# American Institute of Mathematical Sciences

July  2020, 16(4): 1835-1859. doi: 10.3934/jimo.2019031

## Determining personnel promotion policies in HEI

 1 Department of Management / ETSEIB. Universitat Politcnica de Catalunya, Av. Diagonal 647, 7th floor, Barcelona, 08028, Spain 2 Department of Management / IOC / ETSEIB. Universitat Politcnica de Catalunya, Av. Diagonal 647, 11th floor, Barcelona, 08028, Spain 3 Department of Management / IOC / ETSEIB. Universitat Politcnica de Catalunya, Av. Diagonal 647, 7th floor, Barcelona, 08028, Spain 4 Department of Industrial Management. Ghent University, Technologiepark 902, 9052 Zwijnaarde, Belgium

* Corresponding author: R. de la Torre

Received  March 2018 Revised  October 2018 Published  May 2019

This paper addresses the determination of personnel promotion policies in public Higher Education Institutions (HEI) considering aspects such as worker's promotion rules, hiring and laying off, workforce diversity and budget constraints. The problem is formulated as a Mixed Integer Linear Program. The objective of the proposed optimization model is not only expressed in economic terms but also addressing the achievement of a preferable staff composition and service level. The model is formulated generally, hence it can be useful for different types of universities taken into account their specificities and characteristics. Specifically, this paper addresses the problem of finding the relationship between economic resources for workers'promotion and the pursued preferable staff composition. The model is applied to a real case, in which several analyses are performed under different scenarios characterized by possible trends in the available budget and the demand. The analyses are for different workforce structures, which reflect different academic and personnel policies. The results address the performance of the proposed model in achieving the preferable structure and also on how promotions --and associated expenditures--, are for young researchers and experienced personnel according to each considered scenario.

