Simulation of the role of emphasis on scheduling in the optimal incentive scheme for marine engineering employee's routine job and information security compliance

doi:10.1016/j.joes.2022.05.024

Abstract

Abstract:

In the organizational context of marine engineering, employee individual often prefers to concentrate herself to the day-to-day routine job, but to shirk the responsibilities of the Information Security Policies (ISPs) compliance, after she has been delegated by the employer to perform the two different tasks in the same time period. This would lead to negative influences on the security of marine information systems and the employee's routine job performance. In view of the task structures of employee's routine job and marine ISPs compliance, the variables of emphasis on scheduling are incorporated into a multi-task principal-agent model to explore the optimal incentive scheme to motivate and control the employees to select appropriate effort levels for conducting the two highly structured tasks. The role of emphasis on scheduling on the incentive intensities for the two tasks have been clarified through modeling and simulation, and the corresponding incentive tactics are suggested. The new two-task incentive scheme is expected to provide useful insight for understanding and controlling marine engineering employee's routine job and ISPs compliance behavior.

Key words: Marine engineering, Incentive scheme, Information security policy compliance, Task structure, Scheduling, Simulation

Xiaolong Wang. Simulation of the role of emphasis on scheduling in the optimal incentive scheme for marine engineering employee's routine job and information security compliance[J]. Journal of Ocean Engineering and Science, 2024, 9(1): 1-8.

Xiaolong Wang. [J]. Journal of Ocean Engineering and Science, 2024, 9(1): 1-8.

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URL: https://www.qk.sjtu.edu.cn/joes/EN/10.1016/j.joes.2022.05.024

https://www.qk.sjtu.edu.cn/joes/EN/Y2024/V9/I1/1

Figures/Tables 6

Table 1. Three numerical examples for

C_{12} = 0 .

Numericalexamples	Valueassignment	Incentivecoefficients
NE1	$C_{11} = 0$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ ,and $0 \leq p_{1} \leq 1$ .	$γ_{1} = \frac{1}{1 + 0.25 / p_{1}^{2}}$ , $γ_{2} = 0$ .
NE2	$C_{22} = 0.8$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 10$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{1}{1 + 4 / p_{2}^{2}}$ .
NE3	$C_{11} = 0.5$ , $C_{22} = 0.9$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $σ_{2}^{2} = 10$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{p_{1}^{2}}{p_{1}^{2} + 0.25}$ , $γ_{2} = \frac{p_{2}^{2}}{p_{2}^{2} + 4.5}$ .

Table 1. Three numerical examples for

C_{12} = 0 .

Numericalexamples	Valueassignment	Incentivecoefficients
NE1	$C_{11} = 0$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ ,and $0 \leq p_{1} \leq 1$ .	$γ_{1} = \frac{1}{1 + 0.25 / p_{1}^{2}}$ , $γ_{2} = 0$ .
NE2	$C_{22} = 0.8$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 10$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{1}{1 + 4 / p_{2}^{2}}$ .
NE3	$C_{11} = 0.5$ , $C_{22} = 0.9$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $σ_{2}^{2} = 10$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{p_{1}^{2}}{p_{1}^{2} + 0.25}$ , $γ_{2} = \frac{p_{2}^{2}}{p_{2}^{2} + 4.5}$ .

Table 2. Three numerical examples for

C_{12} < 0 .

Numericalexamples	Valueassignment	Intensivecoefficients
NE4	$C_{11} = 0.5$ , $C_{12} = - 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{0.5 p_{1}^{2} + 0.7 p_{1} p_{2}}{0.5 p_{1}^{2} - 0.12}$ , $γ_{2} = 0$ .
NE5	$C_{11} = 0.5$ , $C_{12} = - 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{0.5 p_{2}^{2} + 0.7 p_{1} p_{2}}{0.5 p_{2}^{2} - 0.06}$ .
NE6	$C_{11} = 0.5$ , $C_{12} = - 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ ,and $σ_{2}^{2} = 0.5$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{(\begin{matrix} (0.5 p_{1}^{2} + 0.7 p_{1} p_{2}) (0.5 p_{2}^{2} - 0.06) - \\ (0.7 p_{1} p_{2}) (0.5 p_{2}^{2} + 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ , $γ_{2} = \frac{(\begin{matrix} (0.5 p_{2}^{2} + 0.7 p_{1} p_{2}) (0.5 p_{1}^{2} - 0.12) - \\ (0.7 p_{1} p_{2}) (0.5 p_{1}^{2} + 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ .

Table 2. Three numerical examples for

C_{12} < 0 .

Numericalexamples	Valueassignment	Intensivecoefficients
NE4	$C_{11} = 0.5$ , $C_{12} = - 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{0.5 p_{1}^{2} + 0.7 p_{1} p_{2}}{0.5 p_{1}^{2} - 0.12}$ , $γ_{2} = 0$ .
NE5	$C_{11} = 0.5$ , $C_{12} = - 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{0.5 p_{2}^{2} + 0.7 p_{1} p_{2}}{0.5 p_{2}^{2} - 0.06}$ .
NE6	$C_{11} = 0.5$ , $C_{12} = - 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ ,and $σ_{2}^{2} = 0.5$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{(\begin{matrix} (0.5 p_{1}^{2} + 0.7 p_{1} p_{2}) (0.5 p_{2}^{2} - 0.06) - \\ (0.7 p_{1} p_{2}) (0.5 p_{2}^{2} + 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ , $γ_{2} = \frac{(\begin{matrix} (0.5 p_{2}^{2} + 0.7 p_{1} p_{2}) (0.5 p_{1}^{2} - 0.12) - \\ (0.7 p_{1} p_{2}) (0.5 p_{1}^{2} + 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ .

