Information Security Policies (ISPs) have been established in many organizations of marine engineering to safeguard their information systems [1], [2], [3], [4]. When interacting with these systems, the marine engineering employees are required to comply with the specific rules and responsibilities formulated by the marine ISPs [5], [6], [7], [8]. The marine ISPs are only effective to the extent that employees comply with them [7]. In practice, many employees often prefer to comply with the marine ISPs with insufficient effort, but to pay attention almost exclusively to their day-to-day routine jobs, after they are delegated by the marine engineering employer to carry out the two different tasks in the same time period [9,10]. Previous investigations [11], [12], [13], [14], [15], [16], [17], [18], [19] have shown that employee's failure to comply with the marine ISPs may impair not only the asset, reputation and competitiveness of the organization, but also the performance of her routine job [9,10,20]. A number of factors, such as information security awareness, organizational culture and punishment, are known to influence employee's intentional compliance behaviors [7,14,16,17,21]. However, the selection of the ISPs compliance effort levels is rarely discussed in a multi-task context of marine engineering in the previous studies. In most cases, the marine ISPs compliance task is bound with the employee's routine job because the completing of her routine job needs to use the marine information systems. Task dissonance, i.e., the discord arising in employee's cognition of conflicting utilities between her routine job and marine ISPs compliance, may appear [22]. For instance, sending an encrypted e-mail according to the specific marine information security rules requires more steps than sending a regular e-mail. The additional complication of sending the encrypted e-mail is considered by the employee as extra work load without any payoffs. The employee would perceive that the marine ISPs compliance task interferes with her routine job [20,23]. Although the marine engineering employer expects that the routine job and the marine ISPs compliance task are both performed by the employee with high efforts, the latter is often ignored. Therefore, motivating a marine engineering employee to allocate appropriately her efforts between the two tasks appears to be crucial for eliminating the security threats from the marine ISPs non-compliance and improving her routine job performance.

There exist a few extant studies dealing with the allocation of employee's efforts for the marine ISPs compliance from the economic perspective. Beautement et al. [9,10] proposed a concrete paradigm, i.e., the compliance budget, to understand the expense of employee's effort for the compliance task. Their results indicate that the employee's compliance budget can be used by the employer to grasp how an employee perceives the cost and benefit of her compliance. Herath and Rao [23] pointed out that a moral hazard problem naturally occurs because the ISPs compliance behavior of an employee is hard to be monitored constantly by the employer without high costs. Fang et al. [24] further proposed a comprehensive mechanism that can address the moral hazard problem, provide accountability and offer incentives at the inter-organizational level under some specified conditions. Apart from the moral hazard problem, cost substitution [25] may also exist between the routine job and the marine ISPs compliance task. In such a case, an employee of marine engineering is likely to select performing her routine job with high effort but shirking the compliance duty. Therefore, an incentive scheme is necessarily needed to motivate the marine engineering employee to allocate appropriate efforts for the two different tasks.

For the design of an optimal incentive scheme, the specificity of the marine ISPs compliance task should be considered. From the task structure [26,27] point of view, the marine ISPs compliance task is highly structured since the task-related duties and responsibilities are clearly defined in the ISPs. It has been demonstrated that the psychological state that an employee experiences while performing a highly structured task may negatively influence the organizationally valued outcomes, such as job involvement and organizational commitment [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]. Hence, a high task structure of the marine ISPs compliance may decrease the quality of the compliance performance of an employee. Considering that the absence of ambiguity in a highly structured task matches the marine engineering employee's strong preference to know how to schedule her activities involved in the task, emphasis on scheduling has been found to be capable of moderating the negative effects of task structure [27,[36], [37], [38], [39]]. Here, emphasis on scheduling refers to how the marine engineering employee structures and makes sense of her social world in a temporal sense, which is a selective facet of the temporal orientation at the individual level [27,29,40]. For an employee who places high emphasis on scheduling, the negative effects of a highly structured task are weaker than for the one who does not emphasize scheduling of activities [27]. Since the principal-agent theory inherently lacks the recognition of the temporal preferences of human behaviors [23,41,42], emphasis on scheduling may be incorporated as a variable into the principal-agent theory to design the incentive scheme. In the present study, the variables of emphasis on scheduling are combined with the multi-task principal-agent model to explore a two-task optimal incentive scheme for motivating the marine engineering employee individual to allocate appropriate efforts for her routine job and ISPs compliance task.