Citation: Rocio de la Torre, Amaia Lusa, Manuel Mateo, El-Houssaine Aghezzaf. Determining personnel promotion policies in HEI. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1835-1859. doi: 10.3934/jimo.2019031
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Scope of the paper
Relationship between assumed additional resources for encouraging worker's promotions $c_{kt}{\theta}_k$ and category $k$. Values are expressed as relative to ${c_{1, 1}}{\theta_1}$ (category 1)
Relationship between assumed additional resources for encouraging worker's promotions and category, expressed as relative to workers' capacity
Global discrepancy for scenarios 1 to 21 (so considering the institution model A as the preferable composition), considering different initial compositions as well as different temporal trends in budget and demand
Global discrepancy for scenarios 22 to 42 (so considering the institution model B as the preferable composition), considering different initial compositions as well as different temporal trends in budget and demand
Global discrepancy for scenarios 43 to 63 (so considering the institution model C as the preferable composition), considering different initial compositions as well as different temporal trends in budget and demand
Comparison between the achieved workforce composition per group of scenarios and the initial workforce structures per categories, while pursuing institution models A, B and C. The initial number of workers adopting institution models A, B and C are included in parenthesis
Average promotional ratio for personnel within $KT$ and $KC$, under the conditions of all the scenarios
Total number of promotions for all groups of scenarios and for the considered time horizon
Total cost incurred for personnel promotions (during the time horizon and for all the scenarios), expressed as relative to the average cost in scenarios within Groups X, R and U
List of category groups and their associated tasks
 Category group Description of workers Tasks Full Professor (highest categories within KC and KP groups of categories) This category is composed by the most skilled and experienced workers. Workers within these categories can perform some managerial tasks in the HEI governor (i.e. dean of the faculty). ⅰ) Lead projects / processes, ⅱ) Conduct research, ⅲ) Provide strategic vision for projects in research and technology transfer, as well as for the strategic objectⅳes for the department, ⅳ) Publish scientific results from research, ⅴ) Teach professionals in lower categories, ⅶ) Develop management tasks Tenured Assistant Professor (within KC group of categories) and Tenured Professor (within KP group of categories). This group of categories is composed by high experienced workers in all aspects of teaching and research. Workers have also skills in scientific project leading. ⅰ) Lead projects / processes, ⅱ) Conduct research, ⅲ) Publish scientific results from research, ⅳ) Teach professionals in lower categories. Tenure-track Lecturer (within KT group of categories). This group of categories is composed by professionals with high capacity for carrying out teaching and research actⅳities, with more expertise and knowledge than those in the categories under KT ⅰ) Collaborate in the management of projects and processes, ⅱ) Execute projects required high degree of specialization, ⅲ) Supervise research, ⅳ) Publish scientific results from research, ⅴ) Teach young researchers and pupils. Assistant Lecturer (within KT group of categories) This group of categories is composed by workers starting their career; thus, they are still in training processes for teaching and research purposes. ⅰ) Participate in research and technology transfer projects, ⅱ) Execute projects under the advice of colleagues in upper categories, ⅲ) Support teaching actⅳities.
 Category group Description of workers Tasks Full Professor (highest categories within KC and KP groups of categories) This category is composed by the most skilled and experienced workers. Workers within these categories can perform some managerial tasks in the HEI governor (i.e. dean of the faculty). ⅰ) Lead projects / processes, ⅱ) Conduct research, ⅲ) Provide strategic vision for projects in research and technology transfer, as well as for the strategic objectⅳes for the department, ⅳ) Publish scientific results from research, ⅴ) Teach professionals in lower categories, ⅶ) Develop management tasks Tenured Assistant Professor (within KC group of categories) and Tenured Professor (within KP group of categories). This group of categories is composed by high experienced workers in all aspects of teaching and research. Workers have also skills in scientific project leading. ⅰ) Lead projects / processes, ⅱ) Conduct research, ⅲ) Publish scientific results from research, ⅳ) Teach professionals in lower categories. Tenure-track Lecturer (within KT group of categories). This group of categories is composed by professionals with high capacity for carrying out teaching and research actⅳities, with more expertise and knowledge than those in the categories under KT ⅰ) Collaborate in the management of projects and processes, ⅱ) Execute projects required high degree of specialization, ⅲ) Supervise research, ⅳ) Publish scientific results from research, ⅴ) Teach young researchers and pupils. Assistant Lecturer (within KT group of categories) This group of categories is composed by workers starting their career; thus, they are still in training processes for teaching and research purposes. ⅰ) Participate in research and technology transfer projects, ⅱ) Execute projects under the advice of colleagues in upper categories, ⅲ) Support teaching actⅳities.
Preferable workforce compositions for institution models A, B and C
 Model A Model B Model C Proportion of workers in $KT$ 42% 34% 27% Proportion of workers in $KC$ 17% 18% 16% Proportion of workers in $KP$ 41% 48% 57%
 Model A Model B Model C Proportion of workers in $KT$ 42% 34% 27% Proportion of workers in $KC$ 17% 18% 16% Proportion of workers in $KP$ 41% 48% 57%
List of scenarios for analysis
 Sc. Initial comp. Pref. comp. Dem.-Budget Sc. Initial comp. Pref. comp. Dem.-Budget Sc. Initial comp. Pref. comp. Dem.-Budget 1 A A CC 22 A B CC 43 A C CC 2 A A CD 23 A B CD 44 A C CD 3 A A DC 24 A B DC 45 A C DC 4 A A DD 25 A B DD 46 A C DD 5 A A IC 26 A B IC 47 A C IC 6 A A II 27 A B II 48 A C II 7 A A ID 28 A B ID 49 A C ID 8 B A CC 29 B B CC 50 B C CC 9 B A CD 30 B B CD 51 B C CD 10 B A DC 31 B B DC 52 B C DC 11 B A DD 32 B B DD 53 B C DD 12 B A IC 33 B B IC 54 B C IC 13 B A II 34 B B II 55 B C II 14 B A ID 35 B B ID 56 B C ID 15 C A CC 36 C B CC 57 C C CC 16 C A CD 37 C B CD 58 C C CD 17 C A DC 38 C B DC 59 C C DC 18 C A DD 39 C B DD 60 C C DD 19 C A IC 40 C B IC 61 C C IC 20 C A II 41 C B II 62 C C II 21 C A ID 42 C B ID 63 C C ID
 Sc. Initial comp. Pref. comp. Dem.-Budget Sc. Initial comp. Pref. comp. Dem.-Budget Sc. Initial comp. Pref. comp. Dem.-Budget 1 A A CC 22 A B CC 43 A C CC 2 A A CD 23 A B CD 44 A C CD 3 A A DC 24 A B DC 45 A C DC 4 A A DD 25 A B DD 46 A C DD 5 A A IC 26 A B IC 47 A C IC 6 A A II 27 A B II 48 A C II 7 A A ID 28 A B ID 49 A C ID 8 B A CC 29 B B CC 50 B C CC 9 B A CD 30 B B CD 51 B C CD 10 B A DC 31 B B DC 52 B C DC 11 B A DD 32 B B DD 53 B C DD 12 B A IC 33 B B IC 54 B C IC 13 B A II 34 B B II 55 B C II 14 B A ID 35 B B ID 56 B C ID 15 C A CC 36 C B CC 57 C C CC 16 C A CD 37 C B CD 58 C C CD 17 C A DC 38 C B DC 59 C C DC 18 C A DD 39 C B DD 60 C C DD 19 C A IC 40 C B IC 61 C C IC 20 C A II 41 C B II 62 C C II 21 C A ID 42 C B ID 63 C C ID
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