Using DEA to improve the management of congestion in Chinese industries (1981–1997)

Socio-Economic Planning Sciences 35 (2001) 227–242

Using DEA to improve the management of congestionin Chinese industries (1981–1997)

W.W. Coopera,*, Honghui Denga, Bisheng Gua, Shanling Lib, R.M. Thrallc

aRed McCombs School of Business, University of Texas at Austin, Austin, TX 78712-1175, USAbFaculty of Management, McGill University, Montreal, Canada

cJones Graduate School of Administration, Rice University, Houston, TX, USA

Abstract

Congestion is said to be present when increases in inputs result in output reductions. An ‘‘iron rice bowl’’policy instituted in China shortly after the revolution led by Mao Tze Tung resulted in congestion thatultimately led to bankruptcy in the textile industry, and near bankruptcy in other industries. A major policyshift away from the ‘‘iron rice bowl policy’’ in 1990 led to massive layoffs and increasing social tensions.Were these massive layoffs necessary? Extensions of data envelopment analysis models effected in thepresent paper identified inefficiencies in the management of congestion. Using textiles and automobiles forillustration, it is shown how elimination of such managerial inefficiencies could have led to outputaugmentation without reducing employment. Thus, even in the presence of congestion, it proved to bepossible to identify additional (managerial) inefficiencies that provided opportunities for improvement. Inthe heavily congested textile industry, these output augmentations could have been accompanied byreductions in the amounts of capital used (as an added bonus). In any case, we show how to identify andevaluate new types of efficiencyFviz., the efficiency with which needed (or desired) inefficiencies aremanaged. r 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Efficiency; Congestion; Employment; Data envelopment analysis

1. Introduction

This study focuses on problems of congestion and how they might be treated in Chineseindustries. Following [1], we distinguish between congestion and other types of inefficiency via thefollowing definitions:

*Corresponding author. Tel.: +1-512-471-3322; fax: +1-512-471-0587.

E-mail address: [email protected] (W.W. Cooper).

0038-0121/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 3 8 - 0 1 2 1 ( 0 1 ) 0 0 0 0 5 - 2

Definition 1. Inefficiency (=technical inefficiency). Inefficiency is said to be present when theevidence shows that it is possible to improve some input or output without worsening some otherinput or output.

Definition 2. Congestion. Evidence of congestion is present when reductions in one or more inputscan be associated with increases in one or more outputsFwithout worsening any other inputor output. Proceeding in reverse, congestion occurs when increases in one or more inputs canbe associated with decreases in one or more outputsFwithout improving any other input oroutput.

As should be apparent, these definitions are restricted to ‘‘technical’’ aspects of inefficiency andhence do not require prices or other value units (or weights) to determine a ‘‘worsening’’ or an‘‘improvement’’. Thus, Definition 1 refers to what might be called ‘‘waste’’ in the sense that itrepresents an unnecessary expenditure of resources for some input. That is, these amounts ofresource expenditures could have been avoided without having had to augment other inputs or

Nomenclature

DMU decision making unit. An entity regarded as responsible for converting inputs intooutputs. Here, the entities take the form of time periods for automobiles and textiles.The performance evaluations are effected for each member of a collection of DMUj,j=1 ,y, n, with DMUo representing the entity to be evaluated relative to all nentities (including itself )

yrj; xij amounts of r=1 ,y, s outputs and i=1 ,y,m inputs, respectively, observed in theperformance of DMUj

yro; xio amounts of r=1 ,y, s outputs and i=1 ,y,m inputs, respectively, observed in theperformance of the entity to be evaluated

lj intensity variable to be determined for each of j=1 ,y, n activities with all ljX0 andPnj¼1 lj ¼ 1

sþr ; s@i output slack, r=1 ,y, s, and input slack, i=1 ,y,m, respectively, constrained to be

non-negative#yyro; #xxio adjusted values for each of r=1 ,y, s outputs and i=1 ,y,m inputs obtained from

an optimal solution. These are the coordinates of a point on the efficiency frontierused to evaluate DMUo. See formula (3)

d@ *

i amount of technical inefficiency in the ith input. See formula (5)s@ci amount of congesting inefficiency in the ith input. See formula (5)s@ *

i total amount of slack in the ith input which is decomposed into the above twocomponents, i.e., s@ *

i ¼ d@ *

i þ s@ci , i=1 ,y,m. See formula (5)

e a non-Archimedean element used to symbolize the need to optimize slacks in orderto ensure that all non-zero slack possibilities are identified in any alternate optima(including some with zero slack) that might be present 8i; j; r ¼ All i,j,r

iAI i, an index in the set I of indices

W.W. Cooper et al. / Socio-Economic Planning Sciences 35 (2001) 227–242228

reduce any outputs. Similarly for outputs, waste may be regarded as a lost output opportunitywith an accompanying loss of benefits that could have been realized without expending moreresources or reducing other outputs. The same is true for input congestionFthe only kind ofcongestion dealt with in this paperFwhich can be regarded as an especially severe form ofinefficiency (or waste) in the sense that benefits in both inputs and outputs could be secured byreducing the congesting input amounts.

Example. Excess raw material inventory congesting a factory floor in a way that interferes withproduction. ‘‘Congestion’’ refers to the amount of this inventory that is accompanied by animprovement in production when it is removed. The excess inventory remaining after removal ofthe congesting component represents ‘‘technical inefficiency’’ because it reflects idle capital butdoes not otherwise interfere with production.