The remainder of this study is organized as follows. In Section II, a contract model is proposed for the design of the optimal incentive scheme, from which an optimization problem is derived. In Section III, the optimization problem is solved, and numerical examples are used to show the stand-alone and the correlated influences of the two variables of emphasis on scheduling on the incentive intensity. The incentive tactics applicable for the two tasks are obtained. Concluding remarks of this study are given in Section IV.

A series of assumptions are made to keep our analysis tractable.

(i) Assume that employer and employee are independent individuals in an organization of marine engineering. Consider a two-task principal-agent problem in which an employer (the principal) delegates an employee (the agent) to perform the routine job and the marine ISPs compliance in the same period of time.

(ii) Assume that the routine job is also a highly structured task because it consists of fairly standard and repetitive duties that fill the entire work cycle in a given period of time.

(iii) Suppose a two-dimensional (2D) vector for the marine engineering employee's effort levels, which is a one-time selection [25,43], $\mathit{e}=\left(\begin{array}{c}{e}_1\\ e_2\end{array}\right)$, where $e_1$ and $e_2$ represent the effort levels selected by an employee for her routine job and marine ISPs compliance task, respectively. The employee knows her effort levels for the two different tasks, but the effort levels cannot be measured at low cost by the marine engineering employer.

(iv) Suppose an observable 2D outcome vector, o $=\left(\begin{array}{c}{o}_1\\ o_2\end{array}\right)$, for the two tasks. Since the marine engineering employee who emphasizes the scheduling of the various activities involved in her task fits better with a highly structured task, and is likely to be more productive, we let the outcome of the routine job $o_1=p_1{e}_1+{\theta }_1$, and that of the marine ISPs compliance task $o_2=p_2{e}_2+{\theta }_2$. Here, $p_1$ and $p_2$ are the two variables of emphasis on scheduling, which correspond to the routine job and the marine ISPs compliance task, respectively, $0\le p_1\le 1$, $0\le p_2\le 1$. Each of the variables affects merely the outcome of the effort for the task it corresponds. ${\theta }_1$ and ${\theta }_2$ are unobservable exogenous variables, which are related to the routine job and the marine ISPs compliance task, respectively, and are independent variables. For example, ${\theta }_1$ and ${\theta }_2$ can be used to represent the errors of the performance evaluations of the marine engineering employee's routine job and ISPs compliance task, respectively. ${\theta }_1$follows a normal distribution with a zero mean value and a variance of ${\sigma }_1^2$; ${\theta }_2$ is also normally distributed with mean value zero, but with variance ${\sigma }_2^2$. The larger value of ${\theta }_1$ (or ${\theta }_2$) signals a more favorable state of the exogenous condition. Let $\mathit{\theta }=\left(\begin{array}{c}{\theta }_1\\ {\theta }_2\end{array}\right)$, where $\mathit{\theta }$ is a random vector normally distributed with mean vector zero and covariance matrix $\sum$, $\sum =\left(\begin{array}{cc}{\sigma }_1^2& 0\\ 0& {\sigma }_2^2\end{array}\right)$. Assume that the distributions of $o_1$ and $o_2$ satisfy the first-order stochastic dominance condition. Hence, a larger value of $o_1$ (or $o_2$) implies that a higher effort level for the routine job (or the marine ISPs compliance task) has been selected by the employee.

(v) Assume that the marine engineering employer is risk neutral, whereas the employee is risk averse.

(vi) Assume that the personal cost of the marine engineering employee's efforts can be expressed by a strictly convex function, $C\left(\mathit{e}\right)=\frac{1}{2}{C}_{11}{e}_1^2+C_{12}{e}_1{e}_2+\frac{1}{2}{C}_{22}{e}_2^2$. Here, $C\left(\mathit{e}\right)$ is expressed in monetary units. We obtain: $C_{11}=\frac{{\partial }^{2}C\left(\mathit{e}\right)}{\partial e_1^2}$, $C_{12}=\frac{{\partial }^{2}C\left(\mathit{e}\right)}{\partial e_1{e}_2}$, and $C_{22}=\frac{{\partial }^{2}C\left(\mathit{e}\right)}{\partial e_2^2}$.

