Optimization Model for the Design of Levelling Patterns with Setup and Lot-Sizing Considerations
Production levelling (Heijunka) is one of the key elements of the Toyota Production System and decouples customer demand from production orders. For the decoupling period a levelling pattern has to be designed. Existing approaches for the design of levell
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Abstract Production levelling (Heijunka) is one of the key elements of the Toyota Production System and decouples customer demand from production orders. For the decoupling period a levelling pattern has to be designed. Existing approaches for the design of levelling patterns are majorly limited to large-scale production. Therefore, this article proposes a novel optimization model regarding the requirements of lot-size production. Relevant, sequence-dependent changeovers are considered. An integer, combined lot-sizing and scheduling model is formulated. The four target criteria changeover times, smoothness of daily workload, variance of lot-sizes and similarity of production sequences are aggregated into one optimization model. In a real case study of an existing production plan a clear improvement of changeover times, similarity and smoothness of workloads is realized.
1 Introduction to Production Levelling One major problem of production planning is caused by the limited flexibility which exists in adapting the output of the production resources to a varying, fluctuating customer demand. In a globalized, highly-competitive market only limited rules for the timing of customer orders can be established. Therefore, a strict following of customer orders by production leads to undesired inefficiencies in production plans. One approach to tackle this issue is proposed by the well-known Toyota Production System with the concept of levelling (also production smoothing or Heijunka) [9]. Levelling decouples customer demand from production orders for a fixed period of time. For this levelling period, a levelling pattern needs to be designed. The pattern M. Boning (B) · H. Breier Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany e-mail: [email protected] H. Breier e-mail: [email protected] D. Berbig Robert Bosch GmbH, 70771 Leinfelden-echterdingen, Germany e-mail: [email protected] © Springer International Publishing Switzerland 2017 K.F. Dœrner et al. (eds.), Operations Research Proceedings 2015, Operations Research Proceedings, DOI 10.1007/978-3-319-42902-1_54
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determines at which production day, which product, in which quantity (lot-size) and in which position (order) has to be produced. Levelling aims at patterns which are balanced in production volume as well as in production mix [4]. As a result, a reliable, balanced plan and a smoothened production rhythm can be communicated with all suppliers of the underlying supply chain. The impact of the bullwhip effect can be decreased and spare capacity or stocks to cope with demand peaks can be reduced [5].
2 Existing Approaches and Related Problems The design of levelling patterns is nothing new and many approaches have been described in literature. Existing approaches can be classified into procedure models and optimization models [1]. Procedure models describe systematic approaches which contain a set of structured rules for the design of levelling patterns. Such approaches are presented in [11, 13, 14]. A good s
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