Work recognition model for a higher education unit

Abstract Higher Education frameworks have a strong focus on increasing students’ satisfaction. This vision increases expectations on academic performance that often derive from stringent output measures for staff. The combination of internal and external demands for workers, such as those derived from their interaction with society, could create inadequate working conditions, which highlights the need to develop objective, rational, and robust mechanisms to distribute roles and responsibilities more fairly. This paper introduces a work recognition model for managing higher education units. It accounts for individual effort per discretised academic activity over a range of teaching, research, and administration duties. The model integrates standard academic activities into a mathematical framework characterised by continuous derivable functions that can be used to visualise fluctuations of workload across a complete academic year. The established framework enables optimisation of workloads through redistribution, moving away from diagnosing issues experienced by individuals subject to imbalanced or unfair workloads, to propose a practical solution. It is also possible to enhance the architecture of the proposed model to incorporate further activity or allowances and potentially increase robustness. In addition, the numerical model is relatively easy to implement in a variety of platforms. The proposed model was tested on a case study including 26 academics, mixing three-legged and teaching-focused contracts, showing how it decreases the relative differences of workload by a proportion of 4:1, after redistribution.

ABOUT THE AUTHOR P Martinez-Vazquez The development of a Work Recognition Model to Manage a Higher Education Unit is an attempt to mitigate imbalances in the distribution or roles and responsibilities at work.Notwithstanding the model developed within the academic environment, it could extend to any organisation that manages people.This could potentially benefit further areas of society and improve the quality of life of workers.Dr Martinez-Vazquez is interested in engineering education.His experience and background as a civil engineer allow the use of numerical methods for the qualitative assessment of academic outputs that could eventually support the development of tools for improving current practice.Dr Martinez-Vazquez's leadership role has motivated the development of a work recognition model to manage a higher education unit, and wishes to continue this research path while enhancing collaboration networks worldwide.

Introduction
The United Kingdom established the Council for National Academic Awards (CNAA) along with the development of higher education (HE) system in 1964, which meant that the quality assurance system for British higher education was initially built (Tapper & Salter, 2004).Following the vigorous development of the economy, colleges and polytechnics were established.This resulted in two different assessment systems and assessment results.In 1992, most Colleges were subsequently upgraded to Technological Universities, and the QAA established external assessment systems for all Higher Education Providers (Tapper & Salter, 2004).This progression has derived in a pedagogical philosophy of student-centeredness (Bremner, 2021), a paradigm that has contributed to shape the Standards and Guidelines for Quality Assurance in the European Higher Education Area (ESG, 2015).The UK Quality Code for Higher Education (QAA, 2023) also states that student-centred learning and teaching should be put forward and emphasised so that the protection of students' interests would remain a quality assurance priority in higher education (Gover et al., 2019).Although the fundamental purpose of the institutional framework is to promote Higher Education Providers (HEPs) to raise the level of operation and the quality of teaching and researching (Greere, 2023), it is also true that staff are susceptible to physical and mental health problems caused by imbalanced lifestyles (Pace et al., 2019).National figures in 2012 highlighted that in the UK higher education around 0.2% (1/500) of staff disclosed a mental health condition to their university.Studies by Kinman and Wray (2013) and by Vardi (2009), which focused on stress and wellbeing among university staff, revealed that university staff are more stressed than the average worker and that the problem has become worse in recent years, to the point that researchers often cite the work of academics as labour (Boncori et al., 2020;Papadopoulos, 2017) or part of a chain of manufacture (Dobija et al., 2018(Dobija et al., , 2019;;Hartmann, 2019).Furthermore, Houston et al. (2006) highlighted the lack of recognition of societal issues that, combined with inappropriate output measures, lead to excessive workloads and hence imbalance lifestyles.