(vii) Assume that both the marine engineering employer and the employee prefer to maximize their own expected utilities, and that the employer will stick to her promise and is able to offer monetary compensation to the employee.

(viii) The distributions of $o_1$, $o_2$, ${\theta }_1$, ${\theta }_2$, and the von Neumann-Morgenstern utility functions, etc., are common knowledge shared by the employer and the employee.

Based on the above assumptions, the gross benefit, $B\left(\mathit{e}\right)$, takes the form

where the ownership of $B\left(\mathit{e}\right)$ belongs to the marine engineering employer. The employer can offer an incentive contract, $s\left(\mathit{o}\right)$, to induce the marine engineering employee to carry out both the routine job and the marine ISPs compliance with the effort levels expected by the marine engineering employer:

where ${\beta }_1$ is a fixed income of the marine engineering employee. ${\beta }_1$is not relevant to the outcome, $o$, which is determined by the reservation utility of the marine engineering employee, ${\overline{u}}_1$, i.e., the expected utility she can achieve by working elsewhere. ${\gamma }_1$ and ${\gamma }_2$ are the share ratios of the marine engineering employee, viz., two incentive coefficients, and relation (2) means that the incentive intensity increases by ${\gamma }_1$(or ${\gamma }_2$) with one unit increment in $o_1$(or $o_2)$. Let $\mathit{\gamma }=\left(\begin{array}{c}{\gamma }_1\\ {\gamma }_2\end{array}\right)$ and ${\mathit{\gamma }}^T=\left({\gamma }_1{\gamma }_2\right)$, where the superscript $T$ stands for a transpose operator.

Then, the net benefit of the marine engineering employer is given by

Hence, the expected payoff of the marine engineering employer is

And meanwhile, the certainty equivalence monetary payoff of the marine engineering employee is

where $E\left(s\left(\mathit{o}\right)-C\left(\mathit{e}\right)\right)$ is the mathematical expectation of $s\left(\mathit{o}\right)-C\left(\mathit{e}\right)$, $\frac{1}{2}{\eta }_1{\gamma }^T\sum \gamma$ gives the risk premium of the marine engineering employee, ${\eta }_1$ measures her risk aversion, and since she is risk averse, ${\eta }_1>0$, ${\gamma }^T\sum \gamma$ is the variance of payoff once she accepts the contract and makes efforts to perform her routine job and marine ISPs compliance.

If the magnitude of the certainty equivalence is smaller than that of the marine engineering employee's reservation utility, ${\overline{u}}_1$, she will decline the contract. Then, the individual rationality constraint of the marine engineering employee can be expressed by the following relation:

The incentive compatibility constraint of the marine engineering employee is

Suppose that the marine engineering employer wishes to obtain the optimal expected payoff. The following problem can be solved by means of picking ${\beta }_1$, ${\gamma }_1$ and ${\gamma }_2$:
$\underset{{\beta }_1,{\gamma }_1,{\gamma }_2}{max}\left(\left(1-{\gamma }_1\right)p_1{e}_1+\left(1-{\gamma }_2\right)p_2{e}_2-{\beta }_1\right)$ s.t.
$\begin{array}{ccc}& & \left(\left({\beta }_1+{\gamma }_1{p}_1{e}_1+{\gamma }_2{p}_2{e}_2\right)-\left(\frac{1}{2}{C}_{11}{e}_1^2+C_{12}{e}_1{e}_2+\frac{1}{2}{C}_{22}{e}_2^2\right)\right)\hfill \\ & & -\left(\frac{1}{2}{\eta }_1{\gamma }_1^2{\sigma }_1^2+\frac{1}{2}{\eta }_1{\gamma }_2^2{\sigma }_2^2\right)\ge {\overline{u}}_1,\hfill \end{array}$

In the following, the two variables of emphasis on scheduling ( $p_1$, $p_2$) are first demonstrated to have stand-alone or correlated influences on the incentive intensities ( ${\gamma }_1$, ${\gamma }_2$) applied to the routine job or the marine ISPs compliance, and then the corresponding incentive tactics are suggested.

