Throughout this study, we defined the assembly line feeding problem as the assignment of parts to line feeding policies, viz., line stocking, boxed-supply, sequencing as well as stationary and traveling kitting. Furthermore, we showed that even the basic problem is an N P-hard prob-lem. To characterize all the complexities the ALFP involves, the scope of the problem is further outlined by means of two dimensions. Firstly, different sub-processes under study are clearly defined as storage, preparation, transportation, line side presentation and usage. Secondly, the decision level of the ALFP is described by distinguishing different strategic, tactical and opera-tional decisions. With the aid of this structure, we hope to make the problem more intelligible and simplify future research.
Based on the provided problem definition, we introduced a classification scheme, including the most important decisions and assumptions in research. This classification scheme serves to classify the existing literature and reveals the most important research fields and streams for future research.
In conclusion, the readers are warmly invited to use the proposed classification and enhance it by new, generic, and relevant fields when needed. We hope that it will hereby become a standard in the field of assembly line feeding, assisting in bundling efforts for thoroughly understanding the field.
Mixed-model assembly line feeding with discrete 3
location assignments and variable station space
“I skate to where the puck is going to be, not where it has been.”
Wayne Gretzy
3.1 Introduction
As discussed in this thesis’s introduction, the complexity increase of assembly systems requires more flexible and agile solution approaches (see also Batta¨ıa et al. (2018)). As the number of parts required for product assembly rises rapidly, congestion at the assembly stations is becoming the norm. As mentioned earlier, one can avoid this by selecting adequate line feeding policies more flexibly by choosing them individually for each part (Lim`ere et al., 2012). One significant trade-off in selecting the optimal policy balances space requirements and the associated costs of all parts needed at any station. Policies that require less space are usually more expensive because of additional efforts for reducing the size by, e.g., splitting up pallets and presorting parts into boxes. In some cases, some stations may need more parts than others due to the outcome of balancing decisions (Chica et al., 2016). E.g., at station A, only very few parts are assembled, and at the adjacent station B, many parts are assembled. In such cases, station B may borrow some space from station A to store parts required for assembly. Space borrowing lowers overall costs as it facilitates space-consuming but cheaper line feeding policies.
With this study, we aim to extend previously developed optimization models in the area of assembly line feeding. The extension is done in manifold ways: (i) Five line feeding policies are incorporated, whereas, in the literature, a maximum of three could be found (e.g., Caputo et al. (2015a); Sali and Sahin (2016)). This is intended to give a more general model and support decision-making in practice as all line feeding policies can easily be implemented. (ii) Furthermore, we incorporate decision making for discrete locations, i.e., every single part is assigned to a discrete location at the BoL. The BoL describes the area next to a station designated to store parts for assembly. An example for those dedicated positions can be seen in Figure 3.1.
Here, the BoL at every station of the assembly line (AL) consists of multiple locations that are available for storing parts. By incorporating discrete locations, walking durations can be estimated more realistically. Furthermore, it will also provide additional information on the design of the border of the line. In previous works, no information on the exact usage of the BoL was given. Only Klampfl et al. (2006) evaluated the effect of different designs through simulation.
(iii) The proposed model does not only assign parts to discrete locations but also allows to assign these discrete locations to stations. By allowing this space borrowing, the available space per station becomes more flexible and allows for cheaper line feeding policies. This is also depicted in Figure 3.1 with station 2 borrowing location 8 from station 1. (iv) Lastly, the model describes mixed-model assembly lines, meaning that various types of product models are produced on a single assembly line in an arbitrary order. An example of these models would be the BMW 5 Series and 7 Series, which we consider distinct models. Therefore, every model allows for the use of different kits. To summarize, it may be stated that in comparison to the existing literature, we include more decisions in the model to make assembly line feeding optimization models more applicable for complex, real-world assembly systems. In addition to these extensions, oriented towards applicability, we also propose a more efficient procedure for solving the problem. More elaborate solving procedures are necessary to include discrete locations, multiple line feeding policies, different product models, and space borrowing, making this model harder to solve than
models previously described in the literature.
AL: Assembly line BoL: Border of line
Sl: Stations that may usel l: Number of location
Locations used by station 1 Locations used by station 2 Figure 3.1Example of space borrowing
The remainder of this chapter is organized as follows: In the next section, literature related to decision making in assembly line feeding is reviewed. This is followed by a more formal problem definition and an explanation of the setting in which the proposed optimization model is applied. Afterwards, in Section 3.4, a newly developed mathematical optimization model is proposed, describing a general ALFP with space constraints at the BoL, taking into account all five line feeding policies. In Section 3.5, we firstly prove that the proposed model is N P-hard.
Secondly, we propose improvements to the solving procedure of the model by preprocessing, Valid Inequalitys (VIs), and applying cuts. The latter are added in a Branch & Cut manner and in the form of VIs (also referred to as Cut & Branch). Next, in Section 3.6, data generation and experimental design are described and results are analyzed. Implications and limitations of this research are discussed in Section 3.7. Finally, the chapter is concluded by summarizing results and indicating ideas for future research.