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Int. J. Production Economics ] (]]]]) ]]]– ]]]

Evaluating the efficiency of 3PL logistics operations

Amer HamdanÃ, K.J. (Jamie) Rogers1

Industrial and Manufacturing Systems Engineering Department, Box 19017,

The University of Texas at Arlington, Arlington, TX 76019, USA

Received 2 April 2006; accepted 18 May 2007

Abstract

This paper introduces data envelopment analysis (DEA) as a tool to evaluate the efficiency of a group of third-party

logistics (3PL) warehouse logistics operations. DEA is a linear programming technique used to evaluate the efficiency of

decision-making units (DMUs) where multiple inputs and outputs are involved. The paper starts with a general review of

the DEA models and basic definitions, and then provides a review of warehousing functions and performance measures.

First, a basic (unrestricted) DEA model is applied to a group of homogeneous warehouses that have similar inputs and

outputs. Then, a revised (restricted) DEA model with additional constraints is presented; the revised model incorporates

weight restrictions and value judgment. The relative efficiency scores for the warehouses used in the study were analyzed

before and after the use of weight restrictions. As a result, we were able to determine the impact of each input and output

on the efficiency of each warehouse, and also, we were able to examine specific warehouse characteristics and develop a set

of recommendations for assisting managers and engineers in the improvement and design of more efficient operations.

r 2007 Elsevier B.V. All rights reserved.

Keywords: 3PL; Warehousing; Logistics performance; DEA

1. Introduction

In this research, a new warehouse efficiency

model is presented to evaluate the overall efficiency

of a group of third-party logistics (3PL)-operated

warehouses at the enterprise level where multiple

inputs and multiple outputs are involved. Thismodel is developed using data envelopment analysis

(DEA) as a multi-factor productivity model for

measuring the relative efficiencies of a homogeneous

set of decision-making units (DMUs), or in this

case, the set of warehouses used in the study, where

the relative efficiency score of each warehouse is

calculated in the presence of multiple inputs and

multiple outputs. The new model that was devel-

oped from the basic (unrestricted) DEA model

originally presented by Cooper et al. (2000)

incorporates (through additional constraints to theoriginal model) strategic thinking that stems from

the organization’s goals and objectives as well as

expert opinion. In a related study by Hackman et al.

(2001), the authors offered a DEA model that

examines specific characteristics of warehouses;

although the study provided valuable characteristics

of warehouses, it used warehouse data for a wide

range of products that included auto parts, electro-

nics, fine paper, mail order apparel, photographic

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0925-5273/$- see front matterr 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.ijpe.2007.05.019

ÃCorresponding author. Tel.: +1 817 375 5744.

E-mail addresses: [email protected] (A. Hamdan),

[email protected] (K.J. (Jamie) Rogers).1Tel.: +1817 2722495.

Please cite this article as: Hamdan, A., (Jamie) Rogers, K.J., Evaluating the efficiency of 3PL logistics operations. International Journal

of Production Economics (2007), doi:10.1016/j.ijpe.2007.05.019

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supplies, and other products. This wide range of

products indicate that these warehouses have

different processes and handling techniques and

equipment, whereas one of the basic requirements

of DEA models is to ensure that all DMUs are to be

homogeneous.

2. Warehousing

A warehouse is a location where a firm stores or

holds raw materials, semi-finished goods, or finished

goods for a varying length of time (Keebler and

Durtsche, 2001). The core processes for the ware-

houses used in this study include all inbound,

outbound, and inventory control activities. These

are as follows:

1. Receiving: A set of inbound activities that startwith unloading goods and materials on the

receiving dock, staging, and checking and ver-

ification of materials’ quality and quantity.

2. Put-away: The physical and logical movement of

materials to designated storage locations.

3. Picking: The disbursement of materials from

storage location or picking location to fill

customer orders.

4. Packing: Packaging, pricing, labeling, scanning

individual items or cartons, and other customer

instructions.5. Shipping: Staging materials on the shipping dock

for verification of order quantity, visible damage,

order/invoice accuracy, and loading materials on

the designated truck.

