Computers and Chemical Engineering 26 (2002) 1321 – 1332 Makespan minimization for chemical batch processes using non-uniform time grids Rainer E. Burkard a, *, Tiziana Fortuna a , Cor A.J. Hurkens b a Institute of Mathematics B, Technical Uniersity Graz, Steyrergasse 30, A-8010 Graz, Austria b Department of Mathematics and Computing Science, Eindhoen Uniersity of Technology, P.O. Box 513, 5600 MB Eindhoen, The Netherlands Accepted 10 April 2002 Abstract We present a mixed-integer linear programming model for minimizing the makespan of batch processes occurring in the chemical industry. The formulation of the model is based on the starting and processing times of the batches without using an external uniform time grid. A special form for the objective function is chosen and additional redundant constraints are added in order to speed up the solution process. A comparison with the classical uniform time discretization model shows that in many cases the size of the new model as well as its solution time is smaller. Computational results on several instances are reported. The modular structure of the model allows a combination with other continuous-time models for batch processing problems. © 2002 Elsevier Science Ltd. All rights reserved. Keywords: Multi-product and multi-facility production planning; Batch production systems; Scheduling problems Nomenclature batch type b set of tasks or batch types B B (m ) set of batches which can be processed on machine m d i external demand minimal stock size of i that has to be produced in order to satisfy the demands of the final D I products greatest rational number such that each batch processing time can be expressed as an integer G multiple of G i resource machine m set of machines or facilities M number of possible batch starting times N n b minimal number of batches of type b necessary for the final demand maximal number of batches of type b necessary for the final demand N b R set of resources (products and raw materials) initial stock size S i init maximal stock size S i max minimal stock size S i min www.elsevier.com/locate/compchemeng * Corresponding author E-mail addresses: burkard@opt.math.tu-graz.ac.at (R.E. Burkard), tizianafortuna@hotmail.com (T. Fortuna). 0098-1354/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved. PII:S0098-1354(02)00097-2