To bring this all into sharper focus we now define efficiency in the following manner.

Definition 3. Efficiency (technical efficiency). Efficiency is achieved if and only if it is not possibleto improve some inputs or outputs without worsening other inputs or outputs.

Hence, in the case of efficiency, in contrast to Definitions 1 and 2, an improvement in any inputor output involves either increases in other inputs or reductions in other outputs.Not much attention has been devoted to congestion as a topic for research in western

economics.1 However, F.aare and Svensson [2] initiated a reawakening of interest in this topic,while F.aare and Grosskopf [3] were subsequently able to give it operationally implementable formin what would now be termed a ‘‘data envelopment analysis (DEA) model’’ using ‘‘radialmeasures’’. More recently, Cooper et al. [4, 1996] introduced a different treatment via an additive(non-radial measure) model. This was subsequently extended and used by Brockett et al. [1] totreat the topic of congestion in Chinese production. See also the exchange recorded in F.aare andGrosskopf [5,6] and Cooper et al. [7,8].It is the approach in [1] on which we build to examine congestion (and other inefficiencies) in

Chinese production. We will also extend the model in [1] in order to provide alternative methodsfor evaluating performances in the presence of congestion. In particular, we will provide methodsfor detecting and evaluating possible output improvements associated with removing managerialinefficiencies in the presence of congestion.

Remark. Too many miners in an underground mine may lead to congestion by interferingwith output. Managerial inefficiency may cause output to fall still further. Identifying thiscomponent may then make it possible to augment output even in the presence of an excessnumber of miners.

Moving in this direction opens a new chapter in the evaluation of congestion with DEA. It alsoadds new ways to deal with the problem of providing adequate employment for China’s huge

1Indeed, Stigler [9, 1976] argued that ‘‘congestion’’ was not a proper topic for research in economics.

W.W. Cooper et al. / Socio-Economic Planning Sciences 35 (2001) 227–242 229

labor force. A population exceeding 1.2 billion persons with more than 14 million new entrantsinto the labor force each year should make clear the magnitude of this problem. (See [1] forcitations to sources for this information.) In fact, to deal with employment maintenance, a policy(sometimes referred to as the ‘‘iron rice bowl’’ policy) was inaugurated and remained a mainstayof Chinese policy starting as far back as 1949Fi.e., shortly after the victory of Mao Tse Tung.However, to improve deteriorating industrial performances after the Cultural Revolution thatended in 1978, this policy was altered in 1990.This important shift in policy can be summarized in four parts as follows: First, any industry

with a record of poor performance was to remove as many ‘‘unnecessary employees’’ as possible.Employees aged 35 or over, or ‘‘unskilled’’ employees, could be asked to retire in returnfor specified compensation. Second, investments in poorly performing industries were to becarefully examined and justified by reference to market studies and demand forecasts, evenwhen this led to further reductions in the labor to be utilized. Third, in order to control inflation,the Chinese economy was to be monitored, coordinated and planned at a macro-level ratherthan at the micro-level used in previously state formulated plans. Fourth, and finally, a1993 congress of communist representatives formally issued a statement to the effect that thepreviously used state planned economic policy was to be replaced by a market-oriented economicpolicy.The policy to remove unnecessary employees was first experimented with in the textile industry

and then extended to other industries such as the automobile industry. Focusing on these twoindustries, the data we use in the present study cover the period 1981–1997. This coverage issufficient, we believe, to provide a basis for (a) identifying the kinds of problems and causes thatled to these reforms, and (b) evaluating their effects. Equally important, from our standpoint, thisperiod of coverage is enough to provide an opportunity to evaluate possible alternatives to thesepolicies of ‘‘mass layoffs’’. Our interest in such alternatives is justified, in part, by the fact thatdepartures from the ‘‘iron rice bowl’’ policies have not been without cost. As Business Week,August 9, 1999, p. 30, reports, ‘‘Social tensions inside China are running high. A further 15million people are expected to lose their jobs this year because of Prime Minister Zhu Rongji’sreformsy’’2

2. Stage one analysis

2.1. BCC model3

There are three different approaches to congestion analysis based on DEA. One proceeds viaradial measure models that use a two-stage approach as described in [10]. Another approach is viause of additive (non-radial measure) models which also proceed in a two-stage manner [7]. Thethird approach, which is the one we use here, proceeds via a radial measure model in stage one,and then uses an additive model in stage two.4 As in [1], the approach we use thus consists of a

2Premier Zhu Rongji was Minister of Economics when these reforms were initiated.3This and other types of DEA models are described and developed in detail in [11].4A comparative evaluation of this approach and the one used in [10] may be found in [12].


hybrid which we begin to describe with the following model:BCC model:

Max fþ ePs

r¼1 sþr þ

Pmi¼1 s

@i

� �

Subject to fyro ¼Pn

j¼1 yrjlj@sþr ; r ¼ 1;y; s;

xio ¼Pn

j¼1 xijlj þ s@i ; i ¼ 1;y;m;

1 ¼Pn

j¼1 lj;

lj; sþr ; s@i X0 for 8i; j; r:

ð1Þ

As noted in the Nomenclature, yrj and xij refer, respectively, to observed values of r=1 ,y, soutputs and i=1 ,y,m inputs for each of j=1 ,y, n decision making units (DMUs) regarded asthe entities responsible for converting inputs into outputs. One of these entities is singled out forevaluation and designated as DMUo. Its outputs and inputs are positioned on the left of (1)without removing them on the right. Hence, a solution is always available with f ¼ 1. We musttherefore have max f ¼ f�

X1, where * represents an optimal value.This leads to the following way of implementing Definition 3.

