Minimization of off-grade production in multi-site multi-product plants by solving multiple traveling salesman problem

Continuous multi-product plants allow the production of several products (product grades). During grade transitions off-spec products are produced. The economic losses and the environmental impact of these transitions are sequence dependent, so the amount of off-grade products can be minimized by scheduling the sequence of the production of different products. Applying parallel production sites increases the flexibility of multi-product plants. Since market demands are changing, the production cycles of these sites should be re-scheduled in certain intervals. Therefore, our task is to design production cycles that contains all required products by minimizing the total length of grade transitions. Most production scheduling problems such as the one considered in this paper are NP-hard. Our goal is to solve realistic problem instances in no more than a couple of minutes. We show that this problem can be considered as a multiple traveling salesmen problem (mTSP), where the distances between the products are based on the time or costs of the grade transitions. The resulted mTSP has been solved by multi-chromosome based genetic algorithm. The proposed algorithm was implemented in MATLAB and is available at the website of the authors (Abonyi). For demonstration purposes, we present an illustrative example. The results show that multi-product multi-site scheduling problems can be effectively handled as mTSPs, and the proposed problem-specific representation based genetic algorithm can be used in wide range of optimization problems.