European Real Estate Society (ERES) 22nd Annual Conference
Istanbul, 27th June 2015
Dr. Alexandra Bay
Senior Researcher, Wincasa AG
Efficiency measurement of
Swiss shopping centers using
Data Envelopment Analysis (DEA)
Master thesis – MAS UZH in Real Estate (2014)
2
Shopping center
ICSC / ULI Definition
� ‘A group of retail and other commercial establishments that is planned, developed,
owned and managed as a single property. On-site parking is provided. The center’s size
and orientation are generally determined by the market characteristics of the trade
area served by the center. The two main configurations of shopping centers are malls
and open-air strip centers’.
� ‘[…] defines a European shopping center as a retail property that is planned, built and
managed as a single entity, comprising units and “communal” areas, with a minimum
Gross Leasable Area (GLA) of 5’000 square metres (m2)’.
3
Shopping center
Classification
� Format: traditional, innovative, specialised ...
� Location: city center, urban quarter, suburban, greenfield
� Catchment area: neighbourhood center, community center, regional center,
super-regional center
� Accessibility: walking distance, car, public transport, parking lots …
� Size / sales area: GLA, NLA, ICSC classes (very large, large, medium, small) …
� Tenant: mono-category vs. multi-categories, fashion center, convenience center …
� Anchor: super market, fashion, media / electronic; one anchor vs. several anchors …
� Specialisation: retail park, urban entertainment center, factory-outlet center,
theme-oriented center, lifestyle center …
4
Productivity of shopping centers
Performance drivers
� Production function: a shopping center “produces” with several inputs several
different outputs
� Inputs
� Endogenous: sales area, parking lots, number of tenants, anchor, number of
employees, wages, marketing-mix, opening hours / days, etc.
� Exogenous: purchasing power, population, location, accessibility, competition,
demography, socio-economic characteristics, etc.
� Outputs
� Monetary: sales, profit, financial key figures, etc.
� Non-monetary: customer satisfaction / loyalty, service quality, etc.
� Productivity: performance measure � Ratio = ������
�����
5
Productivity of shopping centers
Performance measures
� Productivity: performance measure � Ratio = ������
�����
� Employee productivity � Ratio = ���
�� ���� ����
� Sales productivity � Ratio = ���
������
� Output: sales
� Input: sales area
� Examples with ONE input factor and ONE output factor
� Performance ≈ Efficiency ≈ Productivity
6
Efficiency measurement – sales productivity
Efficient frontier (DEA) vs. regression line
SC 1
SC 2
SC 3
SC 4
SC 5
SC 6
SC 7
SC 8
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
Sa
les
Sales area
Shopping Center Efficient fron er Regression line
7
Data Envelopment Analysis (DEA)
Definition
� ‘Data Envelopment Analysis (DEA) is a “data-oriented” approach for evaluating the
performance of a set of peer entities called Decision-Making Units (DMUs), which convert
multiple inputs into multiple outputs. The definition of a DMU is generic and flexible’.
(Cooper, Seiford, and Zhu (2011))
� ‘The name Data Envelopment Analysis, as used in DEA, comes from this property because
in mathematical parlance, such a frontier is said to “envelop” these points’.
(Cooper, Seiford, and Tone (2006))
� ‘DEA was designed to measure the relative efficiency where market prices are not available
[…]. Such previous DEA studies provide useful managerial information on improving the
performance. In particular, DEA is an excellent tool for improving the productivity of service
businesses […]’. (Zhu (2009))
DEA vs. regression analysis
8
DEA method – efficient frontier
� touches at least one point
� example: efficient point SC 2
� points, i.e. shopping centers, are
either on or below the efficient
frontier
� refers to the best DMU(s) / shopping
center(s) (best in class approach)
� Benchmark: point / shopping center
� example: SC 2
Regression analysis
� goes through the middle of all the
