Quantifying Performance to Develop Benchmarks for Warehouse Operations

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Quantifying Performance to Develop Benchmarks for
Warehouse Operations

• By
• Andy Johnson
• Leon McGinnis

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Goal

• Goal To create and demonstrate theory-based,
  cost-effective, and practical operational
  performance assessment methods that will allow
  organizations
• (1) to assess operational resource efficiency
  correctly and consistently

(2) to establish realistic best performance
goals and (3) to identify best practices
appropriate to their business environment
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Old Way to Improve Warehousing
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New Way to Improve Warehousing
www.isye.gatech.edu/ideas
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How Does iDEAs Work?
Over the Internet
Your data is private and secure
Html documents
Database
Solver
At your site
Georgia Tech Server
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iDEAs Provides

• Evaluating overall resource efficiency, based on
  a warehouse constructed from a large peer
  group ONLINE
• A comparative analysis of partial productivities,
  relative to the best in the peer group,
  identifying the true opportunity for
  improvement ONLINE

• An industry-level analysis of key factors
  affecting resource efficiency OFFLINE

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Chen, Wen-chih. and L.F. McGinnis, Reconciling
ratio analysis and DEA as performance assessment
tools. European Journal of Operational Research,
2006. Accepted
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Inputs and Outputs for Warehousing

• Output(y)
• Broken case lines
• shipped
• Full case lines
• shipped
• Pallet lines shipped
• Accumulation
• Storage function

• Input(x)
• Labor
• Space
• Capital Inv.

Operations
Hackman, et. al. Benchmarking warehousing and
distribution operations An input-output
approach. Journal of Productivity Analysis,
2001. 16 p. 79-100.
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Practices and Attributes
Operations
Output(y)
Input(x)
Practices Cross docking Use of temporary labor
Forward Reserve Velocity based slotting
Attributes Demand variability Number of
suppliers Seasonality Sku churn
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Peer Group
All other warehouses All other warehouses in your
industry All other warehouses using the same
predominate picking mode Your set of warehouses
and their past performance
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Initial Results
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Data Set

• iDEAs has had over 450 users per year since 2001
• From this data set we are able to verify 390
  records containing complete input and output data
  for the 3 input / 5 output model

• Concerned if all warehouses was too diverse of a
  group, we also collected data on 25 warehouse
  from the publishing industry (this will be called
  the industry specific group)

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Motivation to Investigate Outliers

• On-line data collection requires more scrutiny
  than data collected and analyzed by a single
  person
• What could be the/a cause of a negatively skewed
  efficiency distribution

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Motivation to Investigate Outliers

• To investigate the impact of environmental
  characteristics on efficiency the two-stage DEA
  method has been developed
• A data set is identified as using a similar
  technology
• In the first stage efficiency estimates are
  calculated
• In the second stage the estimates are regressed
  against environmental characteristics

• In this setting over stated observations are a
  problem in the first stage, but both overstated
  and understated observations are a problem in the
  second stage

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An Outlier Detection Methodology with
Consideration for an Inefficient Frontier

• A proposed improvement on the current method
  requires an outlier methodology
• First, identify outliers relative to both the
  efficient and inefficient frontier
• Use a two-stage DEA method where DEA estimates
  are calculated in the first stage and regressed
  against environmental variables in the second
  stage

• Use bootstrapping in the second stage to deal
  with the problem of correlation among the error
  terms

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Outlier Detection

• As suggested by Simar 2003 an outlier needs to be
  identified by both an input and an output
  oriented detection method

• If the hyperbolic distance function is used to
  measure the extent to which an observation is
  dissimilar to the rest of the observations only a
  single program needs to solved

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Hyperbolic Orientation
Seiford, L.M. and J. Zhu, Infeasibility of
super-efficiency data envelopment analysis
models. Infor, 1999. 37(2) p. 174-187
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Hyperbolic Orientation
output
e
d
c
b
a
input
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Hyperbolic Orientation

• Given all data are positive, allows super
  efficiency measure to be calculated
• Not only has application in outlier detection,
  but is also important in measuring technical
  progress via the Malmquist index