Performance indicators of academic practice include the Teaching and Research Excellence
Frameworks, known as TEF (OFS, 2020) and REF (REF, 2021), respectively.The TEF is a national exercise that assesses excellence in teaching at universities and colleges, and how each higher education provider ensures excellent outcomes for their students in terms of graduate-level employment or further study (OFS, 2020).As for the REF, research funding bodies shared policy aims at securing the continuation of a world-class, dynamic, and responsive research base across the full academic spectrum (REF, 2021).
The government introduced the TEF as a way of: • Helping the participating universities and colleges to meet unified national quality requirements.
• Encourage universities and colleges to provide a better student experience by working with their pupils.
• Raising esteem for teaching amongst HE providers.
Whilst the purpose of the REF being: • Provide accountability for public investment in research and produce evidence of its benefits.
• Benchmarking information and establishing reputational yardsticks.
• Inform the selective allocation of funding for research.
University staff are thus subject to high-quality performance metrics that, past a certain threshold, could result in severe or unfair workloads, which is also reflected in student-staff ratios (National Statistics, 2022).These metrics are, however, unable to assess other values and priorities that underlie individual performance (Lazarsfeld & Morgan, 2009;Söderlind & Geschwind, 2019).Nonetheless, the focus of past research has centred on diagnosing the problem as opposed to developing practical solutions.Franco-Santos and Doherty (2017) and Kenny (2017) found that a direct performance management approach which highly relies on performance measures and targets was negatively related to academics' well-being although, by focusing on the learnings of stewardship, emphasising staff involvement and development, which gives academics a better experience of their work.In a separate investigation, Acton et al. (2015) highlight that teaching and learning for students need to be creative in sustaining and managing the instructor workforce to avoid further investment for supporting faculty.The critique published on the subject is abundant, which contrasts with numerical algorithms that could capture those findings.Bitzer (2007), Cawood et al. (2008), and others have put forward detailed parameterisation of quantifiable activity divided in areas such as teaching, research, community service, management, and administration, although neither of those studies offered platforms for processing information.More in-depth approaches to manage workloads are reported in Nnadozie (2015) and Sood (2016).These are attempts to establish more formal frameworks to quantify teaching, research and admin work.However, these do not distinguish sub-activities contained in each heading.On the other hand, descriptors issued by Higher Education institutions tend to provide more detail of what academic work entails to include some examples of good practice, see, for example UCL (2023), but those descriptors do not crystallise rational methods that enable to weigh sub-activity before the data are processed.
The above identifies the need for objective and transparent mechanisms for allocating work, bearing in mind examples of good practices such as those presented in Athena forums (Whitelegg et al., 2018), namely: The improvement of working conditions would allow progression of the implementation of hybrid teaching and blended-learning, digital tools, and the strengthening external collaborations (Bebbington, 2021), amongst other initiatives that, due to work overburden, have been delayed or left behind.
The present investigation intends to fill in knowledge gaps by introducing a model that enables balancing workloads through an optimisation algorithm.It establishes a mathematical description of academic activity including its parameterisation.The algorithm enables re-distribution of workload, allows transparency and flexibility while bearing in mind broader recognition of tasks such as outreach and citizenship (Whitelegg et al., 2018).It also provides alternatives to address personal issues such as parental leave and could be adjusted through further optimisation stages during an academic year.The proposed model is tested on a case study including 26 academics based on a higher education unit in the United Kingdom.

Overview of academic activity
Three-legged contracts in HE institutions comprise teaching, research and administrative duties (HESA, 2023) that can be discretised as shown in Table 1.
It becomes necessary to standardise time associated to each task listed in Table 1 by combining quantity and quality through specific weighing values (Brady & Bates, 2016).For example, it will be considered that each teaching credit involves 10 hr of staff work when it relates to an existing course and 20 hr if it relates to new material.The metrics include about 22 hr a year for mentoring students through personal or group meetings.This activity became part of the workload to guide students on university-wide activity as they engaged with online learning, otherwise they could oversee important information related to their studies.Pastoral support therefore quantifies separately as it does technical support provided to design groups.
Similar metrics apply to research (Hause & Zettelmeyer, 2016).For example, to assign 50 hr of effort for chairing steering committees or 100 hr when acting as co-investigator-who typically oversees work done by research fellows.Each postgraduate research student and each publication would require 20 hr of supervision and 80 hr of effort, respectively.And one researcher would spend 24 hr in dissemination events through an academic cycle.
Depending on the leadership roles) undertaken, one could fix the amount of time required by the task (NASUWT, 2023).Noting that the weighting of activity above results from internal records, hence it lies on a semi-empirical or pragmatic base.It would be the manager(s) of the academic unit who could designate tasks and weigh these depending on availability, skills, and personal interests.Each activity area is thus undertaken by academics to configure individual workloads.
The following paragraphs show how the academic activity outlined above integrates into a model, while Section 3 illustrates its applicability through a case study.

