A Mathematical Model for the Single Machine Scheduling Considering Sequence Dependent Setup Costs and Idle Times

Planning and scheduling are among the most important parts of the management’s duties. Development of an efficient scheduling method can results in productivity improvement of an organization. Given the importance of production scheduling in an organization, this research seeks to propose a solution for one of the important problems for the production managers. This problem occurs if a considerable percentage of available production times is allocated to machine setup times. The objective of this research is to find a scheduling method to reach minimum of total production time, earliness and tardiness times. In previous researches not all effective factors on this scheduling method such as machine idle times and machine setup costs have been studied simultaneously. A mathematical model for the optimization of multi-product single-machine scheduling problem have been developed which considered sequence dependent setup costs, costs due to delay in delivery, holding costs, and costs related to machine idle time. Comparative results for the random small size test cases show that the proposed mathematical model can obtained an optimal solution in a relatively low computation time, however, for the large-scale cases this model is not efficient and an approximate method is required for these cases.