6. Other processes: Cycle counting, physical inven-

tory, and value-added services (VAS) (Hamdan

and Rogers, 2004; Schefczyk, 1993).

3. Measuring performance

According to Keebler and Durtsche (2001), in the

case of logistics performance measurement, five

recent studies published by the Council of Supply

Chain Management Professionals (CSCMP), for-

merly known as the Council of Logistics Manage-

ment (CLM), indicate that most firms do not

comprehensively measure logistics performance,

and even the best-performing firms fail to realize

their productivity and service potential available

from logistics performance measurement. In addi-

tion, logistics competency will increasingly be

viewed as a competitive differentiator and a key

strategic resource for the firm.

Traditionally, warehouse performance measures

were mostly financial measures such as the total cost

per order, warehousing cost per unit, etc. While

these bottom-line measures may be considered inmany cases as good indicators of whether or not

logistics strategy is being properly implemented and

executed, they do not improve the performance of a

process, and they are usually captured and tracked

at high levels without providing visibility to those

who are accountable for the process. Non-financial

measures, on the other hand, such as inventory

accuracy, order fill rate, and space utilization rate,

are tangible measures that are driven by the

organization’s vision and goals. Non-financial

measures include customer satisfaction, quality,

flexibility, and productivity.

4. DEA

In 1978, Charnes et al. demonstrated fractional

programming techniques as an extension to Ferrell’s

(1957) single productivity efficiency measure to

solve multiple input and multiple output problems.

This technique is called DEA. DEA is a non-

parametric linear programming technique used for

the evaluation of DMUs when multiple inputs and

multiple outputs are involved. DEA identifies the‘‘best’’-performing or the most efficient DMU and

measures the efficiency of other units based on the

deviation from the efficient DMU.

DEA is also defined as a quantitative technique

that derives the utilization efficiency of a specific

unit’s use of inputs (resources such as labor hours,

space, and materials) relative to specified outputs. It

computes, through iterative processes, the ‘‘effi-

ciency score’’ of each unit evaluated. It also ranks

and compares each unit’s performance relative to

the other units, where each DMU represents an

entity with multiple inputs and multiple outputs.

DMUs may include hospitals, banks, libraries,

universities, and other profit and non-profit orga-

nizations. Generically each DMU is regarded as the

entity responsible for converting inputs into outputs

and whose performances are to be evaluated.

The CCR (Charnes, Cooper, Rhodes) model is

originally a fractional programming problem solved

to obtain values for weighted inputs vi (i ¼ 1, 2ym)

and weighted outputs ur (r ¼ 1, 2y s). The objective

here is to obtain weights (vi ) and (ui ) that maximize

the ratio of DMUo being evaluated, while satisfying

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the inputs vs. outputs ratio constraints, which

should not exceed 1.

Let the DMUj to be evaluated on any trial

designated as DMUo (where o ¼ 1, 2yn), and then

this model is presented as follows:

ðFPoÞ Maxy ¼ u1y1o þ u2y2o þ Á Á Á þ usyso

v1x1o þ v2x2o þ Á Á Á þ vmxmo

¼P

ruryroPi vi xio

subject tou1y1j þ Á ÁÁ þ usysj

v1x1j þ Á ÁÁ þ vmxmj

p

Pruryrj Pi vi xij

p1 for j ¼ 1 . . . n,

v1; v2 . . . vmX0 for i ¼ 1 . . . m;

u1; u2 . . . usX0 for r ¼ 1 . . . s;

where y is the objective function value that

maximizes the ratio of DMUo, which is also called

the ‘‘relative efficiency score’’, vi the weight for inputI , ur the weight for output r, xio the value for input x

of DMUo and yro the value for output y of DMUo.

This fractional program (FPo) is then replaced by

the following linear program (LPo):

ðLPoÞ Maxy ¼X

r

uryro

subject toX

i

vi xio ¼ 1.

