Scheduling IT Staff at a Bank: A Mathematical Programming Approach

The objectives are to minimize the overtimes and maximise the satisfaction of employees in terms of desired days off. These objectives are weighted according to their priority such that $(\beta 1 > \beta 2)$

$\operatorname{Min} Z=\beta 1 \sum_{i=1}^{n_{j}} \sum_{j=1}^{2} \sum_{w=1}^{4} d_{i j w}+\beta_{2} \sum_{i=1}^{n_{j}} \sum_{j=1}^{2} R_{i j}$

The highest importance level $(\beta 1)$ is given to minimize the overtime, whereas the second highest priority level $(\beta 2)$ is given to satisfaction of desired employee preferences. Since our model involves determining the weights of the two objectives, therefore, for our problem we use the two levels; level 2 represents the major objective of the problem: to minimise the overtime. Level 1 represents the degree of satisfaction of employee preferences. The weights $\beta i(i=1,2)$ will be equal to the grade of the level $(\beta 1=2$ and $\beta 2=1$).