Assembly line and product characteristics

The line feeding policies, as well as the assembly line and product characteristics, are described within the so-calledα-field. It contains decisions on possible line feeding policies and considera-tions on theusageprocess (Figure 2.2), being characteristics and demand of products and parts.

Throughout the classification, the symbol◦ denotes an empty field.

Table 2.4Search terms used in Web of Science and research fields used to exclude not related papers

Search terms Exclusion of fields

”assembly line*” AND ”feeding” Optics, plant sciences, chemistry,...

”assembly” AND ”material* supply”

”assembly” AND ”part* supply”

”assembly line*” AND ”material* provision”

”assembly” AND ”part* provision”

”assembly” AND ”kitting”

”assembly” AND ”line stocking”

”assembly” AND ”feeding” cell biology, ecology, microbiology,...

Line feeding policies

As shown in Subsection 2.2.1, five policies are distinguished in this framework.

α1∈ {L, B, S, Ks, Kt}.

• α₁=L: Full load carriers are stored at the border of line (line stocking).

• α1=B: Parts are repacked into smaller load carriers (boxed-supply).

• α1=S: Sequenced parts are delivered to assembly lines.

• α₁ = Ks. Parts are sorted in stationary kits, which are supplied to specific stations requiring these.

• α₁=Kt. Parts for multiple stations are gathered in a common kit, which is delivered to an entry point of the assembly line and travels along (part of) the line with the product.

As we experienced in company visits, the production control of feeding material for assembly can differ for different line feeding policies. E.g., more standardized parts might be triggered by a pull signal, whereas highly specific kits might be controlled in a push manner. The way of controlling part replenishment might have an impact on the stock at the BoL and therefore, it might affect holding costs when considered (see Section 2.5.1).

Remark 1. By defining the ALFP as the assignment of parts to line feeding policies, it is implied that more than one policy is examined. This can, e.g., be denoted byα1 ={LKs} to describe that line stocking and stationary kits are compared.

Assembled products

The products assembled in an assembly system can deviate from each other with respect to the part variants used, processing times, or precedence graphs.

α₂∈ {◦, m^λ, M^λ}

• α2=◦: Only a single type of product is produced on the assembly line. In literature, this is described by the term single model assembly (Boysen et al., 2007). This notation is also used when no clear definition of the number and kind of produced models is given in a paper which raises the assumption that a single model is assembled.

• α2=m^λ: Different products are assembled on a single assembly line without the need for setups: the sequence of products is arbitrary. This is referred to as mixed model assembly line (Becker and Scholl, 2006). λ∈ {◦, is}has to be defined.

• α2 =M^λ: Multiple products are assembled batch-wise on a single assembly line. This is called multi model (Becker and Scholl, 2006). In this case, setup times may exist or it may be useful to remove parts, which are temporarily not required, from the BoL when the produced model is changed. λ∈ {◦, is} has to be defined.

– λ=◦: The precedence graphs are considered to be distinct. Hence, the products differ by the required part families and/or task precedence relations. This may affect the kit constellation. When products truly differ with respect to their precedence relations, one should plan kits for every model individually as (some) parts may be used by one model only and thus block space for other parts used in a different product.

– λ=is: The precedence graphs of different products are considered to be isomorphic.

Hence, the products differ only by the required part variants of the same part families.

In these cases, one only needs to plan a single kit type.

In real-world applications, assembly systems often consist of more than one assembly line. One possible consequence of multiple assembly systems is a change in transportation distances and the organization of transportation. However, usually these problems can be decomposed into individual problems, optimizing line feeding for every assembly line individually. Therefore, this trait is not considered further.

Part partitioning

As mentioned earlier, one might make a distinction between parts and part families containing multiple parts of the same kind.

α3∈ {◦, f}

• α3=◦: All parts are assumed to be distinct and there is no interrelation between parts.

• α₃ = f: The set of parts is partitioned in families, each containing up to multiple parts with similar characteristics and a similar functional purpose.

As stated in Section 2.2.2 usually all different parts which can also be referred to as stock-keeping-units are distinguished. Additionally, one might take into account that some of these parts are linked to another (Lim`ere et al., 2015, 2012). This can be described by families which contain multiple parts but all of these parts may substitute each other. Therefore, for a single final product, not more than one part out of a family is used. As the parts within a family are substituting each other, this impacts, e.g., the required volume or weight in a kitting container.

Obviously, demand patterns of individual parts within a family are also not independent but are linked to each other and the demand of the final products. Even if parts are classified in families, the assignment to line feeding policies can still be done on a part level. However, if

the assignment should be similar for all parts within a family, additional constraints need to be included in the mathematical model.

Part demand

Product demand, and subsequently the demand for parts, can either be assumed to be stochastic or deterministic.

α₄∈ {◦,˜λ}

• α4=◦: Demand for products as well as parts is assumed to be deterministic over time. This assumption often results from the use of a master production schedule (MPS), indicating a planned production quantity.

• α₄= ˜λ: Product and part demand are assumed to be stochastic over time.

In operational problems, part demand can be known in advance on a short term basis iftracking systems are used (Choi and Lee, 2002) or afrozen schedule is applied (Boysen and Emde, 2014).

But even then, demand can change due to machine breakdowns, line stoppages, rescheduling or defective parts (Alnahhal and Noche, 2015a). However, in tactical problems, part demand is unknown. This can easily be seen, as the ALFP is often solved before the start of production.

In that case, demand is usually not known. Though, it can be estimated by the use of a MPS or by analyzing the demand of similar products (Faccio, 2014). Therefore, stochastic assumptions seem to be more realistic than deterministic on this level. However, the latter are used in the majority of papers.