Pr

uryrj

ÀPi

vi xij p0 for j ¼ 1 . . . n;

vi X0; urX0; for i ¼ 1 . . . m;

for r ¼ 1 . . . s:

In order to obtain the relative efficiency scores,

y*, this linear program must run n times, and the

optimal solution of the above linear program (LPo)

is represented by (y*, v*, u*), where v* and u* are

the optimal weights for each DMU, and y* is the

relative efficiency score of the DMUs.

DMUo is called CCR-efficient if y* ¼ 1 and there

exist at least one optimal solution (v*, u*), with

v*X0 and u*X0. Otherwise, DMUo is CCR-

inefficient. Thus, there are two possibilities for

CCR-inefficiency: (a) y*o1 or (b) y* ¼ 1 and at

least one element of (v*, u*) equals zero for every

optimal solution of (LPo). For more details on DEA

theory and applications, refer to Cooper et al.

(2000).

In a parallel effort, McGinnis et al. (2002)

developed an Internet-based DEA system (iDEA)

by creating a database for warehouses, where, for

every warehouse in the database, information is

recorded about the resources used (space, labor, and

inventory) and the services produced (items picked

in terms of lines, broken case, full case, and pallet).

The primary goal of this effort is to allow ware-

house managers to make a quick assessment of their

warehouse operations and to compare their effi-

ciency with a large set of other warehouses(McGinnis et al., 2005).

5. Data

The data used in this paper were collected for a

homogeneous set of 19 warehouses operated by a

3PL provider in the US during the year of 2004. The

selected warehouses have common processes, simi-

lar products of consumer electronics and telecom-

munication equipment, and similar inputs and

outputs. Four common inputs and three commonoutputs for all warehouses were used in this study.

The selection of the inputs and outputs is based on

the significance of the resources (inputs) and the

company’s strategic objectives to increase revenue

and raise service levels of the operations. Since the

primary objective of DEA is to make an overall

assessment of the efficiency of DMUs, and since

each DMU’s efficiency is driven by its inputs and

outputs, it is critical to select the most representative

and meaningful inputs and outputs. The set of input

and output data used in this study are outlined in

Sections 5.1 and 5.2. Each input and output musthave a defined unit of measure (UOM) that is

meaningful and measurable. In our case, the UOM

used for each input is listed in Table 1.

5.1. Inputs

1. Labor hours: The total annual man-hours for all

direct full-time employees (FTEs) who are

directly involved in all of the inbound and

outbound warehouse activities; these inbound

activities include unloading and receiving pro-

ducts into the warehouse storage locations, and

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Table 1

Inputs’ unit of measure

Input Unit of measure

Labor Total annual man-hours

Space Total warehouse square feet

Technology Total annual cost of technology

MHE Total annual cost of MHE

MHE: materials handling equipment.

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outbound activities include all activities involved

in picking, packing, and shipping products to

specific customers. The total number of man-

hours used in this study also includes over-time

hours converted into equivalent regular hours.2. Warehouse space: Total warehouse space used for

receiving, storage, staging, order consolidation,

shipping, aisles, MHE staging, and offices.

Table 2 shows a summary of the average floor

space allocated by functional area as a percen-

tage of the total warehouse space.

Warehouse space is mostly interpreted as the

total warehouse floor area in total square feet. In

this research, we also examined the impact of the

warehouse cubic space on the relative efficiency

score; thus, we are considering the height of thewarehouse as a major input in the evaluation

processes. Former studies in this area have

neglected the height of a warehouse, assuming

that it has no significant impact on the overall

efficiency rating.

3. Technology investment: The total annual cost of

technology development that supports each

warehouse operation. This cost includes all

startup technology costs and annual recurring

costs, and it is detailed in the following cate-

gories:

Hardware: Radio frequency (RF) equipment,

computers, printers, servers.

Software license fees.

Infrastructure installation.

Integration of warehouse management system

(WMS) and support applications.

Testing and training.

Project management for system development

and implementation.

4. Materials handling equipment (MHE): The total

annual cost of materials handling equipment

used to handle product within the warehouse.

