BUS606: Operations and Supply Chain Management

This section proposes a new balancing heuristics for mixed AL titled target mobile RPW (RPW-MVM), which relies on heuristics of RPW positional weights originally proposed by Helgeson & Birnie. Such proposition focuses on a production environment amenable to changes in product mix, which cause imbalances on the workstations and generate productive capacity constraints in AL, making it unable to meet the required production demand.

The heuristic allows the AL meets the production demands characterized by several product mix composition, without the need for interventions to balancing adjustment or sequencing of actions to launch the products. This requires that the time of each model on all workstations is less than the AL cycle time. In addition, the proposed heuristic innovates in the tasks distribution format to workstations, proposing a target mobile which aims to improve the tasks distribution between the stations compared to the original RPW. The proposed heuristic is now detailed.

RPW-MVM

The original RPW is fundamentally guided by a pre-established time cycle; therefore, it can be assumed that the amount limiting target of the allocable task to a given workstation is the cycle time, which is fixed. Thus, the tasks allocation to workstations may have an accumulated imbalance in the first workstation, which typically results in significant losses to the AL. It is proposed then a change in this target, which becomes mobile (and called Moving Target - MVM).

The MVM is calculated for each workstation and depends on the number of workstations to be balanced. It serves to improve the tasks distribution between the workstations not balanced according to the time of the not yet allocated tasks. Every changing of the station, the target is recalculated for each model (hence mobile), and then identified the condition that allows allocation of the remaining tasks of the product with longer not yet allocated operations. In other words, MVM allows for each workstation to exchange the entire contents of the working model under review to be distributed evenly among the remaining stations.

Figures 7 and 8 illustrate the RPW without target mobile and with moving target (MVM), respectively. The MVM yields better smoothness index for AL and, therefore, benefit and ergonomic productive character.

Figure 7 Balancing with RPW and without MVM heuristics. Source: The authors.

Figure 8 Balancing with RPW and MVM heuristics. Source: The authors.

Following are presented the steps to perform the RPW-MVM.

Step 1: Set the diagram/equivalent precedence matrix of all models;

Step 2: Unlike the RPW in AL single model, the RPW-MVM is a balancing in a AL with more than one product model, where each model has its own tasks processing time. So for the average processing time for common tasks to the different models, is needed to define the each model proportion to be produced by the Equation 8

$pd_m = \dfrac{d_m}{D}$

where$d_m$ is the product demand in the period $p$ such that $m=1,...,M$; and $D$ is the total demand for all models for the period $p$. The products demand history or the production plan are reference sources for defining the product number of the model $m$.

Step 3: Calculate the cycle time (Tc) based on total production demand to be met by the Equation 2;

$T_{c}=\frac{\text { available time in period p }}{\text { demand inperiod p }}$

Step 4: As mentioned earlier, the RPW-MVM support in times of an equivalent product of mixed AL. Thus, for the tasks allocation in the RPW-MVM, use the Time Weighted Average ($\overline{t_{k}}$) and the weighted average total station time ($\overline{S_{j}}$), calculated using Equations 9 and 10, respectively.

$\overline{t_{k}}=\sum_{m=1}^{M} p d_{m} t_{k, m}$

$\bar{S}_{j}=\sum_{k \in j} \bar{t}_{k}$

where $t_{k, m}$ is the processing time of task $k$ in the model $m$ and $pd_m$ is the proportion of model $m$.

Step 5: Calculate the RPW of each task by adding $\overline{t_{k}}$ to the processing times of all preceding tasks equivalent precedence diagram;

Step 6: Sort the tasks in descending order of RPW;

Step 7: Calculate the minimum number of workstations for balancing ALM (MinW) and then set the last workstation ($W=MinW$) based on the Equations 11 and 12, where $CTT_m$ is the total workload the m model.

$C T T_{m}=\sum_{k=1}^{N} t_{k, m}$

$MinW = \dfrac{CTT_m}{T_c}, m = 1, ... M$

Step 8: Set $j = W$;

Step 9: Calculate the moving target of the latest workstation for all models $(MVM_{j, m = 1, ...M})$. The MVM is required for each product model and should be recalculated every new balanced workstation during application of the RPW-MVM. The moving target the $j^{th}$ workstation to the model $m (MVM_{j, m})$ is calculated by Equation 13 based on the not yet allocated workload residue divided by the total workstations still unbalanced for the m model. Equation 14 sets the total charge allocated at station $j$ of the m model ($CTA_{j, m}$).

$CTA_{j, m} = CTA_{j+a,m} + S_{j,m}$

$MVM_{j,m} = \dfrac{CTT_m - CTA_{j+1,m}}{MinW - (MinW-j)}$

Step 10: Allocate most task $RPW$ to the station $j$, while respecting the precedence relation of the equivalent diagram of precedence, and the weighted average total station time [so that it does not exceed the largest $MVM (\bar{S}_{j} \leq (major MVM_{j,m=1,...M}))]$; Furthermore, pay attention to that the total time m model at the station does not exceed the cycle time $(S_{j,m=1,..M} \leq T_C)$;

Step 11: Repeat the process designating the task to stations until there is no feasible task to at least one of the models;

Step 12: Set $(j = j -1)$ e recalculate $MNM_{j,m=1,...M}$;

Step 13: Validate the inequality $((major AVM_{j,m=1,....M) \leq T_C})$; if met, proceed to the next step; otherwise, return to step 8, reset $(MinW = MinW + 1)$ and restarting the task allocation process; and

Step 14: Repeat steps 10 through 13 until all of the tasks are allocated.

Balancing assessment generated by the RPW-MVM

The balancing analysis of the resulting RPW-MVM heuristic relies on static indicators, ie without the use of dynamic simulation methods. Thus, in some cases, they are calculated in the AL bottleneck position (g), where production is limited according to Peinado & Graeml (2007). The indicators are: (i) the amount of AL workstations; (ii) capacity in the bottleneck situation (Cap_b), as depicted in Equation 15; and (iii) crossing time estimated in the bottleneck position (TCestm_b); (iv) Line Efficiency bottleneck situation (LE_b) and (v) balancing efficiency (BE).

$Cap_b = \dfrac{\text{available time in the period p}}{T_g}$

Where $T_g$ is the bottleneck processing time, defined by the major $S_{j = 1, ...W, m=1,....M}.$

Likewise, the crossing time estimated by the bottleneck situation ($TCestim_b$), shown in Equation 16 also uses the bottleneck processing time in obtaining it.

$TCestim_b = (\text{Number of workstations + A}) \times T_g$

where A is the number of products not allocated to workstations, but located between the beginning and the end of AL (eg, buffers).

Line Efficiency bottleneck situation (LEb) is calculated by Equation 17, whereas the balancing efficiency (BE) is given by Equation 18.

$LE_b = \dfrac{\sum_{k = 1} ^ {N} \overline t_k}{W \times T_s}] \times 100$

$BE = [1- \dfrac {\sum_{j = 1} ^ {W} |\overline S_{j} - S_{av}|} {W \times S_{av}} ] \times 100$