Using Mathematical Programming to Establish the Feasibility of Modeling Breaks in a Staffing Model for a Service Center with Flexible Servers
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The shift scheduling problem is a problem of assigning staff to each shift with the aim of minimizing costs and fulfilling the minimum service level. These costs can include hiring cost, switching cost, training cost, etc. Our model considers flexible servers which explains the possibility of switching staff at each period. It might seem there is a need of hiring at least one separate server (staff) who is skillful in that each type of job. However, by considering flexible servers, we can hire fewer servers. Here, the balance between switching cost and hiring cost comes into consideration. If limited staff types are hired, then the switching cost will increase due to the need of having more switches at the beginning of each period. On the other hand, if several server types are hired, the need of switching may decrease but hiring costs will be considerable higher. The existence of breaks in staff schedules is inevitable. In our model, we study the balance between switching and hiring costs while considering breaks and level of skills. To address this problem, we look into different situations of breaks and level of skills. We studied a system with (i) only short breaks, (ii) breaks with the identical server's capability, and (iii) two short breaks with one lunch time (most real applications). A column generation heuristic is developed and used to solve this problem. Experimental results show that by adding more types of servers we can save, on average, 7% of total cost. Peak savings occurs of saving is when server types increase from 5 to 10. Also, by adding more skill levels there is an average of 3% saving in total cost. In general, the performance of this model and heuristic is good. The average gap between the integer program result and the lower bound for different size of problems is 2.47%. Our conclusion is that for problems with the value of switching cost close to 1, computational time is high. On the flip side, a value of switching time near zero yields faster solution time.