First, for the marine engineering employer, the optimal incentive contract should satisfy the equality relation in (6). So,

Insert (9) into (4), and express the marine engineering employer's expected payoff into the matrix form:

Assume that $\left(\begin{array}{cc}{C}_{11}& C_{12}\\ C_{12}& C_{22}\end{array}\right)$ is reversible. From (7), we obtain

There with, the expected payoff of the marine engineering employer is worked out by inserting (11) into (10),

The objective function
$\underset{\beta ,{\gamma }_1,{\gamma }_2}{max}\left(\left(1-{\gamma }_1\right)p_1{e}_1+\left(1-{\gamma }_2\right)p_2{e}_2-{\beta }_1\right)$ can be expressed as

Finally, the two incentive coefficients corresponding to the routine job and the marine ISPs compliance are derived:

It is seen from (14) and (15) that the two variables of emphasis on scheduling, $p_1$ and $p_2$, have stand-alone or correlated influences on the incentive intensities applied to the routine job or the marine ISPs compliance. In the following, the specific stand-alone or correlated influences are first clarified, and based on which the incentive tactics for the two tasks are suggested. Besides this, several numerical examples are presented to examine the role of emphasis on scheduling in the incentive scheme. All these results are summarized in Tables 1, 2, and 3.

(1) When the effort cost of the marine engineering employee's routine job is independent of that of the marine ISPs compliance, viz., $C_{12}=0$, the incentive coefficient and the corresponding incentive tactics are determined in four different cases based on the observability of the task outcomes:

(i) When the outcomes of the routine job and the marine ISPs compliance task are not observable, viz., ${\sigma }_1^2\to \infty$ and ${\sigma }_2^2\to \infty ,{\gamma }_1=0$ and ${\gamma }_2=0$. Based on this result, the incentive component should not be offered to the two tasks. Here, $p_1$ and $p_2$ are not relevant to ${\gamma }_1$ and ${\gamma }_2$.

(ii) When the outcome of the routine job is observable and that of the marine ISPs compliance task is not, viz., ${\sigma }_1^2$ is finite and ${\sigma }_2^2\to \infty$, ${\gamma }_1=\frac{1}{1+C_{11}{\eta }_1{\sigma }_1^2/p_1^2}$ and ${\gamma }_2=0$. In this case, the routine job should be rewarded in accord with ${\gamma }_1$, and the marine ISPs compliance task should not be rewarded. $p_1$ exerts a stand-alone influence on ${\gamma }_1$, whereas $p_2$ has no effect on ${\gamma }_2$. A numerical example, NE1, is used to show the influence of $p_1$ on ${\gamma }_1$, and the explicit relationship of $p_1$with ${\gamma }_1$is illustrated in Fig. 1(a). ${\gamma }_1$ is seen to increase monotonically with increasing $p_1$.

(iii) When the outcome of the marine ISPs compliance task is observable, but that of the routine job is not, viz., ${\sigma }_1^2\to \infty$and ${\sigma }_2^2$ is finite, ${\gamma }_1=0$ and ${\gamma }_2=\frac{1}{1+C_{22}{\eta }_1{\sigma }_2^2/p_2^2}$. There with, the marine ISPs compliance task should be rewarded in accord with ${\gamma }_2$. Moreover, $p_2$ exerts a stand-alone influence on ${\gamma }_2$, whereas $p_1$ does not influence ${\gamma }_1$. The influence of $p_2$ on ${\gamma }_2$ is demonstrated by a numerical example, NE2, and the increasing tendency of ${\gamma }_2$ versus $p_2$ is shown in Fig. 1(b).