Definition 4 (DEA efficiency). DMUo is efficient if and only if the following two conditions aresatisfied

(i) max f ¼ f� ¼ 1.(ii) sþ *

r ¼ s@ *

i ¼ 0 8i; r:

Note that a failure to satisfy either condition means that improvement in one or more outputs orinputs is possible without worsening any other input or output of DMUo. This accords withDefinition 1 in the sense that f� > 1 means that the evidence supplied from other DMUs showsthat all outputs of DMUo could be increased from these observed values without worsening anyother input or outputFwhile additional improvements are also possible without worsening if anys@ *

i , sþ *

r > 0:It is to be noted that e > 0 refers to a ‘‘non Archimedean’’ element which is defined to be

smaller than any positive real number. As discussed in [13], it is not necessary to explicitly assign avalue to this element and, indeed, it is not possible to do so since all real numbers areArchimedean.5 This problem is dealt with in most DEA computer codes in a two-stage manner asfollows: Let max f ¼ f* be obtained in a stage one solution to (1). To satisfy the prescribedproperty, we are not permitted to exchange a reduction in f* (even a very small one) forany real number value (even a very large one). Hence, in stage 2 we fix the value of fat f* in the constraints and then maximize the slacks to obtain max.

Psr¼1 s

þr þPm

i¼1 s@i ¼

Psr¼1 s

þ *

r þPm

i¼1 s@ *

i . The combination of this optimal sum of slacks and f* thenmakes it possible to determine whether DMUo is efficient by reference to Definition 4Fandhence, also, to Definition 1.

5 I.e., all real numbers have the following property: given any positive real number n>0, however small, it is always

possible to choose a smaller positive real number as in n>n/2>0.


In addition, this solution allows us to identify the sources and amounts of inefficiencies. To seethat it is so, we form the following expressions which are available from a solution to (1),

f*yro þ sþ *

r ¼Pn

j¼1 yrjl*j ¼ #yyro; r ¼ 1; :::; s;

xio@s@ *

i ¼Pn

j¼1 xijl*j ¼ #xxio; i ¼ 1; :::;m:

ð2Þ

This gives

#yyro ¼ f*yro þ sþ *

r Xyro; r ¼ 1; :::; s;

#xxio ¼ xio@s@ *

i pxio; i ¼ 1; :::;m:ð3Þ

The values on the right in (3) are the observed (or recorded) outputs and inputs. Because f*X1and sþ *

r ; s@ *

i X0 it follows that the values on the left are always at least as good as the values onthe right. Moreover, strict inequality in any of these expressions means that improvement ispossible and can be accomplished without worsening any other input or output. In particular,0pDyro ¼ #yyro@yro and 0pDxio ¼ xio@ #xxio represent the amounts of inefficiency (zero, whenequality holds) in the corresponding output or input. Hence the amounts as well as the sources ofinefficiency (if any are present) can be obtained from this solution for each of the r=1 ,y, soutputs and each of the i=1 ,y,m inputs of DMUo.Failure to satisfy condition (i) in Definition 4 identifies what is sometimes referred to as ‘‘purely

technical inefficiency’’.6 No change in ‘‘mix’’ is involved because ‘‘mix’’ refers to the input (or output)proportions used. Changes in mix are, however, associated with any non-zero slacks that may bepresent in a solution to (1) since, in general, non-proportional changes in the observed inputs willoccur when the inefficiencies associated with these non-zero slacks are removed. See (2) and (3).Now we note that the above two-phase procedure and associated identification of sources and

amounts of inefficiency may be implemented repeatedlyFas is done in most DEA computercodesFas each of the j=1 ,y, n DMUs is brought into the objective for evaluation in (1).Geometrically speaking, each DMU is then evaluated relative to a linear facet generated by asubset of efficient DMUs. The result is a portion of an ‘‘efficiency frontier’’ formed in piecewiselinear fashion from these facets as each DMUj is identified as a DMUo to be evaluated. In fact,the point on the efficiency frontier used to effect each evaluation is represented by coordinateswith the values #yyro, #xxio given in (3).

Remark. The objective in (1) is not ‘‘units invariant’’. This means that the choice of optimal slackvalues may depend on the units in which inputs and outputs are measured. Moreover, utilitytheoretic considerations reflected in, say, different weights assigned to different input slacks in theobjective can also lead to alterations in a choice of optimum programs and the values of theirobjectives. In order to avoid further preparatory discussion, however, we do not treat this topichere. Instead we refer readers to Thrall [15,16]. See also [14,17].