Table 3. Three numerical examples for

C_{12} > 0 .

Numericalexamples	Valuesassignment	Intensivecoefficients
NE7	$C_{11} = 0.5$ , $C_{12} = 1$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{0.5 p_{1}^{2} - p_{1} p_{2}}{0.5 p_{1}^{2} - 0.375}$ , $γ_{2} = 0$ .
NE7	high degree substitution, $C_{11} = 0.5$ , $C_{12} = 10$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{0.5 p_{1}^{2} - 10 p_{1} p_{2}}{0.5 p_{1}^{2} - 49.875}$ , $γ_{2} = 0$ .
NE8	$C_{11} = 0.5$ , $C_{12} = 1$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{2} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{0.5 p_{2}^{2} - p_{1} p_{2}}{0.5 p_{2}^{2} - 0.1875}$ .
NE8	high degree substitution, $C_{11} = 0.5$ , $C_{12} = 10$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{2} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{0.5 p_{2}^{2} - 10 p_{1} p_{2}}{0.5 p_{2}^{2} - 24.9375}$ .
NE9	$C_{11} = 0.5$ , $C_{12} = 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{2} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} =$ $\frac{(\begin{matrix} (0.5 p_{1}^{2} - 0.7 p_{1} p_{2}) (0.5 p_{2}^{2} - 0.06) + \\ (0.7 p_{1} p_{2}) (0.5 p_{2}^{2} - 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ , $γ_{2} =$ $\frac{(\begin{matrix} (0.5 p_{2}^{2} - 0.7 p_{1} p_{2}) (0.5 p_{1}^{2} - 0.12) + \\ (0.7 p_{1} p_{2}) (0.5 p_{1}^{2} - 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ .

Table 3. Three numerical examples for

C_{12} > 0 .

Numericalexamples	Valuesassignment	Intensivecoefficients
NE7	$C_{11} = 0.5$ , $C_{12} = 1$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{0.5 p_{1}^{2} - p_{1} p_{2}}{0.5 p_{1}^{2} - 0.375}$ , $γ_{2} = 0$ .
NE7	high degree substitution, $C_{11} = 0.5$ , $C_{12} = 10$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $0 \leq p_{1} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = \frac{0.5 p_{1}^{2} - 10 p_{1} p_{2}}{0.5 p_{1}^{2} - 49.875}$ , $γ_{2} = 0$ .
NE8	$C_{11} = 0.5$ , $C_{12} = 1$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{2} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{0.5 p_{2}^{2} - p_{1} p_{2}}{0.5 p_{2}^{2} - 0.1875}$ .
NE8	high degree substitution, $C_{11} = 0.5$ , $C_{12} = 10$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{2} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} = 0$ , $γ_{2} = \frac{0.5 p_{2}^{2} - 10 p_{1} p_{2}}{0.5 p_{2}^{2} - 24.9375}$ .
NE9	$C_{11} = 0.5$ , $C_{12} = 0.7$ , $C_{22} = 0.5$ , $η_{1} = 0.5$ , $σ_{1}^{2} = 1$ , $σ_{2}^{2} = 0.5$ , $0 \leq p_{2} \leq 1$ ,and $0 \leq p_{2} \leq 1$ .	$γ_{1} =$ $\frac{(\begin{matrix} (0.5 p_{1}^{2} - 0.7 p_{1} p_{2}) (0.5 p_{2}^{2} - 0.06) + \\ (0.7 p_{1} p_{2}) (0.5 p_{2}^{2} - 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ , $γ_{2} =$ $\frac{(\begin{matrix} (0.5 p_{2}^{2} - 0.7 p_{1} p_{2}) (0.5 p_{1}^{2} - 0.12) + \\ (0.7 p_{1} p_{2}) (0.5 p_{1}^{2} - 0.7 p_{1} p_{2}) \end{matrix})}{(\begin{matrix} (0.5 p_{1}^{2} - 0.12) (0.5 p_{2}^{2} - 0.06) - \\ {(0.7 p_{1} p_{2})}^{2} \end{matrix})}$ .

Fig.1

γ_{1}

γ_{2}

as a function of

p_{1}

p_{2}

(when

C_{12} = 0

) for (a) NE1, (b) NE2, and (c) and (d) NE3, (NE: numerical example).

Fig.1 $γ_{1}$ , $γ_{2}$ as a function of $p_{1}$ or $p_{2}$ (when $C_{12} = 0$ ) for (a) NE1, (b) NE2, and (c) and (d) NE3, (NE: numerical example).

Fig.2

γ_{1}

γ_{2}

as a function of both

p_{1}

and

p_{2}

(when

C_{12} < 0

) for (a) NE4, (b) NE5, and (c) and (d) NE6, (NE: numerical example).

Fig.2 $γ_{1}$ , $γ_{2}$ as a function of both $p_{1}$ and $p_{2}$ (when $C_{12} < 0$ ) for (a) NE4, (b) NE5, and (c) and (d) NE6, (NE: numerical example).

Fig.3

γ_{1}

γ_{2}

as a function of both

p_{1}

and

p_{2}

(when

C_{12} > 0

) for (a) and (b) NE7, (c) and (d) NE8, and(e) and (f) NE9, (NE: numerical example).

Fig.3 $γ_{1}$ , $γ_{2}$ as a function of both $p_{1}$ and $p_{2}$ (when $C_{12} > 0$ ) for (a) and (b) NE7, (c) and (d) NE8, and(e) and (f) NE9, (NE: numerical example).

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