• Allows efficiency to be calculated even when data
  are not all positive

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An Outlier Detection Methodology with
Consideration for an Inefficient Frontier
output
input
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Iterative Outlier Detection

• Identify outliers based on hyperbolic orientation
  detection method
• Remove identified outliers
• Rerun outlier detection method

• Continue for the number of outlier detected is
  below some limit or for a set number of iterations

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Results of Outlier DetectionLarge Sample
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Results of Outlier DetectionSmall Sample
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Results of Outlier DetectionCritical Value

• For the iDEAs data set a critical value of 7.1 is
  necessary to keep 80 of the observations for a
  3x5 model

• For the industry specific data set a critical
  value of 5.6 is necessary to keep 80 of the
  observations for a 3x5 model

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Benefits of a New Outlier Detection Method

• Developed a method to identify overly inefficient
  observations by identifying an inefficient
  frontier
• Recommend a hyperbolic orientation to avoid
  infeasibility issues
• Implemented the iterative outlier detection method

• Demonstrated this method on both a large and
  small data set to show how the results might be
  used to investigate the quality of the match
  between the method and available data or model

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Pastors Model Specification

• This model requires specifying a minimum
  percentage of observations whose value change by
  a minimum amount. If a smaller percentage of
  observations change the input or output under
  analysis should be removed
• For the values of (10, 10) the initial Hackman
  model of warehousing is reduced from 5 outputs to
  3 outputs and inputs remained at 3

Pastor, J.T., J.L. Ruiz, and I. Sirvent, A
statistical test for nested radial DEA models.
Operations Research, 2002. 50(4) p. 728-735.
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Bootstrapping method for the second stage of the
two-stage DEA method

• Necessary because of the correlation among error
  terms in the second stage regression

• Sample n observations, call this set b, with
  replacement from the set of input/output data
• Calculate efficiency estimates for each of the
  original n observations relative to the set b
• Repeat these two steps 2000 times, construct
  confidence intervals and bias estimates for each
  of the original n obs.

Simar, L. and P.W. Wilson, Estimation and
inference in two-stage, semi-parametric models of
production processes. Journal of Econometrics,
2005. Forthcoming
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Small Sample Issue

• The appropriate model is multi-input /
  multi-output,
• due to lack of homogenous reference units or the
  proprietary nature of data, sample is small

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A Quantile-based Approach

• Use Shephards distance function to aggregate
  input information
• Identify input distance function
• Use it as the dependent variable in a translog
  regression equation
• Run the full regression model and calculate the
  quantile statistics for each observation

Lovell, C.A.K., et al., Resources and
functioning A new view of inequality in
Australia, in Models and Measurement of Welfare
Inequality, W. Eichorn, Editor. 1993, Springer
Verlag Griffin, P.M. and P.H. Kvam, A
quantile-based approach for relative efficiency
measurement. Managerial and Decision Economics,
1999. 20 p. 403-410
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MQBA Efficiency
Output
Regression line based on all observations except
e
Frontier
Deleted residual value for e
e
Input
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Quantile Results
DEA Efficiency
DEA Rank
Quantile Efficiency
Quantile Rank
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MQBA Contribution

• Benefits
• This method can be used when a relatively small
  number of observations available
• The level of inputs and outputs determines the
  ordering of observations
• Does not require assumptions about the efficient
  frontier

• Shortcomings
• Only produces an ordering, not absolute
  efficiency

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iDEAs Results

• Increase efficiency
• Inventory turns
• Decrease efficiency
• Temporary labor percentage
• Total Replenishments
• Inventory ()
• Sku span
• Sku churn

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Industry Study Results

• Increase efficiency
• Inventory accuracy
• Size
• Decrease efficiency
• Locations per sku

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Consistent In Both Studies

• Increase efficiency
• Cross-docking
• Decrease efficiency
• Seasonality

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Summary

• Developed a new outlier detection methodology for
  application to the two-stage method with distinct
  advantages over the previous method
• Introduced the hyperbolic orientation to the
  super efficiency DEA model. Showed the benefit
  of this orientation in an outlier detection
  context.

• Developed an efficiency ordering method based on
  the deleted residual technique for multi-input /
  multi-output models

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Thank You