points / shopping centers
� there are shopping centers deviating
from the mean / average – upwards
or downwards
� refers to the average DMU / shopping
center; tendency to the mean
� Benchmark: average SC – built from
SC 2 and SC 6
� Benchmark: e.g. SC 3 or SC 8
9
DEA: theoretical framework / terminology
Charnes-Cooper-Rhodes-Model (CCR-Model)
� Output-to-input-ratio with several inputs and several outputs: ∑ ���������
∑ ���������
� DMU: n homogenous Decision Making Units (DMUs) with DMUj , j = 1, ... , n
� DMUs ≈ Shopping centers
� Inputs: m input factors; xij > 0 the amount / number of the input factor i, i = 1, ... , m used
by DMUj ; vi the weight of input factor i � weighted sum of inputs:
� Outputs: s output factors; yrj > 0 the amount / number of the output factor r, r = 1, ... , s
produced by DMUj ; ur the weight of output factor r � weighted sum of outputs:
10
CCR-Model
Optimisation problem – in words
� Output-to-input-ratio: ∑ ���������
∑ ���������
� Maximise the efficiency – the output-to-input-ratio – for the DMUo under the
constraint that:
� for all the DMUs: 0 ≤ output-to-input-ratio ≤ 1 (normalisation)
� all the weights vi and ur ≥ 0
� sequential processing of all the DMUs (o = 1, ... , n)
11
CCR-Model
Optimisation problem – fractional form
To be solved for each DMUo (o = 1, ... , n)
Output-oriented CCR-Model in the envelopment form
12
13
BCC- and Additive Models as extensions of the CCR-Model
� Charnes-Cooper-Rhodes-Model (CCR-Model, 1978)
� constant returns-to-scale assumption (CRS)
� input orientation OR output orientation
� Banker-Charnes-Cooper-Model (BCC-Model, 1984)
� variable returns-to-scale assumption (VRS)
� input orientation OR output orientation
� convexity constraint
� Additive Model (Charnes et al. (1985))
� convexity constraint
� input orientation AND output orientation
simultaneously
SC 1
SC 2
SC 3
SC 4
SC 5
SC 6
SC 7
SC 8
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9
Sa
les
Sales area
Shopping Center CCR: Efficient fron er
SC 1
SC 2
SC 3
SC 4
SC 5
SC 6
SC 7
SC 8
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9
Sa
les
Sales area
Shopping Center BCC: Efficient fron er
SC 1
SC 2
SC 3
SC 4
SC 5
SC 6
SC 7
SC 8
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
0 1 2 3 4 5 6 7 8 9
Sa
les
Sales area
Shopping Center ADD: Efficient fron er
Slack s-: Input-Reduc on of 2
Slack s+: Output-
Increase of 1
Point (3, 3)
DEA method
Pros – Cons
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Pros
� DEA simultaneously handles
multiple input factors and
multiple output factors in a
single aggregated efficiency measure
without prior fixing of the factor weights
� no assumptions regarding
� probability distribution
(� non-parametric)
� input-output-function
� best practice approach
� Operations Research based linear
programming approach
Cons
� extreme value method
� dependency on the selection of DMUs
� relative – not absolute – efficiency
� numerically challenging
15
DEA method
Summary
� Which DMUs are efficient and why?
� What are the sources of inefficiency?
� Which efficient DMU / combination of efficient DMUs should an inefficient DMU
compare to?
� What are the benchmarks / reference DMUs in a peer group comparison?
� Which factors do bear some potential for efficiency enhancement
(input reduction and / or output increase)?
16
Applications
� DMUs: Swiss (Wincasa) shopping centers (21)
� Set of factors (Wincasa data 2013)
� Inputs: sales area in 1 000 m2, number of parking lots, gross rent in Mio. CHF,
Occupancy Cost Ratio (OCR) in %, population (residents / employee) in 1 000
� Outputs: sales in Mio. CHF, sales productivity in 1 000 CHF / m2,
ratio 1/OCR = sales/gross rent
� DEA-Models: output-oriented CCR-Model (CCR-O), output-oriented BCC-Model
(BCC-O), Additive Model (ADD) – in the envelopment form
� Three cases: DEA versus sales productivity, ratios as factors, focus: gastronomy /
restaurants
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Results – Case 1
DEA vs. Sales
productivity
Output Output Output Output Output
