A Mathematical Model for Simultaneous Parallel Multiple Source Scheduling Problems

Abstract

Manufacturing companies engaged in textile manufacturing engaged in the Job Order system with an extensive net work and market orientation require companies to pay attention to product quality and services that meet consumer requirements, one of which is by fulfilling orders at a pre-agreed time. The problem that is often found in companies like this is the frequent delays in completing orders. This is caused by the less optimal scheduling of job orders with different weights or penalties for each job which will ultimately result in a large total weighted delay originating from the accumulation of job delays with these different weights. This paper is intended to help companies create a new, more optimal schedule with the aim of minimizing the total weighted delay of order completion. The model proposed in this paper is a mathematical model for simultaneous parallel multiplesource scheduling problems for multiple-jobs and multiple-operations. The initial step of using this model is the formulation of decision variables, the objective function is minimizing tardiness or total weighted delay, and limiting functions. After the jobs to be examined are formulated into a model, data processing is carried out using a computerized system. The software used in processing this data is Win QSB. At the end of the paper a numerical example is given to use the proposed model. From data processing using Win QSB, it can be seen how much total weighted delay is obtained from scheduling with an integer linear programming model for this scheduling.