2.2. Data

Table 1, below, provides the data on textile and auto performances which we will use to effectour evaluations with (1). In the same manner as Brockett et al. in [1], we will treat each year in

6See [14] for a more detailed discussion.


each industry as a DMU. The results we achieve will then identify when each inefficiency occurred(and its sources and amounts) as we apply (1) and (3) to each of these two industries (textiles andautomobiles) in turn.These two industries were selected because they are representative (in different ways) of the

situation with respect to labor that we wish to study. Both make extensive use of labor in assemblyor semi-assembly operations. Both industries are highly automated (which also reduces the laborskills required) but neither has achieved the ‘‘high tech’’ status in which, inter alia, direct costs area minor part of total cost.We collected these data from the Statistical Year Book of China of the Chinese Bureau of

Statistics, as published regularly in China every year. All values have been adjusted to a 1991 baseperiod to eliminate the impact of price variations.7 The thus adjusted input and output data arepresented in Table 1. It is interesting to observe that Table 1 shows rapid labor increases fortextiles until 1991 followed by a decline and a brief pickup but at a lower level in 1994 and adecline thereafter. As can be seen, a jump in capital appears in automobiles, starting in 1992, whenlarge foreign investments by German and American automobile companies began to appear.

Table 1Input and output data in textile and auto industries of China (1981–1987)a,b

Year Textile Automobile

Labor Capital Output Labor Capital Output

1981 389.00 19.86 856.02 90.43 3.81 70.471982 412.30 21.16 866.85 94.28 4.13 82.07

1983 423.50 17.08 956.04 104.66 5.56 117.781984 417.30 18.10 1082.94 121.24 9.50 168.291985 570.00 12.61 1273.20 140.72 21.44 273.991986 600.50 13.45 1230.72 129.08 20.95 212.89

1987 641.10 15.91 1410.66 134.83 30.99 273.191988 715.30 23.72 1728.16 150.58 41.29 407.291989 736.00 25.97 2109.57 157.07 37.88 481.02

1990 745.00 18.24 2291.08 156.53 41.30 492.491991 756.00 14.40 2533.27 170.39 58.93 704.481992 743.00 17.50 2899.16 184.87 102.75 1191.05

1993 684.00 25.08 3520.74 193.26 164.27 1792.001994 691.00 25.45 4949.93 196.88 198.77 2183.101995 673.00 29.35 4604.00 195.25 231.34 2530.87

1996 634.00 23.05 4722.29 195.06 194.90 2399.091997 596.00 25.02 4760.28 197.81 203.96 2668.69

aData source: The Statistical Year Book of China, the Bureau of Statistics, China.bNote: Both capital and output values are stated in units of 1 million Ren Min Bi (Chinese monetary unit) adjusted to

1991 prices. Labor is expressed in units of 1000 persons.

7We would have preferred a 1980 base period for comparability with [1,18], but the price data needed for thisconversion were not available. Similar unavailability of unit prices and costs made it necessary to confine our analysis to

technical aspects of efficiency.


However, even in these circumstances the growth of labor in automobiles was relatively steady.This is in contrast to the textile industry, which went through ups and downs in labor employmentin the last two decades.

2.3. Computational results from the BCC model

For a more systematic analysis, we applied model (1) to the data in Table 1 and obtainedthe results reported in Table 2. Both industries show output shortfalls as indicated by values off� > 1 in the periods prior to the 1990 reforms with improvements thereafter. In terms of theseoutput shortfalls, the pre-1990 record for textiles is markedly worse than for automobiles, withparticularly serious deficiencies (100% and more) occurring in 1988 and 1989. The fact thatthese severe output shortfalls are accompanied by large amounts of labor slack in these twoperiods suggests that they may be associated with congestion. This is the topic to which weturn (in the next section) after first seeking to compare our results with reports from otherstudies.Earlier period results of textile operations are generally consistent with those reported in [1] but

fail to be so in 1988, the terminal year in their analysis. However, we do not pursue thiscomparison further since our interest centers on the effect of the 1990 (and following) periodreforms which their paper does not address. We do note, however, that our results are consistentwith the more detailed analysis at the individual company (Nanjing Textile Corporation) level

Table 2DEA results (stage-one model) for textile and automobile industries

Year Textile industry Automobile industry

DEA

efficiencyratio

Labor

slack

Capital

slack

Output

slack

DEA

efficiencyratio

Labor

slack

Capital

slack

Output

slack

1981 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.001982 1.49 0.00 0.72 0.00 1.00 0.00 0.00 0.001983 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00

1984 1.00 0.00 0.00 0.00 1.00 14.73 0.00 0.001985 1.00 0.00 0.00 0.00 1.18 28.60 0.00 0.001986 1.34 0.00 0.00 0.00 1.48 17.19 0.00 0.001987 1.81 0.00 0.00 0.00 1.63 18.23 0.00 0.00

1988 2.77 65.39 0.00 0.00 1.42 29.14 0.00 0.001989 2.35 45.00 0.00 0.00 1.11 37.24 0.00 0.001990 1.53 43.16 0.00 0.00 1.17 35.09 0.00 0.00

1991 1.00 0.00 0.00 0.00 1.14 40.67 0.00 0.001992 1.14 30.72 0.00 0.00 1.15 34.58 0.00 0.001993 1.40 1.79 0.00 0.00 1.20 14.08 0.00 0.00

1994 1.00 0.00 0.00 0.00 1.19 1.51 0.00 0.001995 1.07 0.00 3.98 0.00 1.03 0.00 32.15 0.001996 1.00 0.00 0.00 0.00 1.06 1.50 0.00 0.00

