Flexible layouts for the mixed-model assembly of heterogeneous vehicles

Abstract

The increasing vehicle heterogeneity is pushing the widespread mixed-model assembly line to its limit. The paced, serial design is incapable of coping with the diversity in workloads and task requirements. As an alternative, the automotive industry has started to introduce flexible layouts for segments of the assembly. In flexible layouts, the stations are no longer arranged serially and no longer linked by a paced transportation system but by automated guided vehicles. This paper investigates the initial configuration of such systems. The flexible layout design problem (FLDP) is the problem of designing a flexible layout for a segment of the assembly of heterogeneous vehicles. It comprises an integrated station formation and station location problem. Moreover, the FLDP anticipates the operational flow allocation of the automated guided vehicles. We formalize the FLDP in a mixed-integer linear program and develop a decomposition-based solution approach that can optimally solve small- to mid-sized instances. In addition, we transform this solution approach to a matheuristic that generates high-quality solutions in acceptable time for large-sized instances. We compare the efficiency of flexible layouts to mixed-model assembly lines and quantify the benefits of flexible layouts which increase with vehicle heterogeneity.

Appendices

Appendix A

Instance generation scheme

Appendix B

Benchmark mixed-model assembly line balancing model adapted from Bukchin and Rabinowitch (2006)

We adapt the mixed-model assembly line balancing model formulation by Bukchin and Rabinowitch (2006). Table 10 shows the required additional notation. We introduce a new index set $s\in S$ that represents the stations on the line. Parameter c denotes the cycle time. We add parameter $\alpha \ge 0$ to vary between closed and open stations. $\alpha$ represents the percentage of cycle time that workers are allowed to drift out into downstream stations. Next, we denote three sets of decision variables. The binary variable ${\bar{X}}_{t,m,s}$ shows whether task t for model m is assigned to station s. ${\bar{Y}}_{t,s}$ is a binary variable as well. It indicates whether task t is assigned to station s for any model. Last, the continuous variable ${\bar{Z}}$ represents the number of stations used and is to be minimized (23).

Table 10 Additional notation for mixed-model assembly line balancing problem

Constraints (24) force the workload of a task for a particular model to be assigned to a single station. Note again that splitting the workload of one model among task duplicates at different stations is not allowed on mixed-model assembly lines. Precedence relations are satisfied by constraints (25). Constraints (26) limit the total processing time for each model at each station. For $\alpha =0$, we evaluate closed stations, in which workers are not allowed to drift out into downstream stations. For $\alpha >0$, workers are allowed to drift out into the neighboring stations by $\alpha \%$ of the cycle time. In order to make sure that the overall capacity of the station is not violated, we add constraints (27) to the model by Bukchin and Rabinowitch (2006). The number of stations used is derived in constraints (28). Constraints (29) link the two binary variables by checking whether a task is performed for any model at a certain station. As an extension to the model by Bukchin and Rabinowitch (2006), we introduce constraints (30) that limit the maximum number of task duplicates. Without these constraints, the mixed-model assembly line solution would not be comparable to the flexible layout solution. Finally, in constraints (31)–(33), we restrict the domains of the decision variables.

$$\begin{aligned} min~Z^L&= {\bar{Z}} \end{aligned}$$

(23)

s.t.

$$\begin{aligned} \sum \limits _{s{\in }S}{\bar{X}}_{t,m,s}&=1&\forall m{\in }M,t{\in }T_m \end{aligned}$$

(24)

$$\begin{aligned} \sum \limits _{s_1{\in }S}s_1\cdot {\bar{X}}_{t_1,m,s_1}&\le \sum \limits _{s_2{\in }S}s_2\cdot {\bar{X}}_{t_2,m,s_2}&\forall m{\in }M,t_1{\in }T_m,t_2{\in }V_{m,t_1} \end{aligned}$$

(25)

$$\begin{aligned} \sum \limits _{t{\in }T_m}q_{m,t}\cdot {\bar{X}}_{t,m,s}&\le c\cdot (1+\alpha )&\forall m{\in }M,s{\in }S \end{aligned}$$

(26)

$$\begin{aligned} \sum \limits _{m{\in }M}d_{m}\cdot \sum \limits _{t{\in }T_m}q_{m,t}\cdot {\bar{X}}_{t,m,s}&\le \tau&\forall s{\in }S \end{aligned}$$

(27)

$$\begin{aligned} {\bar{Z}}&\ge \sum \limits _{s{\in }S}s\cdot {\bar{X}}_{t,m,s}&\forall m{\in }M,t{\in }T_m \end{aligned}$$

(28)

$$\begin{aligned} {\bar{Y}}_{t,s}&\ge \frac{1}{|M|}\cdot \sum \limits _{m{\in }M|t{\in }T_m}{\bar{X}}_{t,m,s}&\forall t{\in }T,s{\in }S \end{aligned}$$

(29)

$$\begin{aligned} \sum \limits _{s{\in }S}{\bar{Y}}_{t,s}&\le n_t&\forall t{\in }T \end{aligned}$$

(30)

$$\begin{aligned} {\bar{X}}_{t,m,s}&\in \lbrace 0,1 \rbrace&\forall m{\in }M,t{\in }T_m,s{\in }S \end{aligned}$$

(31)

$$\begin{aligned} {\bar{Y}}_{t,s}&\in \lbrace 0,1 \rbrace&\forall t{\in }T,s{\in }S \end{aligned}$$

(32)

$$\begin{aligned} {\bar{Z}}&\ge 0 \end{aligned}$$

(33)