Mathematical Programming Model for a Single Machine Scheduling in an IT Manufacturing Firms

We suggest a mixed integer programming model for solving a scheduling problem in a single machine shop. The scheduling problem considered here addresses two urgencies of jobs, i.e., urgent jobs and normal jobs, in which can be occurred in the real IT manufacturing firms, to minimize total tardiness for urgent ones and total completion time of normal ones. Two linear mathematical formulations by using time indexed methods are proposed for this problem and these are compared with the existing algorithms used in the real situation. Computational experiments with randomly generated instances are conducted and results of the experiments show that proposed time indexed formulation can obtain optimal solutions in shorter time than another mathematical formulation.