The type of MHE varies slightly by the type and

configuration of the products handled in each

warehouse. Most of the warehouses use a

combination of non-powered and powered con-

veyors, counterbalance forklifts, swing-reach

trucks, electrical order pickers, electrical pallet

trucks, and manual pallet trucks. Table 3

summarizes the input data for the 19 DMUs

used in this study.

5.2. Outputs

Shipping volume: Warehouse volume is usually

measured as units, boxes, pallets, or other mean-

ingful units of measure. In Table 4, the number of

boxes represents the number of boxes shipped in

2004 from each warehouse, based on the equivalent

conversion factor applied for each warehouse to

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Table 2

Warehouse space allocation

Area % Space

Storage space 51

Encumbrances (staging, aisles, and MHE) 37

Office space 5

Facilites (restrooms and breakroom) 3

Value-added services 4

Total warehouse space 100

Table 3

Summary of warehouse inputs

Warehouse

(CCR)

(I)

Labor

(I)

Space

(I)

Technology

(I) MHE

W1 122,720 556,000 903,000 226,800

W2 62,400 225,000 590,000 113,400

W3 91,520 347,000 650,000 162,000

W4 204,160 108,000 512,000 194,400

W5 167,040 200,000 463,000 145,800

W6 343,200 400,000 924,000 1,123,600

W7 74,880 192,177 132,000 121,500

W8 68,640 85,000 455,000 81,000

W9 37,440 60,000 325,000 56,700

W10 39,520 200,000 287,000 81,000

W11 37,440 110,000 180,000 64,800

W12 41,600 70,000 216,000 56,700

W13 151,840 358,152 383,000 113,400

W14 145,600 102,344 409,000 72,900

W15 104,000 208,145 250,000 97,200W16 70,720 80,000 125,000 32,400

W17 276,640 218,000 916,000 318,700

W18 245,440 400,000 436,000 97,200

W19 224,640 204,556 498,000 340,100

Table 4

Outputs unit of measure

Output Unit of measure

Throughput Total annual boxes shippedOrder fill Total annual boxes filled (for complete orders)

Space utilization Total cubic feet utilized






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obtain the equivalent standard cubic volume per

box (6.2 cubic ft/box).

1. Order filling: defined as the total number of

orders filled completely and on time. The ‘‘order

filling’’ data provided in Table 4 is based on thetotal number of boxes associated with the orders

that were filled complete.

2. Space utilization: calculated as the total product

cubic displacement divided by the total ware-

house cubic space. In our model, we decided to

calculate space utilization using three dimensions

instead of two in order to examine the impact of

warehouse height on its efficiency. It is important

to note here that warehouse space is considered

as a resource (input), and it is actually one of our

inputs used in this study; however, we are also

interested in evaluating the utilization of ware-house space (total cubic space utilized). The

output data for the 19 DMUs are provided in

Table 5.

5.3. Input– output assumptions

Input-oriented DEA model : We used the input-

oriented CCR-I model since the inputs are more

controllable than outputs used in this model;

input-oriented models aim at reducing the input

amounts by at least the present output levels.

Constant returns (CR) to scale: The assumption

of CR to scale is based on the scalability of inputs

and outputs of the selected DMUs; under CR to

scale assumption, if we scale the input levels of a

feasible input–output correspondence up or

down then another feasible input–output corre-spondence is obtained in which the output levels

are scaled by the same factor as the input levels.

For the different types of model orientation and

return to scale assumptions, see Cooper et al.

(2000) and Thanassoulis (2001).

6. DEA model results

In Table 6, a summary of the DEA-solver results

show each warehouse with its overall efficiency

score and rank. DMUo is called CCR-efficient if itsefficiency score y* ¼ 1 and there exists at least one

optimal (v*, u*), with v*X0 and u*X0. Otherwise,

DMUo is CCR-inefficient (Cooper et al., 2000). The

efficient warehouses are listed as W7, W10, W11,

W12, W13, and W18, while all other warehouses in

the group are deemed inefficient since their effi-

ciency score is below 1.