1997 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00


reported in [19, pp. 318–319] for the period 1988–1989. They are also consistent with theanalysis of deficiencies in the state-owned industry performances that are reported for textiles in[20].We also secure confirmation by reference to events such as the following. In 1990, the textile

industry (although state owned) went bankrupt in the sense that it could not meet its obligations,including its payrolls. This precipitated the initiation of a (previously thought to be unneeded)‘‘bankruptcy law’’ in 1991 as well as the new policies originating in 1990 which we discussedearlier. In fact, the new policies, with their accompanying departures from the earlier ‘‘iron ricebowl’’ policies, were undertaken experimentally first in textiles. Subsequently implemented inother industries, the planned restructuring associated with these demand-oriented policies wasgenerally completed by 1994. The resulting improvements in output performance efficiencies areapparent in the DEA efficiency ratio columns for both industries after 1994. In fact, theimprovements appear earlier in textiles (by 1991) than in automobiles.In Table 2, we notice that, besides the labor slacks, capital slacks appear in some years in both

industries. (See the capital slacks in 1982, and 1995 for the textile industry, and in 1995 for theautomobile industry). This is an indication that the Chinese government did not use its capitalresources efficiently. Since 1978, the Chinese government invested heavily in various industriessuch as textiles and automobiles. Meanwhile, foreign investors (e.g. General Motors, Ford,Honda, etc.) began to establish joint ventures by adding more investments in some industries suchas automobiles. This double investment (from both the Chinese government and foreigninvestors) may also have led to some of the over-expenditures of capital that are indicated inTable 2. See, for example, the relatively large capital slack for autos in 1995.

3. Stage two analysis

3.1. Congestion model

As noted earlier, the appearance of large output slacks (which represent shortfalls in output)and large labor slacks (which represent excesses in the amount of labor used) suggest the possiblepresence of congestion. We therefore turn to a use of DEA to identify whether congestion mightbe present and, if so, in what amounts and when. The model we employ, as taken from [1], is usedin a second stage after a solution to (1) has been obtained. This second stage model is

maxPm

i¼1 d@i

subject to #xxio ¼Pn

j¼1 xijlj@d@i ; i ¼ 1; :::;m;

#yyro ¼Pn

j¼1 yrjlj; r ¼ 1; :::; s;

1 ¼Pn

j¼1 lj;

s@*i Xd@i ; i ¼ 1; :::;m;

ð4Þ

where the #xxio and #yyro values on the left are defined in (3) and all variables are constrained to benon-negative.Notice that the inequality for the inputs implied in the first i=1 ,y,m constraints is reversed

from the usual form exhibited in (1) (cf. the change in sign for the slacks). The objective in (4) is to


maximize the sum of the input slacks8 with the additional constraint s@ *

i Xd@i limiting each slackto the maximum value obtained in the preceding solution to (1). The difference may berepresented as

s@ci ¼ s@ *

i @d@ *

i X0; ð5Þ

where, for each i=1 ,y,m, d@ *

i is obtained by solving (4) after s@ *

i has been subtracted from xioas in (3).These s@c

i values, when positive, represent the congesting amounts in each of the i=1 ,y,minputs while the d@ *

i X0 represent the corresponding technical inefficiency components. Thusreferring to s@ *

i as ‘‘total slack’’ (as obtained from (1)), we have s@ *

i ¼ d@ *

i þ s@ci , i=1 ,y,m.

That is, each ‘‘total slack’’ as obtained from (1) has two components: ordinary technicalinefficiency in amount d@ *

i and a congesting amount s@ci .

Fig. 1, below, can help explain what is intended. Note, for instance, that point C withcoordinates (x,y)=(3,2) is inefficient relative to B because B produced the same 2 units of outputas C but did so with only 2 units of input. Hence, C used an excess of 1 unit of input. There is nooutput reduction associated with this input excess, however, so the resulting inefficiency is ‘‘purelytechnical’’.While no evidence of congestion is present in the performance of C, all points to the right of C,

do, in fact, exhibit congestion. For illustration, we apply models (1) and (4) to E. Application of(1) yields the following model:

max fþ eðsþ þ s@Þ

subject to 1f ¼ 0:5lA þ 2lB þ 2lC þ 1lD þ 1lE þ 1:2lF þ 1:2lG@sþ;

4 ¼ 1lA þ 2lB þ 3lC þ 5lD þ 4lE þ 4lF þ 4:5lG þ s@;

1 ¼ lA þ lB þ lC þ lD þ lE þ lF þ lG;

0plA; :::; lG; sþ; s@:

ð6Þ

This has as its solution f* ¼ 2; l*B ¼ 1; s@ * ¼ 2. E is thus inefficient since both (i) and (ii) inDefinition (3) fail to be satisfied.To ascertain whether congestion is present, we turn to (4) and use the results we have just

secured to replace the preceding model with

max d@

subject to 2 ¼ 0:5lA þ 2lB þ 2lC þ 1lD þ 1lE þ 1:2lF þ 1:2lG;

2 ¼ 1lA þ 2lB þ 3lC þ 5lD þ 4lE þ 4lF þ 4:5lG@d@;

1 ¼ lA þ lB þ lC þ lD þ lE þ lF þ lG;

2Xd@;

0plA; :::; lG; d@:

ð7Þ

8 If desired, these slacks may be stated relative to the observed xio, as in [8], in order to obtain a measure of congestion

which is invariant to the units of measure used.


