ISEN 316Project

May 9, 2015

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Team Oriental : Heran Guan Kyohei Okuhara

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Key Performance Measures

• Service Time: The amount of time it takes to process a job.

• Occupancy: The amount of jobs in the facility. • Sojourn Time: The amount of time a job spends

in the factory. • Throughput: The rate at which jobs flow through

the factory.

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Production System Analysis Flow Diagram

Start Get data from the facility

Model the facility in a flow-diagram

Find the routing matrix and

gamma matrix

Calculate the utilization

Calculate the squared COV for

arrival time

Calculate WS performance

measures

Calculate total performance

measures

Graph performance

curve

Find potential production

performanceFinish

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Calculate Utilization of each station

• Throughput of each workstation

• Utilization u

• λ = throughput matrix[1 x n]

• γ = gamma matrix (external arrival) [1 x n]• P = routing matrix (probabilities) [n x n]• I = identity matrix

[n x n]

• u = Utilization matrix [n x n]

• λi = throughput for i-th workstation• µi = 1/E[Ts(i)] (service rate for i-th workstation)• E[Ts(i)] = Expected service time for i-th workstation

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Calculate Ca2 for each station

• Coefficient of variance for arrival time for each workstation

[1 x n]• b matrix

[1 x n]

• d matrix [1 x n] i = 1,…,n ; n = total number of workstations

• squared coefficient of variation for service time of each station

[n x n]

• Q matrix

[n x n]

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Calculate the performance measures of each workstation.

• Kingman Diffusion Approximation

CTq(G/G/1)CTq(M/M/1)

• Cycle Time of each workstation Combining the equation for total cycle time

and the Kingman Diffusion Approximation,

• WIP of each workstation Using Little’s Law,

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Calculate the total performance measure for facility.

• Total WIP WIPT =

• Total CT CTT =

• WIPT = total WIP

• WIP(i) = WIP of i-th workstation

• CTT = total CT

• λ = external arrival rate (known as the sum of the elements of γ matrix from earlier)

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Example

• Get sufficient data from the facility in order to model the service time of each workstation (server) as a general distribution with known mean and variance and the out-flow rates of each workstation as well as the external arrival rate.

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Flow Diagram

WS1

WS2

WS3

WS4

1/3

2/3

1/10

3/10

1

2/10

1

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Routing matrix and Gamma matrix

• Gamma matrix: γ = [5 0 0 0]• Routing matrix: P = [0 2/3 1/3 0 0 0 0 1 0 0 0 1 0.1 -0.2 0.3 0]

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Bottleneck Analysis

• Utilization matrix:

u = [0.8125 0 0 0 0 0.8667 0 0 0 0 0.9333 0 0 0 0 0.8000]

 

• Workstation with the highest utilization is the bottleneck, which is station 3.

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Calculate the Ca2

• Ca2 matrix:

Ca2 = [1.0191 1.0840 1.1874 1.0852]

• Calculate the performance measures of each workstation

Workstation i CT(i) WIP(i)1 0.7087 hr 4.42942 1.3379 hr 8.91973 1.9273 hr 11.24284 0.5154 hr 6.4425

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Calculate the total performance measure for facility.

• WIPT = 31.0344 jobs• CTT = 6.2069 hrs

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Potential production performance

Workstation i newCT(i) newWIP(i)1 0.1301 hr 0.81312 0.1413 hr 0.94183 0.2097 hr 1.22354 0.0159 hr 0.1989

New WIPT = 3.1774 jobsNew CTT = 0.6355 hrs

Decrease each expected service time by 0.05 (from training) and cut the coefficient of variance for service time in half (assumption due to the decrease in variability).

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Performance Curve

Legend:• . = original CT with λ=5 for

each station

• Δ= new CT with λ=5 for each station

• *= new CT with λ=7.65 for each station

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Performance curve for Bottleneck

• Legend:• upper curve = old CT vs

utilization for bottleneck station

• lower curve = new CT vs utilization for bottleneck station

• + = original CT with λ=5 for bottleneck

• Δ= new CT with λ=5 for bottleneck

• *= new CT with λ=7.65 for bottleneck

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Example Conclusion

• This new total WIP and new total CT concludes that this production operation is 89.75% faster than the original facility with the same throughput.

• Increase the throughput until the new total CT equals the old total CT. Calculate the percent increase in the new throughput compared to the original through put. This equals the percent increase in the profit.

• New λ = 7.65/hr

• so the throughput increased by 53% which means that the profit is also increased by 53%.

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Thank You!