A lagrange relaxation based algorithm for parallel injection machine scheduling problem

Enjection molding machines produce semi-finished and finished products necessary for many industries.Shops with these machines in parallel are referred to as parallel injection machine shops. In the productionof orders, the connection of injection molds to the machines and the determination of the suitability of thesemolds for the machines are frequently addressed in the literature. This study is inspired by a parallel injectionmachine shop producing healthcare plastic products. The problem addressed in this study is significantlydifferent from problems in the literature. It involves dividing orders among machines, processing a stack oforders from different customers, labor costs for production, penalty costs for products produced after thedelivery time, injection machines with different production speeds, energy costs, and considering thecompatibility of orders-molds-machines. A mathematical model is proposed for the problem incorporatingthese differences, ensuring linearity with all constraints and the objective function. Furthermore, a tool isdeveloped for solving real-life problems using Lagrange relaxation technique. Test problems of various sizesare created to validate the proposed model and algorithm. It is observed that the proposed algorithm converges better to the optimum solution and performs better than the model.