Competence-oriented project team planning – university case study

Figures & data

Figure 1. Project structure (a) and project schedule (b).

Table 1. Competence framework $G$.

	Operation
Employee	$Z_1$	$Z_2$	$Z_3$	$Z_4$	$Z_5$	$Z_6$	$Z_7$	$Z_8$	$Z_9$	$Z_{10}$
$P_1$ (B, D)	0	0	0	0	1	1	1	0	0	1
$P_2$ (A, B)	1	1	1	1	1	1	1	0	0	0
$P_3$ (A, B, C)	1	1	1	1	1	1	1	1	1	0
$P_4$ (A, C, D)	1	1	1	1	0	0	0	1	1	1

Figure 2. Replacement scenarios for the individual employees: $P_1$ (a), $P_2$ (b), $P_3$ (c) and $P_4$ (d).

Table 2. A competence framework G robust to the absence of one employee.

	Operations
Employee	$Z_1$	$Z_2$	$Z_3$	$Z_4$	$Z_5$	$Z_6$	$Z_7$	$Z_8$	$Z_9$	$Z_{10}$
$P_1$ (B, D)	0	0	0	0	1	1	1	0	0	1
$P_2$ (A, B)	1	1	1	1	1	1	1	1	1	0
$P_3$ (A, B, C)	1	1	1	1	1	1	1	1	1	0
$P_4$ (A, C, D)	1	1	1	1	0	0	0	1	1	1

Table 3. FECS syllabus (file ‘Syllabus.xlsx’ at https://github.com/erykszw/JIT).

$Z_i$	$q_i$	$l_i$
$Z_1$: History of technics 1	16	5
$Z_2$: History of technics 2	5	5
$Z_3$: Inventics	12	5
$Z_4$: Economics	9	5
$Z_5$: Foundations of mathematical analysis	20	5
…	…	…
$Z_{74}$: Programming in.NET environment	21	5
…	…	…
$Z_{213}$: Distributed information processing	6	5
$Z_{214}$: Artificial Intelligence Methods	6	5

Table 4. Competency framework $G$ of FECS employees (file ‘G_base.xlsx’ at https://github.com/erykszw/JIT).

$G$	$Z_1$: History of technics 1	$Z_2$: History of technics 2	$Z_3$: Inventics	$Z_4$: Economics	$Z_5$: Foundations of mathematical analysis	$Z_6$: Mathematical analysis and linear algebra	…	…	$Z_{74}$: Programming in.NET environment	…	…	$Z_{212}$: Selected branches of physics	$Z_{213}$: Distributed information processing systems	$Z_{214}$: Artificial Intelligence Methods
$P_1:$Mills	1	1	0	0	0	0	…	…	0	…	…	1	0	0
$P_2:$Garner	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_3:$Ray	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_4:$MacPherson	0	0	0	0	0	0	…	…	{0,1}	…	…	0	0	0
$P_5:$Burnham	0	0	0	0	0	0	…	…	{0,1}	…	…	0	0	0
$P_6:$Davis	0	0	0	0	0	0	…	…	0	…	…	0	0	{0,1}
$P_7:$Crockett	{0,1}	{0,1}	{0,1}	0	0	0	…	…	{0,1}	…	…	0	1	{0,1}
$P_8:$Hudson	{0,1}	{0,1}	{0,1}	0	0	0	…	…	0	…	…	0	0	0
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
$P_{18}:$ Roach	0	0	0	0	0	0	…	…	1	…	…	0	0	{0,1}
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
$P_{47}:$Fox	0	0	0	1	0	0	…	…	0	…	…	0	0	0
$P_{48}:$Porterfield	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_{49}:$Johnson	0	0	0	0	0	0	…	…	0	…	…	0	0	0

Table 5. Limits on the hours of the members of the staff employed by FECS.

	$s_k$	$z_k$		$s_k$	$z_k$		$s_k$	$z_k$		$s_k$	$z_k$
$P_1:$Mills	180	360	$P_{14}:$Buckley	240	480	$P_{27}:$Slaughter	240	500	$P_{40}:$Hansen	240	480
$P_2:$Garner	360	600	$P_{15}:$Johnston	360	600	$P_{28}:$Gardner	360	600	$P_{41}:$Thorpe	180	360
$P_3:$Ray	180	360	$P_{16}:$Bullock	180	360	$P_{29}:$Richardson	190	480	$P_{42}:$Rice	340	600
$P_4:$MacPherson	180	360	$P_{17}:$Dowling	360	600	$P_{30}:$Byrne	240	480	$P_{43}:$Whitehead	240	480
$P_5:$Burnham	360	600	$P_{18}:$Roach	180	360	$P_{31}:$Curran	240	480	$P_{44}:$Lacroix	20	120
$P_6:$Davis	120	240	$P_{19}:$Schneider	240	480	$P_{32}:$Owens	180	400	$P_{45}:$Nichols	50	120
$P_7:$Crockett	128	360	$P_{20}:$Reyes	240	480	$P_{33}:$Hoover	345	600	$P_{46}:$Cooley	20	120
$P_8:$Hudson	240	480	$P_{21}:$Barnes	120	240	$P_{34}:$Reynolds	240	480	$P_{47}:$Fox	30	120
$P_9:$Whittaker	240	480	$P_{22}:$Meyer	360	600	$P_{35}:$Morrow	180	360	$P_{48}:$Porterfield	150	300
$P_{10}:$ Middleton	360	600	$P_{23}:$ Sharpe	120	240	$P_{36}:$ Fitch	240	480	$P_{49}:$ Johnson	50	100
$P_{11}:$ Sloan	330	600	$P_{24}:$ Sinclair	160	360	$P_{37}:$ Clay	240	480
$P_{12}:$Flynn	360	600	$P_{25}:$Mahoney	180	360	$P_{38}:$Manning	240	480
$P_{13}:$Pope	240	480	$P_{26}:$Kirkland	240	480	$P_{39}:$Ramsey	180	360

