Integer Relaxation on Binary Quadratic Programming for Batching and Sequencing in Single Formulation to Minimize Total Actual Flow Times Criteria


  • Zahedi Zahedi Bina Nusantara University



actual flow time, batching, sequencing, simultaneous formulation, optimal solution


This paper examines batch scheduling problem that has batching and sequencing in single formulation for multiple-item case. The first step is to develop a model for single item single resource discussed in Zahedi (2008). The model determined batch sizes and their schedule simultaneously in single item case. This paper develops the model and algorithm for multiple-item case. The model functions to minimize total actual flow times. An algorithm for the model is developed using a relaxation of the binary constraints. The binary values for the decision variables are obtained from steps provided in algorithm. A numerical experience showing characteristics of this problem is presented.



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Halim, A. H., Toha, I. S., Zahedi. (1998). Simultaneous Resource Scheduling to Minimize Total Actual Flow Times. Proceeding of Pacific Congress of Manufacturing and Management. Victoria, Australia.

Zahedi. (2007). The Solution for Binary Quadratic Programming to Multiple Resources Scheduling Problem. Jurnal MatStat, 5 (1), September 2007. Jakarta: Binus University.

Zahedi. (2008). Integer Relaxation for Binary Quadratic Model in Batching and Scheduling with Minimize Total Actual Flow Times. Proceeding of National Conference in Mathematics, November 2008. Palembang, Indonesia.

Zahedi. (2008). Optimal Block Measurement Optimization to Minimize the Total Actual Flow Time. Jurnal MatStat, 6 (1), January 2008. Jakarta: Binus University.






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