Mathematical model for scheduling operations in cascaded continuous processing units

The scenario under consideration involves n cascaded continuous processing units responsible for processing m product lines. Each product line needs to be processed by all the units in the same sequence, and has dedicated finite capacity storage tanks before and after every processing unit. A unit can process only one product line at a time. Inputs for all the product lines arrive continuously and simultaneously on the input side of the first unit in the sequence. There are multiple intermediate due dates for the final products. An optimal schedule for the units calls for a trade-off among spillage costs, upliftment failure penalties and changeover costs. A mathematical model is developed for the purpose and the resulting MINLP is linearized using standard techniques. The MILP has been tested using GAMS for three units and three product lines as encountered in a refinery situation. The model could output optimal schedules for a ten day scheduling horizon within reasonable time.