Here, #yy ¼ 2 and #xx ¼ 2 as represented on the left are obtained by inserting the preceding solutionvalues into (3). Similarly, s@ * ¼ 2 (from the preceding solution) bounds the admissible values ofd@ as in (4).The solution to the just stated problem is l*C ¼ 1; d@ * ¼ 1. Substitution of d@ *

in (5) thereforegives s@c ¼ 221 ¼ 1 as the congesting amount of this input in the behavior of E. Hence, the totalslack, at s@ * ¼ 2, as obtained from the first model, is decomposed in our solution to a value ofd@ * ¼ 1 for ‘‘purely technical inefficiency’’ and s@c ¼ 1 for the ‘‘congesting’’ part of this ‘‘totalslack’’.All of this information, which is automatically available, can be related to Fig. 1 by noting that

s@ * ¼ 2 is the reduction in the x=4 units of input used by E in order to obtain coincidence withthe input of B. At the same time, s@c ¼ 1 is the reduction in the input of E needed for coincidencewith the input of C. Further, d@ * ¼ 1 is the amount (here=one unit) of technical inefficiency thatneeds to be removed from the input of C9 to attain coincidence with the input of B. Finally,comparing the units of output at C with the one unit of observed output for E shows the amountof output reduction (=one unit) that is associated with the s@c ¼ 1 unit of congesting input.10

3.2. Measuring congestion

Table 3, below, reports results from applying the procedures we have just described to the datadisplayed in Table 1 for the Chinese textile and automobile industries. Technical inefficiency in theinputs is equal to the corresponding total slack (labor or capital), so there are no plateau-likephenomena such as is portrayed between points B and C in Fig. 1. Hence, in most casesFseeformula (5)Fthe congesting amounts are the same as the total slack values given in Table 2.

Fig. 1. Numerical example. Source: Brockett et al. [1].

9This is the same (maximal) output value obtained from (6) and incorporated in the output constraint for (7).10As will be seen in Section 4, however, there is also a managerial inefficiency component to be accounted for in this

amount of output reduction.


Two features of these results are to be noted. One is that automobiles have a longer history incoping with congestion than is the case for textiles. Another feature is the sudden appearance oflarge amounts of labor congestion in 1988–1990 in textiles with (apparently) no prior experiencein managing this kind (or degree) of congestion. This lack of prior experience together with themagnitude of the congestion to be dealt with is likely to have contributed to the crisis and thesubsequent bankruptcy and policy changes in China during this period.These circumstances suggest that an improved management might have ameliorated the crisis in

textiles and, possibly, automobiles, as well. This is a topic that we will explore in the next section.To close the present discussion, however, we simply note that the policy changes initiated in 1990are apparently reflected in the reduced labor congestion first in textiles in 1991 and then in bothautomobiles and textiles after 1992. The reduction in labor congestion is particularly striking fortextiles which, we recall, was the industry to which the reforms were first applied (on anexperimental basis).As we also noted, the capital congestion in automobiles is high at 32,150,000 RMB. Given the

rapidly increasing demand for cars in the Chinese market, this might have been caused byoverexpansion in the automobile industry and also, perhaps, new experience with combinations ofdomestic and foreign investments. See our earlier discussion.Even with a large capital excess in 1995, the resulting output shortfall is relatively minor as

indicated by the value of f� ¼ 1:03 for automobiles and f� ¼ 1:07 for textiles (Table 2). This is incontrast with the much larger output shortfalls that occurred with large labor excesses in the 1980sand early 1990s. Apparently, the latter excess is more difficult to manage. In the next section wetherefore focus on clues to possible improvements in managing labor congestion.

Table 3Summary of congesting inputs

Year Textile industry Automobile industry

Labor

congestion

Capital

congestion

Labor

congestion

Capital

congestion

1981 0.00 0.00 0.00 0.00

1982 0.00 0.72 0.00 0.001983 0.00 0.00 0.00 0.001984 0.00 0.00 14.73 0.001985 0.00 0.00 28.60 0.00

1986 0.00 0.00 17.19 0.001987 0.00 0.00 18.23 0.001988 65.39 0.00 29.14 0.00

1989 45.00 0.00 37.24 0.001990 43.16 0.00 34.34 0.001991 0.00 0.00 40.67 0.00

1992 30.72 0.00 34.58 0.001993 0.00 0.00 14.08 0.001994 0.00 0.00 1.51 0.00

1995 0.00 3.98 0.00 32.151996 0.00 0.00 0.00 0.001997 0.00 0.00 0.00 0.00


3.3. Stage three analysis: inefficiency in managing congestion

As just noted, labor congestion may be more difficult to manage than capital congestion.Massive layoffs may, for instance, give rise to social tensions like those cited in the quotation fromBusiness Week at the end of our introduction. Thus, the Chinese government (and others) may beinterested in whether improvements might be made without massive layoffs even in the presence ofcongestion. This is the topic to which attention will now be turned.We use point E in Fig. 1 for illustration. As discussed earlier, E and the other points to the right

of C exhibit congestion. However, we can see that F has a better output performance with thesame level of input as E. This suggests that F was able to manage better than E in the face of thesame amount of congestion. In a complementary manner, we may observe that D was able toobtain the same output as E while utilizing an even larger amount of this congesting input.Finally, G was able to improve upon the output record for E while simultaneously managing aneven larger amount of this congesting input.A variety of objectives can be used in models to detect a ‘‘managerial efficiency’’ component in

the way ‘‘congestion’’ is handled. For use in our present example, however, we note that theemphasis was on improving output in the 1990 (and subsequent) reforms in China. Hence, weorient our model toward evaluating management by reference to the shortfalls exhibited in itsoutput record when operating in a congested manner.The model we propose for this purpose is directed to maximal output augmentations and

formulated as follows:

maxPs

r¼1 sþr

subject to yro ¼Pn

j¼1 yrjlj@sþr ; r ¼ 1; 2; :::; s;

xio ¼Pn

j¼1 xijlj@s@i ; i ¼ 1; 2; :::;m;

