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This paper studies the problem of capacitated lot-sizing and scheduling in job shops with a carryover setup 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.

This article addresses multi-level lot sizing and scheduling problem in capacitated, dynamic and deterministic cases of a job shop manufacturing system with sequence-dependent setup times and costs assumptions. A new mixed-integer programing (MIP) model with big bucket time approach is provided to the problem formulation. It is well known that the capacitated lot sizing and scheduling problem (CLSP) is NP-hard. The problem of this paper that it is an extent of the CLSP is even more complicated; consequently, it necessitates the use of approximated methods to solve this problem. Hence, two new mixed integer programming-based approaches with rolling horizon framework have been used to solve this model. To evaluate the performance of the proposed model and algorithms, some numerical experiments are conducted. The comparative results indicate the superiority of the second heuristic.

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