Work recognition model
The model described below attempts to tackle the lack of objective, rational, robust, and flexible mechanisms to quantify academic activities undertaken by academics.The model's scope and parameterisation derive from the author's own experience when managing academic staff in a Higher Education Institution in the United Kingdom.The data presented are therefore real and correspond to internal records that higher education managers tend to use regularly.For example, they always know what staff is dedicated to each task and in what amounts or period.Managers also have access to personal records where staff declare illness or leave, which informs their decisions to manage human resources.
The details presented in this study have shown little variation over time, which makes them reliable.For this reason, no external consultations or surveys to collect information were deemed necessary.As neither teaching nor research outputs are in use, personal identities are not at risk.The information is anonymised, and personal details have been replaced with a generic ID number to identify each of the 26 academics, as shown in Figure 2.

General framework
We quantify total workloads per activity area with Equation ( 1)-( 3) and considering the coefficients listed in Table 2.
Where T T , T R , and T A , represent workloads associated with teaching, research, and administration, respectively.The remaining variables in Equation ( 1)-( 3) are defined in Table 1.1)-( 3) (HoD) (DHoR) (REF) (Outreach) (Senior Tutor) (DubaiC) (ECPanel) (Labs) (Train-Rig) Constant values θ, ρ, α, in Table 1 result from a consultancy with young and senior colleagues within one HE institution.The proposed values could therefore change from one educational system to other.For example, the scope and duration of final-year projects assumes that supervision and assessment require 5 hr and 2.5 hr, respectively.Those supervision meetings span over a period of 12 weeks-approximately one 25 min meeting per week, while the assessment is on a 10-page report marked by reviewers with an automated system that reduces man hours.Noting that those metrics derive from internal records of the HE unit addressed in the investigation.
The total workload per area is thus given by, The solution to Equation (5) for teaching, research, and administration, respectively, is as in Equation ( 6).
Table 2 summarises suggested values for constant parameters employed to resolve Equation ( 5)the reader can see the full solution within the APPENDIX.Equation (4) provides the idealised work delivery through one calendar year as shown in Figure 1.
In Figure 1, the main teaching periods centre around m = 2 and m = 10 with a notable decrease around m = 6.According to this, teaching related activity continues throughout the full year.As the teaching peaks appear, research activity decreases.This may not be a rule for all but would represent a tendency across three-legged staff who manage activity to complement it across different periods (Department of Education, 2018).This includes administrative work which shows fewer seasonal fluctuations, with peaks taking place during and past assessment periods.The combined curve illustrates net variations over time, according to this model.The current model highlights fluctuations of work throughout an academic year.This would be evident on an individual basis but suggests some areas of improvement, since one could argue that a perfectly balanced workload would result in a combined curve with zero gradient.
The delivery of work determined by Equation ( 6) enables a quick quantification of workload imbalances that might occur during administration and planning stages that precede an academic cycle.By working out average values for C 1 , C 3 , and C 5 , one could determine the differential of workload per staff through Equation ( 7), where χ represents the constant term affecting C k expressed in Equation ( 6).Noting that ΔT T in Equation ( 7) yields total allocated time below or above average workloads.
Furthermore, the derivation of either Equation ( 1)-( 3) with respect to a given sub-activity (Z) equals a constant value # j i.e., either coefficient θ j , ρ j , or α j , as in Equation (8).It is therefore possible to use Equation ( 9) for deriving the rate of work that modifies any initial distribution for a given sub-activity, namely: C; G; M; T; D; P; E; S; W; F; orR, for any staff, by using Equation (10), noting that the value of ΔT k is not always positive.
We now proceed to test the established framework on a specific case study.