1 ¼Pn

j¼1 lj;

0plj; s@i ; sþr ; 8i; j; r:

ð8Þ

As is evident in this model, the objective is to maximize the possible output increases over theobserved output values yro for DMUo without decreasing any of its inputs.We can further refine this model by focusing on a set iAI of inputs where increases are desirable

if they do not interfere with the already attained outputs. Then we can distinguish these fromother inputs which we designate as iA %II where decrements are favored over increments. WithI, %II ¼ S; the set of all inputs for DMUo, and I- %II ¼ F, where F designates the empty set, thereis no ambiguity of classification for these inputs if we replace the input constraints in (8) with thefollowing

xio þ s@i ¼Pn

j¼1 xijlj; iAI

xio@s@i ¼Pn

j¼1 xijlj; iA %IIð9Þ

while retaining the other constraints in the form presented in (8).In our case, the set iAI consists of the constraint for labor while the set iA %II consists of

the constraint for capital. For this single output case, the objective to be maximized is sþ, so (8)


and (9) become

max sþ

subject to yo þ sþ ¼Pn

j¼1 yjlj

x1o þ s@1 ¼Pn

j¼1 x1jlj

x2o@s@2 ¼Pn

j¼1 x2jlj

1 ¼Pn

j¼1 lj

0psþ; s@1 ; s@2 ; lj; j ¼ 1; :::; n;

ð10Þ

where the subscripts i=1, 2 refer, respectively, to labor and capital. Thus, s@1 > 0 increases laborin the same way that sþ > 0 increases output while s@2 > 0 decreases capital in the same way thatall inputs are treated in (1).11

Table 4 provides results that correspond to solutions with the constraints in (10). Hence, byreducing capital (but not labor), the output in textiles is improved significantly. Our results showthat the output improvement in 1988 is even larger than the corresponding current output levelrecorded in Table 1, and this is accompanied by a relatively small reduction in capital. Similarly,

Table 4Output improvements, labor increases and capital decrementsa

Year Textile Automobile

Output

increase

Labor

increase

Capital

decrease

Output

increase

Labor

increase

Capital

decrease

1981 0 0 0 0 0 0

1982 0 0 0 0 0 01983 0 0 0 0 0 01984 0 0 0 0 0 01985 0 0 0 0 0 0

1986 0 0 0 95.57 0 01987 0 0 0 160.57 0 01988 2318.31 0 2.4 134.16 0 0

1989 1167.29 0 8.17 0 0 01990 651.16 0 1.97 36.5 0 01991 0 0 0 0 0 0

1992 117.44 0 0.89 0 0 01993 0 0 0 0 0 01994 0 0 0 414.41 0 0

1995 0 0 0 7.6 0 32.151996 0 0 0 0 0 01997 0 0 0 0 0 0

aFor units used: see Table 1.

11An analogous treatment is used in [21] for a treatment of capacity utilization. (We are indebted to a referee for this

citation.)


between 1989 and 1992, significant output improvement could be achieved in company withreductions in capital. This suggests that serious mix inefficiencies were present. In any event, theindication is that very significant shortfalls in output are due to managerial inefficiencies and thatremoval of these inefficiencies could have improved output without recourse to massive laborlayoffs.We can clarify the situation further by turning to the results recorded for automobiles in Table

4, which are less spectacular than for textiles. Nevertheless, it is of interest to note that outputimprovements were shown to be possible without altering the labor or capital utilized. Absentevidence to the contrary, it therefore seems fair to attribute these output shortfalls to inefficiencyin the way the two inputs were managed.In order to identify this difference between congestion inefficiency and its management, we note

from Tables 3 and 4 that the (congesting) capital amount of 32,150,000 RenMinBi in 1995 couldhave been eliminated and accompanied by the relatively small (=3%) output augmentationrecorded for 1995 in Table 2. These gains are associated only with the removal of congestion. Thiscontrasts with the relatively large augmentation of 414,410,000 RMB which could havebeen achieved in 1994 without any change in inputs. As previously noted, we attribute thisoutput shortfall to inefficiency in the way the (relatively small) congesting amount of input forlabor was managed. See the 1994 row for labor congestion in the automobile industry in Table 3.Hence, we can identify an additional managerial inefficiency in the way this labor congestion wasmanaged.

