An improved model and a heuristic for capacitated lot sizing and scheduling in job shop problems

This paper studies the problem of capacitated lot-sizing and scheduling in job shops with a carryover set-up and a general product structure. After analyzing the literature, the shortcomings are easily realized; for example, the available mathematical model is unfortunately not only non-linear but also incorrect. No lower bound and heuristic is developed for the problem. Therefore, we first develop a linear model for the problem on-hand. Then, we adapt an available lower bound in the literature to the problem studied here. Since the problem is NP-hard, a heuristics based on production shifting concept is also proposed. Numerical experiments are used to evaluate the proposed model and algorithm. The proposed heuristic is assessed by comparing it against other algorithms in the literature. The computational results demonstrate that our algorithm has an outstanding performance in solving the problem.