The results of the DEA model seem to be realistic

when compared with the general current perfor-

mance assessment used by the company. This

assessment is mostly based on a set of key

ARTICLE IN PRESS

Table 5

Summary of warehouse outputs

Warehouse

(CCR)

(O) Boxes (O) OrderFill (O) CFT Utlz

W1 1,490,820 1,481,875 11,564,800

W2 2,305,338 2,300,728 4,725,000

W3 1,811,927 1,802,868 7,328,640

W4 1,225,514 1,164,238 2,499,120

W5 1,139,700 1,138,560 5,100,000

W6 2,307,875 2,277,873 9,216,000W7 4,160,000 4,151,680 4,520,003

W8 1,222,000 1,197,560 2,023,000

W9 702,000 694,980 1,314,000

W10 1,313,270 1,301,451 5,600,000

W11 432,000 429,408 3,168,000

W12 737,100 727,518 1,926,400

W13 609,550 599,797 9,036,175

W14 683,645 679,543 2,378,475

W15 541,660 537,868 4,745,706

W16 605,834 594,323 1,651,200

W17 937,650 846,698 5,232,000

W18 758,160 744,513 9,968,000

W19 883,872 873,266 4,639,330

Table 6

CCR-Iresults

No. DMU Score Rank

1 W1 0.742521 19

2 W2 0.802969 16

3 W3 0.754892 18

4 W4 0.869497 9

5 W5 0.900334 8

6 W6 0.817374 157 W7 1 1

8 W8 0.92539 7

9 W9 0.833945 12

10 W10 1 1

11 W11 1 1

12 W12 1 1

13 W13 1 1

14 W14 0.830694 13

15 W15 0.858018 10

16 W16 0.818223 14

17 W17 0.840078 11

18 W18 1 1

19 W19 0.795554 17






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performance indicators (KPIs); these KPIs include

financial and operational performance measures for

each warehouse. At least four of the six CCR-

efficient warehouses (W7, W10, W13, and W12) are

known to be among the best performers not only in

the set of warehouses included in the study, but alsoin the broad list of warehouses currently operated

by company. Other warehouses, such as W1 and

W8, although they were not efficient in our results,

are considered ‘‘best performers’’ by the company.

Further investigation of the slack and surplus

variables for W1 and W8 indicates that both

warehouses were penalized by the DEA model;

W1 was penalized for the high cost of technology

and low throughput volume, while W8 was pena-

lized for the high cost of technology and excess

labor hours. From the standpoint of efficiency, it

seems reasonable that a firm should be penalized forinvesting in technology but failing to reap the

benefits.

These results are a typical situation in DEA since

no restriction is placed on the weights of inputs and

outputs other than the non-negativity constraints

on the components of the multiplier vectors v and u.

Thus, by imposing additional constraints on the

basic DEA model, we can obtain an improved DEA

model that takes into account specific information

that reflects the significance (importance) of specific

inputs and outputs. In Section 7, we show how theseconstraints are developed and applied to the basic

(unrestricted) DEA model.

7. Incorporating strategic thinking into DEA models

So far, we have used the basic (unrestricted) DEA

CCR model as originally presented by Charnes et al.

(1978). The unrestricted DEA model allows each

DMU to choose the weights of its inputs and

outputs in order to maximize its efficiency with

respect to the others. Since the unrestricted DEA

models allow complete flexibility in choosing the

weights for each input and output, the model will

often assign unreasonably low or unreasonably high

weights (multipliers) in the process of trying to drive

the relative efficiency scores (Charnes et al., 1978).

Many researchers argued that DEA allows too great

a flexibility in the determination of the weights on

inputs and outputs when assessing the relative

efficiency of a DMU. This can lead to some DMUs

being assessed only on a small subset of their inputs

and outputs, while their remaining inputs and

outputs are all but ignored (Thanassoulis and

Dyson, 1988).

Although the flexible DEA model restricts all

weights to be positive and does not allow for any

input or output to have a zero weight value, the

lowest weight allowed, e, is so small that for allpractical purposes an input or output can be

ignored in the assessment (Thanassoulis and Dyson,

1988). According to Golany (1988), in practical

situations some inputs and outputs may be more

fundamental and important than others to the

DMU being assessed. For example, in a logistics

operation, service level is more important than

space utilization of the warehouse. Thus, imposing

weight bounds in DEA ensures that the most

important inputs and outputs are attached higher

weights than the less important ones.