4. Conclusion

We have now extended previous approaches to congestion in order to identify managerialinefficiency as a possible additional source of output shortfalls in the presence of congestion. Thiswas done in a manner that made it possible to reduce some of the congesting inputs whileincreasing (or, at least not decreasing) other inputs that are also congesting. This wasaccomplished by models that make it possible to control the reductions and augmentationsthat may need to be considered. This was also accomplished in a flexible manner, making itpossible to deal with extraneous (but important) considerations such as the social tensions thatcan accompany massive layoffs in labor while, in addition, reducing inputs (such as capital) byidentifying possible managerial improvements that might otherwise be overlooked.Data from the textile and automobile industries in China were used to identify uses of these

approaches in a manner that adds to results obtainable from previous efforts to treat congestion inChinese production. Our work will hopefully stimulate additional research in the relatively sparseliterature involving congestionFa condition which, as noted in our introduction, began to becorrected only with F.aare and Svensson [2]. The development of implementable forms of modelingstarted in [3,10], and was subsequently augmented with the models formulated in [4]. As applied in[1] to problems in Chinese production, the CTT (Cooper, Thompson and Thrall) model was hereextended and used to treat additional problems (and data). For other models and approaches, see[7,8]. For a discussion (including critiques) of still other models, see [22,20], and for exchanges onthis topic see [5,23] as well as [22,12].


Acknowledgements

W.W. Cooper wishes to express his appreciation to the IC2 Institute of the University of Texasfor support that underlies this research and S. Li would like to acknowledge a Canadian NSERCGrant for support of her research. Acknowledgement is also due to Barnett Parker, the editor,and an anonymous referee for suggestions that resulted in improvements to an earlier version ofthis paper.

References

[1] Brockett PL, Cooper WW, Hong Chul Shin, Yuying Wang. Inefficiency and congestion in Chinese productionbefore and after the 1978 economic reforms. Socio-Economic Planning Sciences 1998;32:1–20.

[2] F.aare R, Svensson L. Congestion of factors of production. Econometrica 1980;48:1743–53.[3] F.aare R, Grosskopf S. Measuring congestion in production. Zeitschrift f .uur National .ookonomie 1983;43:257–71.[4] Cooper WW, Thompson RG, Thrall RM. Introduction: extensions and new developments in DEA. Annals of

Operations Research 1996;66:3–46.[5] F.aare R, Grosskopf S. Congestion: a note. Socio-Economic Planning Sciences 1998;32:21–3.[6] F.aare R, Grosskopf S. When can slacks be used to identify congestion? An answer to Cooper WW, Seiford L, Zhu

J. Socio-Economic Planning Sciences 2001;35:1–10.

[7] Cooper WW, Seiford LM, Zhu J. A unified additive model approach for evaluating efficiency and congestion.Socio-Economic Planning Sciences 2000;34:1–26.

[8] Cooper WW, Seiford LM, Zhu J. Slacks and congestion: a response to the comments of R. F.aare and S. Grosskopf.

Socio-Economic Planning Sciences 2001;35:1–11.[9] Stigler GJ. The X-istence of X-efficiency. American Economic Review 1976;66:213–6.[10] F.aare R, Grosskopf S, Lovell CAK. The measurement of efficiency of production. Boston: Kluwer-Nijhoff

Publishing, 1985.[11] Cooper WW, Seiford LM, Tone K. Data envelopment analysis: a comprehensive text with models, applications,

references and DEA-solver software. Norwell, MA: Kluwer Academic Publishers, 1999.[12] Cooper WW, Gu B, Li S. Comparisons and evaluations of alternative approaches to the treatment of congestion in

DEA. European Journal of Operational Research 2001, to appear.[13] Arnold V, Bardhan I, Cooper WW, Gallegos A. Primal and dual optimality in computer codes using two-stage

solution procedures in DEA. In: Aronson VE, Zionts S, editors. Operations research: methods, models and

applications. Westport: Conn. Quorum Books, 1998.[14] Cooper WW, Park KS, Pastor JT. RAM: a range adjusted measure of inefficiency for use with additive models,

and relations to other models and measures in DEA. Journal of Productivity Analysis 11;1999:5–42.

[15] Thrall RM. Duality, classification and slacks in DEA. Annals of Operations Research 1996;66:109–38.[16] Thrall RM. Measures in DEA with an application to the Malmquist index. Journal of Productivity Analysis

2000;3:125–35.

[17] Cooper WW, Park KS, Pastor JT. A range adjusted measure (RAM) in DEA: a response to the comment by LukasSteinman and Peter Zweifel. Journal of Productivity Analysis 2001;15:145–52.

[18] Cooper WW, Kumbhakar S, Thrall RM, Yu X. DEA and stochastic frontier analyses of the 1978 Chineseeconomic reforms. Socio-Economic Planning Sciences 1995;29:85–112.

[19] Zhu J. DEA/AR analysis of the 1988–89 performance of the Nanjing Textile Corporation. Annals of OperationsResearch 1996;66:311–35.

[20] Seiford LM, Zhu J. Identifying excesses and deficits in Chinese industrial production. (1953–1990)Fa weighted

data envelopment analysis approach. Omega 1998;26:279–96.[21] F.aare R, Grosskopf S, Kokkelenberg. Measuring plant capacity. International Economic Review 1989;655–66.[22] Cherchye L, Kuosmanen T, Post T. Alternative treatments of congestion in DEA: a rejoinder to Cooper, Gu and

Li. European Journal of Operational Research 2001, to appear.[23] F.aare R, Grosskopf S. Slacks and congestion: a response. Socio-Economic Planning Sciences 2000;34:35–50.


Documents

Using DEA to improve the management of congestion in Chinese industries (1981–1997)