A deterministic model to estimate system performance

A deterministic model is used to estimate the system performance. A bottle neck model is a mathematical description of a deterministic model.

The bottleneck model is used to provide starting estimates of the FMS design parameters, such as the production rate and the number of worksta-tions. We performed this bottleneck model with GC’s data. We performed the bottleneck model assuming that 333 bikes will be leaving the system.

Cell formation design is obviously a key issue in CMS design. In gen-eral, for a production facility with a given number of machines and part mix to be processed in the facility, there are three specific decisions in cell formation design:

1. Number of manufacturing cells to be established 2. Machines constituting each cell

3. Parts assigned to each cell

As shown in Table 1.4, part mix is equal to total parts produced by cell divided by total parts produced by system, that is,

Part mix = Total parts produced by cell/ Total parts produced by system Customized products, shorter product life cycles, and unpredictable patterns of demand have challenged the manufacturers to improve the efficiency and productivity of their production activities. Manufacturing systems should be able to adjust or respond quickly to adopt necessary changes in product design and product demand without major invest-ment. Since shorter product life cycles are an increasingly important issue

Table 1.4 Part Mix Is Equal to Total Parts Produced by the Cell Divided by the

Total Parts Produced by the System

Cell Parts Part mix

Frame cell 333 0.2766

Handlebar cell 333 0.2766 Seatpost cell 333 0.2766 Drivechain cell 205 0.1703

Total 1204 1

in cellular manufacturing, one cannot assume that the designed cells will remain effective for a long time. Ignoring the planned new product introductions would necessitate subsequent ad hoc changes to the CMS causing production disruptions and unplanned costs. Thus, one has to incorporate the product life cycle changes in the design of cells. This type of model is called the multiperiod CMS or dynamic CMS. Since the formed cells in the current period may not be optimal for the next period, the reconfiguration of the cells is required.

By completing the calculations to determine the part mix (Table 1.4), the bottleneck is assessed as follows (see Table 1.5):

• By using the average workload and workload per server for each cell we were able to identify the bottleneck as the frame cell with a ratio of 50.82.

• Once the bottleneck was identified the next calculation to complete was the maximum production rate produced by the system; this was determined to be 70.8 (pieces/ hour).

• Other calculations performed during this model consist of the pro-duction rate, utilization, and mean busy servers for each cell.

The bottleneck identification and assessment are performed as follows:

WLi = ΣΣ [Processing time (ijk) × Operation frequency (ijk) × Part mix fraction]

Bottleneck station has largest WLi/ si ratio

Production rate of each product = Rp* × Part mix fraction

Utilization of each station = Server workload/ Bottleneck server workload Mean number of busy server = Station workload × (Rp*)

When comparing the data found by performing the bottleneck model and the data obtained from running the simulation (Table 1.6), the out-comes were consistent with each other. From the bottleneck model it can be suggested that the frame cell is the bottleneck of the operation; when looking at the simulation output it can be seen that the frame cell, handle-bar cell, and seat cell are all utilized 100% of the time. By adding two additional frame cells, the utilization stays at 100% but the number of total entries into the system increases from 100 to 336, just enough to complete the 333 bicycles.

When the additional frame cells were added, it caused the handle-bar cell to be the bottleneck, holding up continued operations. To fix this problem, an additional handlebar cell was also added and the utilization stayed steady at 100%, but the number of entries increased from 282 to 564, which created enough to complete the 333 bikes. These increases in utilization support the fact that they are both bottlenecks in the system.

Table 1.5 Bottleneck Identification and Assessment PartPart mixFreq.

Process time (sec)

Average workload (WL)

# Servers at station (Si)WL/ SiRp* (pc/ sec)Rp* (pc/ hr)Production rate (pc/ hr)Utilization

Mean busy servers Frame cell0.2771735203.285450.820.0270.819.5918100.00%1.0000 Handlebar cell0.2771165 45.635411.4119.5918 22.45%0.8980 Seatpost cell0.2771 60 16.5952 8.29719.5918 16.33%0.3265 Drivechain cell0.170115025.540125.5412.0610 50.25%0.5025

Table 1.6 Output Report for Suggested Production System — — — — — — — — — — — — — — — — — — — — — General Report — — — — — — — — — — — — — — — — — — — — — Scenario : Normal Run Replication : 1 of 1 Warm-Up Time : 100 hr Simulation Time : 108 hr — — — — — — — — — — — — — — — — — — — — — LOCATIONS Location Name

---Scheduled Hours ---Capacity ---

---Capacity---Total Entries

---Average Minutes Per Entry

---Average Contents

---Maximum Contents

---Current Contents ---% Util --- Raw materials Frame cell.1 Frame cell.2 Frame cell.3 Frame cell Handlebar cell Seat cell Drive cell Subassembly 1 Subassembly 2 Drive cell queue Seat cell queue Handlebar cell queue Frame cell queue Final assembly Seat sub 1 Frame sub 1 Handlebar sub Drive sub

8 8 8 8 24 8 8 8 8 8 8 8 8 8 8 8 8 8 8

999999 1 1 1 3 2 1 1 999999 999999 999999 999999 999999 999999 999999 999999 999999 999999 999999

2896 112 112 112 336 564 365 496 732 334 600 5684 3704 6470 353 639 352 3348 3295

0.0 4.28 4.28 4.28 4.28 1.70 1.31 0.83 317.08 0.0 75.43 431.50 390.35 437.35 28.32 244.02 28.40 416.40 435.77

0 1 1 1 1 2 1 0.86 483.55 0 94.29 5109.78 3012.25 5895.16 20.82 324.85 20.82 2904.42 2991.42

1 1 1 1 3 2 1 1 582 1 199 5357 3234 6187 27 386 27 3016 3095

0 1 1 1 3 2 1 1 526 0 104 5320 3142 6137 20 311 18 3014 3095

0.0 100.00 100.00 100.00 100.00 100.00 100.00 86.06 0.05 0.0 0.01 0.51 0.30 0.59 0.0 0.03 0.0 0.29 0.30

Because the seat cell is receiving 365 entries and meets the required quan-tity with one cell, it is sufficient and does not need another. Simulation output used for comparison to the bottleneck model is shown in Table 1.7.

CM is a proven technique in batch- type manufacturing. It improves the efficiency of manufacturing systems through a reduction in setup times, in- process inventories, and throughput times. This has been shown in numerous successful cases of CM implementation. Despite this, some studies suggest that the conversion from conventional batch- type manu-facturing to cellular manumanu-facturing may not always be beneficial. This is mostly due to the imbalanced workload on machines in machine cells, which leads to the accumulation of inventories in front of bottleneck machines. Imbalanced workloads also cause underutilization of non-bottleneck machines. In addition, the organization of machines into dedi-cated machine cells decreases the flexibility in machine selection for the processing of parts.