Although imposing weight restrictions on theDEA model is suggested by many researchers, one

must be careful when setting weights since setting

severe bounds on a subset of weights may lead to an

infeasible program (Ray, 2004). Some degree of

flexibility is desirable, since variation in factor

weights may reflect different circumstances and

different objectives of the DMUs being assessed;

at the same time, total flexibility can disguise serious

inefficiencies in some DMUs (Chaparro et al.,

1997).

The methodology for incorporating weight re-strictions in this research is based on information

derived from the organization’s mission and objec-

tives, as well as value judgment and expert opinion.

The input and output variables can be defined

within the performance measurement framework,

whilst the priorities and values of the mission and

objectives can inform the specification of weight

restrictions and targets (Allen et al., 1997). Fig. 1

ARTICLE IN PRESS

Unrestricted DEA

Model

Restricted DEA

Model

Organization’sObjectives

Constraints

Expert Opinion

Fig. 1. Strategic thinking in performance evaluation.






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illustrates the approach we developed in this

research to incorporate strategic thinking in DEA,

where the unrestricted DEA model is converted into

a restricted DEA model by imposing a set of new

constraints.

7.1. The restricted DEA model

According to Allen et al. (1997) and Sarkis (2000,

1997), value judgment can be incorporated in the

CCR model by applying weight restrictions. These

weight restrictions are detailed in three approaches

as follows:

(1) Direct restrictions on the weights of some or all

of the inputs and outputs.

(2) Adjusting the observed inputs and/or outputslevel.

(3) Restricting the virtual inputs and outputs.

We apply the first approach (direct restrictions on

the weights) as the basis for applying additional

restrictions on the weights of inputs and outputs.

These direct restrictions can be applied in two ways:

(a) Absolute restrictions: involves adding additional

constraints to the existing DEA model, which

impose upper and lower limits on the weights of the inputs and outputs by imposing lower and

upper bounds on the weights in the form

di pvi pti ,

rrpurpZr.

(b) Assurance regions (AR): this approach of AR

was first introduced by Thompson et al. (1986),

and was applied for choosing the ‘‘best site’’ for

the location of a high-energy physics laboratory

(Ray, 2004). It was developed to deal with the

issues and concerns of the optimal weights of

the DEA model for inefficient DMUs, where we

may see many zerosshowing that the DMU

has weakness in the corresponding items com-

pared with other efficient DMUs (Cooper et al.,

2000). As the name implies, AR limit the

region of weights to some special area. As a

result of imposing additional constraints on the

DEA model, the revised DEA model usually

produces lower efficiency scores and fewer

efficient DMUs than the basic (unrestricted)

DEA model. The constraints added under this

approach take the following form (Allen et al.,

1997):

c1pvi

vi þ1

pc2,

where 0oc1oc2 for i ¼ 1 . . . m,

(c) and

d 1pur

urþ1

pd 2,

where 0od 1od 2 for r ¼ 1 . . . s.

These additional constraints will be determined

using a heuristic approach that incorporates strate-

gic thinking and expert opinions. In this study, a

group of senior managers and business unit owners

provided expert opinion on all inputs and outputsused in the model. The participants included

warehouse managers, senior warehouse managers,

engineers, directors of operations, and vice pre-

sidents. Each participant was asked to rate each

input and output on a scale from 1 to 10, with 1

being the least important and 10 being the most

important. The collected data were then analyzed to

derive the lower and upper bounds for the

constraints added to the unrestricted DEA model.

Our approach to derive the lower and upper limits

can be summarized in the following steps:

1. Twenty-five experts provided rating (on a scale

from 1 to 10) for each of the four inputs and the

three outputs used in the model.

2. A 4 Â 25 matrix was compiled to include ratings

for the four inputs, and a 3 Â 25 matrix was

compiled to include ratings for the three outputs

used in the model.