Table 6. Employees allocation $X$ of staff employed by FECS (file ‘X_base.xlsx’ at https://github.com/erykszw/JIT).

$X$	$Z_1$: History of technics 1	$Z_2$: History of technics 2	$Z_3$: Inventics	$Z_4$: Economics	$Z_5$: Foundations of mathematical analysis	$Z_6$: Mathematical analysis and linear algebra	…	…	$Z_{74}$: Programming in.NET environment	…	…	$Z_{212}$: Selected branches of physics	$Z_{213}$: Distributed information processing systems	$Z_{214}$: Artificial Intelligence Methods
$P_1:$Mills	0	0	0	0	0	0	…	…	0	…	…	15	0	0
$P_2:$Garner	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_3:$Ray	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_4:$MacPherson	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_5:$Burnham	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_6:$Davis	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_7:$Crockett	0	0	0	0	0	0	…	…	0	…	…	0	0	0
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
$P_{18}:$ Roach	0	0	0	0	0	0	…	…	80	…	…	0	0	0
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
$P_{47}:$Fox	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_{48}:$Porterfield	0	0	0	0	0	0	…	…	0	…	…	0	0	0
$P_{49}:$Johnson	0	0	0	0	0	0	…	…	0	…	…	0	0	0

Table 7. Analysis of robustness $R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$ of FECS competency framework (Tab. 4).

Number of absent employees $\omega$	Robustness level $R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$	Calculation time [s]
1	0.35	0.9
2	0.1	1.1
3	0.03	1.4
4	0.01	2.2
5	0	4.5
6	0	6.8
7	0	9.2

Table 8. Synthesis of competency framework $G_{OPT}$ following robustness level condition $R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)\ge {}_{}^{\ast }{R}_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$ assumed on $\omega$ employees absenteeism.

Number of absent employees $\omega$	Expected robustness level ${}_{}^{\ast }{R}_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$	Obtained robustness level $R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$	Number of changes introduced to the competency framework $G$	Calculation time [s]
1	0.2	0.23	9	2.8
	0.4	0.49	62	3.2
	0.6	0.77	138	3.5
	0.8	^1) ×	×	3.9
	1	×	×	4.4
2	0.2	0.29	121	11.2
	0.4	0.58	415	12.9
	0.6	×	×	14.1
	0.8	×	×	15.9
	1	×	×	18.3
3	0.2	0.27	170	236
	0.4	0.43	660	291
	0.6	×	×	361
	0.8	×	×	428
	1	×	×	515
4	0.2	0.31	752	1197
	0.4	×	×	1346
	0.6	×	×	>1500
	0.8	×	×	>1500
	1	×	×	>1500

¹⁾ × - no acceptable solution, i.e. there is no the competency framework $G$ which guarantee expected value of robustness: $R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)\ge {}_{}^{\ast }{R}_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$.

Table 9. Synthesis of competency framework $G_{OPT}$ following robustness level condition $R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)=1$ assumed on $\omega$ employees absenteeism, while taking into account the employment of additional staff.

Number of absent employees $\omega$	Obtained robustness level$R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)$	Number of competences in the team of newly employed employees	Calculation time [s]
1	1	21	3.9
2	1	71	14.2
3	1	129	297
4	1	155	1168
5	1	184	>1500
6	1	197	>1500
7	1	204	>1500

Table 10. Synthesis of competency framework $G_{OPT}$ guaranteeing full robustness ($R_{\mathcal{P}}^{\mathcal{Z}}\left(\omega \right)=1$) for different number of employees and courses.

Number of employees $m$	Number of courses$n$	Number of absent employees $\omega$	Calculation time [s]
50	300	1	7
50	300	2	15
50	300	3	267
100	400	1	39
100	400	2	92
100	400	3	1550
150	500	1	61
150	500	2	238
150	500	3	2860
200	600	1	390
200	600	2	1480
200	600	3	>5000