Formula Help Sheet for Introduction to Business Process Modeling DISC 230

Time study sample size

𝑛𝑛 = �𝑧𝑧𝑧𝑧𝑎𝑎𝑥𝑥�

2

Work sampling sample size

𝑛𝑛 = �𝑧𝑧𝑒𝑒�

2 ��𝑝(1 − ��𝑝)

Learning Curve 𝑇𝑇𝑛𝑛 = 𝑇𝑇1 × 𝑛𝑛𝑏𝑏 Where 𝑇𝑇𝑛𝑛 = 𝑇𝑇𝑇𝑇𝑇𝑇𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓 𝑛𝑛𝑛𝑛ℎ 𝑢𝑢𝑛𝑛𝑇𝑇𝑛𝑛 𝑇𝑇1 = 𝑇𝑇𝑇𝑇𝑇𝑇𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓 𝑓𝑓𝑇𝑇𝑓𝑓𝑧𝑧𝑛𝑛 𝑢𝑢𝑛𝑛𝑇𝑇𝑛𝑛 b = ln (learning percent)/ln 2 Observed Time 𝑂𝑂𝑇𝑇 = ∑𝑥𝑥 𝑇𝑇

𝑛𝑛

Normal Time NT = OT x PR Standard time ST = NT x AF Where PR = performance rating AF = Allowance factor Reliability P(no failure before T)= e-T/MTBF, e=2.7183 Z = (T-mean wear out time)/Standard deviation of wear out time

Formula Help Sheet for Operations Management

DISC 332 Mid term

Moving Average Forecast

Ft = MAn =

∑ni=1At−in

where

Ft = Forecast for period t

MAn = Moving Average for n Periods

At−i = Actual Value in Period t− i

n = number of periods

Weighted Moving Average

Ft =

n∑i=1

wt−iAt−i

where

wt−i = Weight of period t− i

Exponential Smoothing

Ft = Ft−1 + α(At−1 − Ft−1)

where

α = Smoothing constant

Linear Trend Equation

Ft = a+ bt

where

b =n∑ty −

∑t∑y

n∑t2 − (

∑t)2

= slope of the line

a =

∑y − b

∑t

n= Value of Ft at time period t equals 0

y = Value of time series

Trend Adjusted Exponential Smoothing

TAFt+1 = St + Tt

Previous TAF + smoothed error = St = TAFt + α(At − TAFt)

current trend estimate = Tt = Tt−1 + β(TAFt − TAFt−1 − Tt−1)

Trend adjusted forecast for period t = TAFt

β = Smoothing Constant

1

Seasonality Adjusted Forecasting

p = periodicity

Centered Moving Average for odd p

Dt =

∑t+( p−12 )

i=t−( p−12 )

Ai

p

Centered Moving Average for even p

Dt =Dt−p/2 +Dt+p/2 +

∑t−1+p/2i=t+1−p/2 2Di

2p

SRIt = Dt/Dt

SRI = Average of SRI’s for all t

De-seasonalized Demand for period t = Dt =Dt

SRIt

Seasonality adjusted forecast for period t = Ft = Ft × SRIt

Mean Absolute Deviation = MAD =

∑t |At − Ft|

n

Mean Squared Error = MSE =

∑t(At − Ft)2

n− 1

Mean Absolute Percent Error = MAPE =

∑t|At−Ft|At

× 100

n

2

Product Layouts

Output rate =Operating time / day

Cycle time

Desired Cycle time =Operating time / day

Desired Output rate

Nmin =

∑t

Desired Cycle Time

where Nmin = minimum number of work stations∑t = sum of task times

% Idle time =Idle time / cycle

Nactual ×Desired Cycle Time× 100

Efficiency = 100%−% Idle time

Work Sampling

n =(ze

)2p(1− p)

n = sample size

p = Sample proportion (Number of occurrences divided by sample size)

z = number of normalized standard deviation needed for desired confidence

e = maximum error

Center of Gravity Method

x =

∑xin

y =

∑yin

x coordinate of location i

y coordinate of location i

n= number of destinations

x =

∑xiQi∑Qi

y =

∑yiQi∑Qi

Qi = Quantity to shipped to location i

3