	8.0	5	1024	4	1.723	1.969	49.21 %

Discussion

The Wage Ratios chosen are indicative of:

• 32 = pre-1980
• 256 = a typical current multiple
• 1024 = high current multiple, but not extreme.

The worst case, giving both the maximum Hierarchical Depth and highest numbers of managers is with the lowest possible fan-out number, F_M = 2.

Organisations with higher Depth have slower lines of communication and more players involved in every decision and report. This was the observation behind the 1980's push to "flatten the organisation".

The management burden reduces considerably with a flattening of the hierarchy, with high management fan-outs. I would expect high fan-outs would only be possible with more routine operations. Organisations with complex, highly variable tasks require more communications in all directions and more management action, causing managerial workloads to quickly increase and hence obtainable fan-outs to decrease.

Whilst the Average Wage multiplier might seem modest, say the middle entry (F_M = 4, D = 7, Ratio = 32), with the organisation's wage being 27% higher than the first-line average wage (eg. $40,000 and ~$60,000), the wages paid to management are a significant proportion of total wages: 41%, quickly rising to be two-thirds of total wages, for no direct contribution to output.

For investors and prospective purchasers of organisations, the management fan-out and management burden provide a new insight into where input costs arise and how gross productivity is effected by them.