Initial estimation of work
The example below considers a group of academics supporting institutional activity areas listed in Table 1. Figure 2 shows the initial distribution of workload across 26 faculty members.
No rule was applied for setting up individual workloads, but these would depict some asymmetry.The total individual activity requires within 734.5 hr and 2196.5 hr whereas ΔT T ¼ ∑ ΔT k ¼ ∑ ΔC k � χ estimated with Equation (7) reports under and over-performances equal to −462.5 hr and +999.5 hr, for staff ID numbers 11 and 17, respectively.Note that the value ∑ ΔT k is negative when the individual workload falls below the average, which in this case stands as 1197 hr.
Extreme values represent 83.46% and 38.64% above and below the average performance measured in hr.It is not within the scope of this paper to scrutinise potential reasons that could trigger such imbalance, although the large scatter will help to test the optimisation algorithm covered in the next section.

Redistribution of workload
The algorithm proposed includes three basic steps.
(a) Identify activity-role per staff to discharge.
(b) Nominate recipients of those activities.
In the case study, we establish threshold values to discharge/re-allocate workload.That would be ±10% around the average value, which leads to the sub-matrix embedded in Table 3.
Table 3 lists in the first column the activity or role for discharge and identifies the relevant individuals in the remaining columns including through specification of the fraction of the partial workload.Unit values in the bottom row of the table identify the recipients of work that is being redirected.These figures are graphically presented in Figure 3 where one can observe the configuration of workload above and below the average that needs reallocation.
The case study includes as many activities/roles to transfer as recipients of the tasks.This would not be a rule, therefore reassigning work would not always imply the one-to-one reallocation of work suggested in Figure 3.The best fit requires permutations as to assign activity/role k to the n-th individual so that the mean square error minimises.That procedure would yield various scenarios whose amount would increase with the number of tasks and recipients to correlate.Figure 4 illustrates two asymmetric scenarios that make less obvious the reallocation pattern.
The numerical method to solve the optimisation problem outlined above is visualised as follows.Consider two spaces with irregular shape and variable dimensions as shown in Figure 5.
In this analogy, Space 1 represents the total workload for discharge which could be measured as the surface enclosed within the space delimited.The domain of this space includes all 17 activities or roles listed in Table 1 hence the amplitude along each of the 17 directions on the place corresponds to the amount of hr for discharge.On the other hand, Space 2 represents the receptive domain indicating in each direction the acceptance of workload per target faculty member, which in the case study above equals 13.
The optimisation task therefore consists of superimposing both spaces.This implies changing the shape of Space 1 to fit within Space 2. In the present investigation, the numerical algorithm to make spaces consistent with each other consists of projecting each radial vectorial amplitude (L) measured in Space 1 on Space 2, using a randomly generated azimuth Θ RAND -see Figure 6.
Re-directing each radial amplitude would modify the shape on Space 1 differently on each realisation.However, the probability that one realisation including 17 new amplitudes for the area enclosed in Figure 5a solves the problem is rather low.It is therefore necessary to introduce a loop to redistribute the workload.Figure 7 illustrates the proposed algorithm following the   -182 -306.5 -130 70.981 92.981 -146.5 -159.5 -247 -462.5 251.98 328.98 321.48 -116.5 258.48 999.48 -46.02 125.48 -74.02 -190.5 -161.5 -372 -354.5 380.48 Figure In this algorithm, Epoch is selected by the user.This implies that the redirection of nominated activity/roles will randomly reallocate amongst recipients epoch-number of times, which is indicated by Θ RAND-j = Rand () -> ΔT k .This expression could be read as reassigning the discharged role-  The random reallocation of work is followed by an update of the individual allocated time and the corresponding standard deviation of the new set, Std (T T;i Þ.In this expression, the subscript T indicates that first-order statistics apply to the full database (all staff), while i relates to the i-th iteration within Epoch.If the standard deviation of the updated configuration of the workload is  lower than in the previous one saved by the algorithm, the partial allocations are overwritten and each individual workload resets to its original value T T;0 .

