# A cyclic production scheme for the synchronized and integrated two-level lot-sizing and scheduling problem with no-wait restrictions and stochastic demand

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## Abstract

In this paper, we propose a production scheme for a two-step packaging system as part of a make-and-pack production process including parallel production units in all stages. In the first stage of the packaging system, flavored liquids are filled into cans of different sizes which are immediately palletized in the second stage, i.e., work-in-progress inventories do not exist. However, each filling unit can feed more than one palletizer at a time. Final products can be stored in a warehouse with limited capacity. Among others, the proposed scheme consists of a periodic production sequence, also referred to as a cycle, for each production unit and a control strategy that keeps cycle lengths close to a target length. In addition, an approach to specifying the parameters of the scheme is developed. This approach accounts for sequence-dependent setup times, downtimes of production units, capacitated storage and uncertain demand for final products that is satisfied from stock or backlogged. We evaluate our approach conducting computational experiments that are based on real-world and random data.

## Keywords

Production Multi-stage Sequencing and lot sizing Cyclic patterns Stochastic demand## Notes

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