3. A 6 Â 25 matrix was constructed for the pairwise

comparisons of inputs, and a 3 Â 25 matrix was

constructed for the pairwise comparisons of

outputs, based on the total number of pairwise

comparisons of (n2– n)/2. (Example: v1/v2 repre-

sents a pairwise comparison of input1 and

input2, and u1/u2 represents the pairwise compar-

ison of output1 and output2.)

4. For each matrix (obtained in step 3), the

minimum and maximum ratios of each row were

selected as the lower and upper bounds, respec-

tively.

5. The minimum and maximum ratios (calculated in

step 4) are used to represent the lower and upper

bounds of the constraints to be imposed on the

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unrestricted DEA model based on Thompson

et al.’s (1986) AR concept.

For our study in the restricted DEA model, the

following set of constraints (1)–(3) is added:

0:21p v1

v2

p4:89, (1)

0:18pv1

v4

p3:93, (2)

0:11pu1

u3p5:65. (3)

In these constraints vi and ur refer to weight for

input i and weight for output r, respectively. To

interpret these constraints, take (1) for example: the

ratio of weights of ‘‘labor input’’ vs. ‘‘space input’’

is not less than 0.21 and not greater than 4.89

(Cooper et al., 2000).

7.2. Solution of the restricted DEA model

The results of the restricted DEA model (see

Table 7) show that the total number of CCR-

efficient DMUs has been reduced from 6 to 4, and in

general, all other efficiency scores were also reduced

to a certain degree as a result of the imposed

constraints (see Fig. 2). The list of optimal (CCR-

efficient) warehouses includes W7, W10, W13, and

W18, whereas W11 and W12 are now considered

CCR-inefficient. The overall score average was also

reduced from 0.88 to 0.81. The reduction in the

efficiency scores is expected and is consistent with

previous findings (Cooper et al., 2000; Thompson

et al., 1986).When we investigated the reasons as to why W11

and W12 became CCR-inefficient under the new

restricted DEA model, we can conclude that, under

the new restrictions, both warehouses (W11 and

W12) suffered from having high labor hours

compared with their peers (W10 and W7, respec-

tively). In addition, W11 is now showing slack

(shortage) in ‘‘throughput volume’’ and ‘‘orders

filled’’, where as W12 is showing surplus (excess) in

‘‘technology cost’’.

DEA is also used to identify DMUs that require

further investigation and attention. If a DMU isefficient, then additional investigation reveals the

reasons behind its success and thus becomes a

model for other DMUs. And if a DMU is deemed

inefficient then further investigation is necessary to

identify opportunities for potential improvement.

The relative efficiency scores are not just index

numbers to indicate whether a DMU is efficient or

not (Bowlin, 1998); since the relative efficiency

scores are actually the objective function value y* of

a DMUo, the inefficiency for DMUo is 1Ày*, which

makes it possible (by performing sensitivity analy-sis) to identify the sources and amounts of

inefficiency in each input and output for every

DMUs. Let us take W8 as an example, with

y* ¼ 0.84, and inefficiency (1y*) of 0.16, we can

see an opportunity for improvement that forces W8

to become efficient. The sensitivity analysis shows

that there is excess amount in all inputs used by W8.

In other words, W8 will become efficient if we

reduce its labor hours by 64.1%, warehouse space

by 6.3%, technology cost by 62.5%, and MHE cost

by 47.1%.

The results of the DEA model also provide useful

information for each DMU; this includes reference

set (the peer group for each DMU), relative

efficiency scores for each DMU, optimal weights

of inputs and outputs, statistics on data and results,

projections of each DMU onto the efficient frontier,

input excesses and output shortfalls, and graphical

representation.