Results
Figure 8, 9 show the best fit between workloads to accept, and the ones accepted once Epoch equals 100 × 10 3 .Figure 8, in terms of Space 1-2 and Figure 9 by providing the full workload configuration.
Note that activity-roles to discharge did not include those within ±10% of the average.This is the reason why only seven columns under this heading appear populated in Table 3. Equally, the original allocated work for the 13 nominated recipients shown in Table 3 and Figure 3, exceeded the ± 10% threshold.
It is also worth highlighting that the time allocated to each activity-role ranges non-uniformly between 15 and 400.This is the reason why one could not expect to have a perfect match past the implementation of the algorithm.Notwithstanding the results obtained showed improvement.The range for ΔT k passed from −462.5 ≤ ΔT k ≤999.5 to −161.6 ≤ ΔT k ≤125.4,while the corresponding standard deviation including all staff workloads passed from 333 to 79.The initial and redistributed workloads are shown in Figure 10.universities as reported by Kenny and Fluck (2022), such as transparency, visibility, equity and flexibility.Additional principles related to connection to performance, and the possibility to negotiate expectations (Naylor et al., 2021), are less visible, but could be covered with a more robust approximation tailored to accept input data collected through surveys or captured via other metrics for performance.

Final remarks
This investigation presents a novel work recognition model that could help to better balance staff workload.The model moves away from traditional approaches focused on efficiency, productivity, and accountability, to allow the accommodation of other headings, for example extra-curricular activities, scholarship, and welfare (Gover et al., 2019;Greere, 2023).Although the latter is not explicitly shown in the equations used to quantify work, these could be easily integrated by expanding the polynomials, which also demonstrates the flexibility of the method.
The referred mathematical description allows the parameterisation of academic activity.It enables quantifying objective and subjective components of academic profiles including but not restricted to teaching credits, research supervision, and leadership roles (NASUWT, 2023); HESA (2023).By keeping these separate in the proposed polynomials, one could integrate or eliminate items from the list as well as weighing these according to the importance of degree of difficulty.
Higher education managers can show and discuss with employees the way their work is being determined (Houston et al., 2006), also addressing the fact that the approach follows best academic practice as reported in Athena Forums (Whitelegg et al., 2018).The way this happens is explained in the following summary, According to this, the model promotes transparency, flexibility, and is not too fine-grained.The model's architecture also enables educational managers to balance workload across years, or exercise refinement through the addition of welfare issues such as parental or sick leave, or other special needs.The level of quantification of tasks added to its capability to redistribute workload (optimise) should tackle gender bias, as equal work for everyone is at the core of the algorithm.The user should note that the weighing of subtasks can be tailored to reflect different criteria or precision.We therefore provide the basis for the potential expansion of tasks or to accommodate the output of separate studies that help us to enhance knowledge on social or welfare issues not totally understood in our times.The fact that the initial imbalance of workload reported in the case study decreased is encouraging.The results reported that the range (max/min) of individual time put into academic activity decreased in a proportion 5:1, while the standard deviation passed from 333 in the original distribution of work, to 79 after re-distribution.
As mentioned above, the model could expand to incorporate individual preferences to take work, work ownership, or when our ability to audit gender bias improves.It could also separate variables to consider time that academics need to use for attending personal issues or training, without such time being excluded from the overall quantification of performance.
Further research could also focus on the degree of satisfaction that academic staff manifests when they benefit from a better distribution of work, ways to verify an expected increase of productivity, and how such benefit materialises to improve the students' learning experience.

•
Not too fine grained • Board recognition of tasks, e.g.outreach/citizenship • Ability to balance workloads across the year • Review of allocations during the year • Automatic additional allowances for parental leave, returners, and new staff • Ability to audit bias • Account taken of individuals' preferences and skills • Giving staff ownership of workload Figure 1.Idealised fluctuation of workload per area throughout one calendar year.

Role
Figure Initial of workload amongst academic staff.
Figure 3. Workload above and below average, selected to reallocate.

Figure 5 .
Figure 5. Spaces to superimpose with minimum error.
Figure 6.Reconfiguration of space 1 through a random operator.

Figure
Figure 9. Final distribution of workload amongst academic staff.
Figure 10.Staff workloads before and after implementing the optimisation algorithm.

Table 1 . Academic activity and its parameterisation TYPICAL ACADEMIC DUTIES Teaching
•Allocated Credits• Tutorial Focus Groups • Mentoring (Support to Project Groups) • Personal Tutees (Pastoral Support) • Design Groups (Technical Advice) • • PhD student supervision • Number of publications

Although these roles are specific to the target HE Unit, any variation for a different institution could easily be integrated in
Equation (

Table 2 .
Constant values used to solve Equation (5