(iv) When the outcomes of the two tasks are both observable, viz., ${\sigma }_1^2$ and ${\sigma }_2^2$ take finite values, ${\gamma }_1=\frac{p_1^2}{p_1^2+C_{11}{\eta }_1{\sigma }_1^2}$ and ${\gamma }_2=\frac{p_2^2}{p_2^2+C_{22}{\eta }_1{\sigma }_2^2}$. In this case, both of the two tasks should be rewarded. $p_1$ and $p_2$ exert a stand-alone influence on ${\gamma }_1$ and ${\gamma }_2$, respectively. A numerical example, NE3, along with Figs. 1(c) and 1(d) are used to show the increasing tendencies of ${\gamma }_1$ and ${\gamma }_2$ versus $p_1$ and $p_2$.

(2) When a complementary relationship exists between the effort cost of marine engineering employee's routine job and that of her marine ISPs compliance task, viz., $C_{12}<0$, the incentive coefficients and tactics are obtained under four different conditions.

(i) When the outcomes of the routine job and the marine ISPs compliance task are not observable, viz., ${\sigma }_1^2\to \infty$ and ${\sigma }_2^2\to \infty$, ${\gamma }_1=0$ and ${\gamma }_2=0$. This means $p_1$ and $p_2$ are not relevant to ${\gamma }_1$ and ${\gamma }_2$. In this case, the incentive component should not be offered to either of the two tasks.

(ii) When the outcome of the routine job is observable, and that of the marine ISPs compliance task is not, viz., ${\sigma }_1^2$ is finite and ${\sigma }_2^2\to \infty$, ${\gamma }_1=\frac{C_{22}{p}_1^2-C_{12}{p}_1{p}_2}{C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2}$ and ${\gamma }_2=0$. Therefore, the routine job should be rewarded in accord with ${\gamma }_1$, and the marine ISPs compliance task should not be rewarded. Because $C_{12}<0$, ${\gamma }_1$ increases with decreasing $C_{12}$. $p_1$ and $p_2$ exert a correlated influence on ${\gamma }_1$, but do not influence ${\gamma }_2$. This kind of correlated influence is demonstrated by a numerical example, NE4, and is illustrated in Fig. 2(a).

(iii) When the outcome of the marine ISPs compliance task is observable, and that of the routine job is not, viz., ${\sigma }_1^2\to \infty$ and ${\sigma }_2^2$ is finite, ${\gamma }_1=0$ and ${\gamma }_2=\frac{C_{11}{p}_2^2-C_{12}{p}_1{p}_2}{C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2}$. There with, the reward component paid to the marine ISPs compliance task should be increased in accord with ${\gamma }_2$, but should not be offered to the routine job. Notice $C_{12}<0$. ${\gamma }_2$ is an increasing function of $C_{12}$. $p_1$ and $p_2$ exert a correlated influence on ${\gamma }_2$, but have no influence on ${\gamma }_1$. Fig. 2(b) shows the specific correlated influence given by a numerical example, NE5.

(iv) When the outcomes of the two tasks are both observable, viz., ${\sigma }_1^2$ and ${\sigma }_2^2$ take finite values, the incentive coefficients turn to be
${\gamma }_1=\frac{\left(C_{22}{p}_1^2-C_{12}{p}_1{p}_2\right)\left(C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2\right)+\left(C_{12}{p}_1{p}_2\right)\left(C_{11}{p}_2^2-C_{12}{p}_1{p}_2\right)}{\left(C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2\right)\left(C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2\right)-{\left(C_{12}{p}_1{p}_2\right)}^2},$
${\gamma }_2=\frac{\left(C_{11}{p}_2^2-C_{12}{p}_1{p}_2\right)\left(C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2\right)+\left(C_{12}{p}_1{p}_2\right)\left(C_{22}{p}_1^2-C_{12}{p}_1{p}_2\right)}{\left(C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2\right)\left(C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right)\eta {\sigma }_2^2\right)-{\left(C_{12}{p}_1{p}_2\right)}^2}.$

In this case, the routine job and the marine ISPs compliance task should be rewarded in accord with ${\gamma }_1$ and ${\gamma }_2$, respectively. $p_1$ and $p_2$ exert a correlated influence on the incentive intensities applied to the two tasks. A numerical example, NE6, is presented to show this correlated influence, and the result is illustrated in Figs. 2(c) and (d).