When we performed sensitivity analysis and

detailed investigation of the results of both models

(the unrestricted and the restricted DEA models),

we were also able to examine and understand

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Table 7

Results of the restricted DEA model

No. DMU Score Rank

1 W1 0.731000 13

2 W2 0.802632 9

3 W3 0.745905 12

4 W4 0.643454 19

5 W5 0.796486 10

6 W6 0.662183 177 W7 1 1

8 W8 0.839998 7

9 W9 0.780593 11

10 W10 1 1

11 W11 0.981106 5

12 W12 0.942871 6

13 W13 1 1

14 W14 0.672894 16

15 W15 0.813998 8

16 W16 0.729014 14

17 W17 0.674016 15

18 W18 1 1

19 W19 0.649951 18






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specific warehouse issues and characteristics that are

now summarized:

(1) Bulk vs. rack storage: When we compared the

performance of warehouses that use bulk

storage of full pallets (where the product is

mostly palletized and floor stacked) as the main

storage media vs. those that use racking or othertypes of storage media for full pallet storage, it

appears that warehouses that use ‘‘bulk storage’’

are generally more efficient than other ware-

houses using other storage media such as

traditional or selective racking.

(2) Narrow aisles vs. wide aisles: The analysis of the

results indicates that warehouse storage layout

has a direct impact on efficiency, especially when

comparing the efficiency of warehouses using

wide storage aisles or narrow storage aisles

(where a storage aisle is defined as the space

between two rows of racks. There are three types

of aisles: 9–12 ft wide aisles, 6–9 ft narrow aisle,

and 4–6 ft very narrow aisles). Each type of

storage layout (and aisle width) requires a

specific type of materials handling equipment,

and accordingly is subject to various levels of

productivity and speed. As a result, warehouses

that use wide aisles are generally more efficient

than those that use narrow aisles.

(3) RF vs. manual receiving and shipping: According

to the results, using RF does not always add

efficiency to an operation. In some cases, using

RF equipment for receiving, picking, and

shipping results in increased cycle time and

lower productivity levels when compared with

similar warehouse without RF equipment.

(4) Warehouse size and efficiency: The results also

indicate that small warehouses are more efficient

than large warehouses. This is also consistent

with previous findings by Hollingsworth (1995)

and Hackman et al. (2001).

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0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

Efficiency Sco

re

W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15 W16 W17 W18 W19

Unrestricted Restricted

Fig. 2. Efficiency scores of the unrestricted and restricted DEA models.

Table 8

Deriving specific warehouse characteristics

Average efficiency score

Storage

Bulk storage 0.903

Rack storage 0.866

Layout

Wide aisles 0.902

Narrow aisles 0.872

Very narrow aisles 0.806

RF processing

RF 0.866

Manual 0.922

Warehouse size

Below 300,000 ft2 0.891

Above 300,000 ft2 0.863






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In Table 8, we provide a summary of the analysis

used to investigate these specific warehouse char-

acteristics and issues. Our approach uses the

average efficiency score (of the warehouses that

belong to the same category) obtained from the

unrestricted DEA model as the basis for evaluation.However, using the restricted model as a basis

should also provide similar results. For example, the

average efficiency score of all warehouses that use

bulk storage is calculated (0.903) and compared

with the average efficiency score of the warehouses

that use non-bulk or rack storage (0.866), where a

higher score means higher efficiency.

8. Conclusions

In this paper, we used data envelopment analysis(DEA) for evaluating a set of 19 homogeneous

warehouses operated by a third-party logistics (3PL)

company; all warehouses use similar processes and

handle similar products with common inputs and

outputs. Four inputs and three outputs were

selected for the study where each input and output

is associated with a specific unit of measure. Using

the input-oriented CCR DEA-solver by Cooper et

al. (2000), we solved an unrestricted DEA model,

and then we incorporated strategic thinking and

expert opinion to develop and solve a ‘‘restricted

DEA model’’. The restricted DEA model was a

result of additional constraints derived from the

company’s objectives and expert opinion. The

results of the model were also validated and

compared with the company’s current performance

assessment tools through a set of specific key

performance indicators (KPIs).

We found that this technique provided significant

insights for managers and supported their initial

impressions of expected performance of their ware-

houses. It also provided some opportunity to

further benchmark and investigate contributionsto efficiency within each of these warehouses. Thus,

practical usefulness and application of DEA can

also be targeted toward continuous improvement

projects.

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