Mathematical Models to Simultaneously Determine Overtime Requirements and Schedule Cells

The problem studied in this paper was inspired from an actual textile company. The problem is more complex than usual scheduling problems in that we compute overtime requirements and make scheduling decisions simultaneously. Since having tardy jobs is not desirable, we allow overtime to minimize the number of tardy jobs. The overall objective is to maximize profits. We present various mathematical models to solve this problem. Each mathematical model reflects different overtime workforce hiring practices. An experimentation has been carried out using eight different data sets from the samples of real data collected in the above mentioned textile company. Mathematical Model 2 was the best mathematical model with respect to both profit and execution time. This model considered partial overtime periods and also allowed different overtime periods on cells. We could solve problems up to 90 jobs per period. This was much more than what the mentioned textile company had to handle on a weekly basis. As a result, these models can be used to make these decisions in many industrial settings.