1. Sales in Mio. CHF 1. Sales in Mio. CHF 1. Sales in Mio. CHF 1. Sales in Mio. CHF 1. Sales in Mio. CHF
Input Input Input Input Input
1. Sales area in 1'000 m2 1. Sales area in 1'000 m2 1. Sales area in 1'000 m2 1. Sales area in 1'000 m2 1. Sales area in 1'000 m2
2. Parking lots 2. Population in 1'000 2. Gross rent in Mio. CHF 2. OCR
CCR-O BCC-O CCR-O BCC-O CCR-O BCC-O CCR-O BCC-O CCR-O BCC-O Ratio
Shopping
Center (SC)
φ CCR φ BCC φ CCR φ BCC φ CCR φ BCC φ CCR φ BCC φ CCR φ BCC Sales
Productivity
SC 1 1.01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 7.4
SC 2 1.27 1.00 1.26 1.00 1.18 1.00 1.27 1.00 1.00 1.00 5.9
SC 3 4.56 3.08 4.56 3.05 4.56 3.08 3.86 3.07 4.56 3.08 1.6
SC 4 1.43 1.39 1.43 1.39 1.12 1.11 1.32 1.24 1.42 1.39 5.2
SC 5 1.56 1.56 1.56 1.56 1.56 1.56 1.48 1.46 1.55 1.54 4.8
SC 6 1.09 1.00 1.09 1.00 1.00 1.00 1.09 1.00 1.00 1.00 6.9
SC 7 1.14 1.00 1.14 1.00 1.06 1.00 1.00 1.00 1.14 1.00 6.6
SC 8 2.37 1.59 2.37 1.56 2.35 1.59 2.36 1.59 2.37 1.59 3.2
SC 9 1.35 1.18 1.35 1.18 1.31 1.18 1.26 1.18 1.35 1.18 5.6
SC 10 3.58 1.00 3.58 1.00 3.40 1.00 2.87 1.00 3.58 1.00 2.1
SC 11 2.94 1.10 2.94 1.00 2.78 1.10 2.28 1.00 2.94 1.00 2.5
SC 12 2.40 2.39 2.40 2.39 2.22 2.18 1.72 1.67 2.39 2.39 3.1
SC 13 2.22 2.06 2.21 1.73 1.11 1.00 1.53 1.36 2.22 2.06 3.4
SC 14 1.24 1.02 1.24 1.02 1.24 1.02 1.23 1.02 1.24 1.02 6.0
SC 15 2.71 2.61 2.71 2.61 2.70 2.54 2.29 2.26 2.71 2.61 2.8
SC 16 2.29 2.28 2.28 2.28 2.27 2.25 2.27 2.26 2.29 2.28 3.3
SC 17 2.82 2.81 2.81 2.81 2.80 2.73 2.11 2.05 2.82 2.81 2.7
SC 18 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 7.5
SC 19 1.37 1.27 1.37 1.27 1.26 1.26 1.37 1.27 1.36 1.27 5.5
SC 20 1.36 1.27 1.36 1.27 1.27 1.27 1.36 1.27 1.35 1.27 5.5
SC 21 2.06 1.89 2.04 1.00 2.06 1.89 2.05 1.89 2.06 1.89 3.6
DEA vs. Sales productivity (SP)
Analysis SP 1 Analysis SP 2 Analysis SP 3 Analysis SP 4 Analysis SP 5
18
Results – Case 2
Ratios as factors
� Shopping center manager: with focus on sales productivity (high), OCR (sustainable)
� Inputs: sales area, number of parking lots
� Outputs: sales productivity, 1/OCR
� Results:
� SC 18 is only BCC-efficient; SC 7 is CCR-efficient
� BCC-O with four factors adequately captures the performance drivers
� alternative to the simple performance measure “sales productivity”
� Advantage: more information in one performance measure
19
Results – Case 3
Focus: gastronomy / restaurants
� Success of a shopping center: tenant mix, third-place qualities � gastronomy
� Inputs: retail sales area, gastronomy sales area (variation: parking lots, population)
� Outputs: retail sales, gastronomy sales (variation: gastronomy 1/OCR, total 1/OCR)
� Results:
� shopping center sample too small
� results are not reliable
� Advantage: new approach of capturing the efficiency of the shopping center’s tenant mix
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Practical implications
Outlook
� Potential as a performance measurement, benchmarking, or rating tool; building a MIS
� Larger universe of input and output factors
� Larger shopping center universe
� Window analysis: efficiency changes over time
� Sensitivity analysis
� Stochastic DEA model: stochastic input and / or output factors
� Reverse optimization: optimal tenant mix
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Dr. Alexandra Bay
� Studies in Economics, Econometrics and Operations Research at the University of
Zurich
� PhD at University of Zurich „Multiperiod ALM-Models with CVaR-Minimisation for
Swiss Pension Funds” (2008)
� Master of Advanced Studies (MAS) UZH in Real Estate at the Department of Banking
and Finance – Center of Urban and Real Estate Management (CUREM); Thesis
„Efficiency measurement of Swiss shopping centers using Data Envelopment Analysis
(DEA)“ (2014)
� Since April 2015: Senior Researcher at Wincasa AG
2009 – 2015: Senior Investment Consultant at ECOFIN Investment Consulting AG
Before: Strategist at Swisscanto Asset Management AG, Research Assistant
at the Department of Operations Research of the University of Zurich and
actuary at Swiss Life