(3) When substitution exists between the employee's effort cost of the routine job and that of the marine ISPs compliance, viz., $C_{12}>0$, the specific incentive coefficients and tactics can also be obtained under four different conditions:

(i) When the outcomes of the routine job and the marine ISPs compliance task are not observable, viz., ${\sigma }_1^2\to \infty$ and ${\sigma }_2^2\to \infty$, ${\gamma }_1=0$ and ${\gamma }_2=0$. Hence, the reward should not be offered to the two tasks. Here, $p_1$ and $p_2$ are not relevant to ${\gamma }_1$ and ${\gamma }_2$.

(ii) When the outcome of the routine job is observable, and that of the marine ISPs compliance task is not, viz., ${\sigma }_1^2$ is finite and ${\sigma }_2^2\to \infty$, ${\gamma }_1=\frac{C_{22}{p}_1^2-C_{12}{p}_1{p}_2}{C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2}$ and ${\gamma }_2=0$. Because of cost substitution, ${\gamma }_1$ should be decreased to prevent the marine engineering employee from only focusing on her routine job. The higher the degree of substitution is, the lower should be the incentive intensity applied to the routine job. $p_1$ and $p_2$ exert a correlated influence on ${\gamma }_1$, but do not influence ${\gamma }_2$. This correlated influence is shown by a numerical example, NE7, and is illustrated in Figs. 3(a) and (b).

(iii) When the outcome of the marine ISPs compliance task is observable, but that of the routine job is not, viz., ${\sigma }_1^2\to \infty$ and ${\sigma }_2^2$ is finite, ${\gamma }_1=0$ and ${\gamma }_2=\frac{C_{11}{p}_2^2-C_{12}{p}_1{p}_2}{C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2}$. There with, the routine job should not be rewarded. Although the marine ISPs compliance task should be rewarded according to ${\gamma }_2$, the incentive intensity should be reduced to prevent the marine engineering employee from only focusing on her compliance task, and as the degree of substitution increases, the incentive intensity should be further reduced. This correlated influence is shown by a numerical example, NE8, along with Figs. 3(c) and (d).

(iv) When the outcomes of the two tasks are both observable, viz., ${\sigma }_1^2$ and ${\sigma }_2^2$ are finite,
${\gamma }_1=\frac{\left(C_{22}{p}_1^2-C_{12}{p}_1{p}_2\right)\left(C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2\right)+\left(C_{12}{p}_1{p}_2\right)\left(C_{11}{p}_2^2-C_{12}{p}_1{p}_2\right)}{\left(C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2\right)\left(C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2\right)-{\left(C_{12}{p}_1{p}_2\right)}^2},$
${\gamma }_2=\frac{\left(C_{11}{p}_2^2-C_{12}{p}_1{p}_2\right)\left(C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2\right)+\left(C_{12}{p}_1{p}_2\right)\left(C_{22}{p}_1^2-C_{12}{p}_1{p}_2\right)}{\left(C_{22}{p}_1^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_1^2\right)\left(C_{11}{p}_2^2+\left(C_{11}{C}_{22}-C_{12}^2\right){\eta }_1{\sigma }_2^2\right)-{\left(C_{12}{p}_1{p}_2\right)}^2}.$

The correlated influences are shown by a numerical example, NE9, along with Figs. 3(e) and (f).

The variables of emphasis on scheduling have been incorporated into a multi-task principal-agent model for designing the optimal incentive scheme for two highly structured tasks of employees, the routine job and the marine ISPs compliance. The role of emphasis on scheduling in the optimal incentive scheme has been analyzed under the conditions that independent, complementary and substitutional relationships exist between the effort costs of the two tasks, and that the observability of the task outcomes is different. The influences of the variables of emphasis on scheduling on the incentive intensities applied to the two tasks have been simulated and discussed, and the corresponding incentive tactics are presented. The new two-task incentive scheme can be used to motivate an employee of marine engineering to allocate appropriately her efforts for the two highly structured tasks performed in the same time period. Finally, it should be noted that the other facets of the temporal orientation such as time urgency may also influence the marine engineering employee's efforts allocation. Their influences on the allocation of the marine engineering employee's efforts will be studied in our future work.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.