Organizations efficiency evaluation by reallocation of human
resources
Maryam Khatibi1*, Bijan Rahmani parchikolaei2, Behroz Daneshian3, Sohrab Kordrostami3
(1) M.Sc. Applied Mathematics of Islamic Azad University, Lahijan Branch (2) Faculty of Islamic Azad University, Noor Branch
(3) Faculty of Islamic Azad University, Lahijan Branch
Copyright 2015 © Maryam Khatibi, Bijan Rahmani parchikolaei, Behroz Daneshian and Sohrab Kordrostami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Organizations performance evaluation for optimal usage of resources towards increasing of efficiency is important and necessary. Frequently organizations performance has been evaluated by data envelopment analysis. The aim of most investigations for increasing organizations efficiency has been decreasing used inputs (work force). Because in some organizations, mach costs and time is allocated to education of people as organization need their knowledge and specialty. Therefore, dismissal of workforce is not profitable, economically. In this work, idea of reallocation of inputs as a way for improvement of organizations efficiency instead of just decreasing the inputs, has been presented as a design by data envelopment analysis. This proposed design has been examined about data related to some fire department stations.
Keywords: Data envelopment analysis; reallocation of resources; centralized organization; efficiency evaluation.
1 Introduction
Data envelopment analysis is a set of mathematical optimize models which is used for evaluation of relative efficiency of a set of decision making units, most evaluations are about a set of independent units. Consider an aggregation unit that includes independent units in different areas. Even if all independent units have efficiency in their own areas, such aggregation unit may not be efficient. The reason for considering this matter is that resources allocation among independent units has not been accomplished optimum. Thus reallocation of resources among independent units is needed for aggregation unit to be efficient [16]. Because reallocation is effective for efficiency of aggregation units, this is called as an important research discussion. Since Athanassopoulos [5] for determining best possible performance among independent units and by assuming the possibility of allocation and being zero cost its, Showed some models for resources allocation in public sector. But if reallocation becomes limited and or very costly, then aggregation units can’t be efficient completely, because of existing limits. Fare et al [12] by considering the cases that
Available online at www.ispacs.com/dea
Volume 2015, Issue 1, Year 2015 Article ID: dea-00080, 8 Pages doi:10.5899/2015/dea-00080
Recently various articles have been presented about allocation and reallocation of resources some of which are:
Thrall [21], Dayson et al [10], Beasley [6], Lozano and villa [17], Hadi vancheh et al [13], Camanho and. Dyson [7], Elena Pachkova [11], Hosseinzadeh Lotfi et al [14], Asmild et al [3], Daneshvar [8], Wang and chanlina [22], Aparicio et al [2], Rahmani Parchkolaei et al [18], Daneshvar et al [9], Hosseinzadeh Lotfi et al [15], Rahmani Parchikolaei et al [19], Rahmani Parchikolaei and Yosefian [20].
By models of allocation, many studies have been done about evaluation of independent unit performance in an organization. The aim of most of them was input-oriented studies for improvement of organizations efficiency by decreasing usable inputs. If we consider organization personnel as organization inputs, because mach cost and time is spent on people education, dismissal of workforce is not economical. Therefore in this article the attempt was to use reallocation of inputs idea as a way for improvement in organizations efficiency instead of only decreasing of inputs. Suggested idea has been evaluated about 8 independent units in fire department.
2 Review of the appearance of DEA basic models
Data envelopment analysis is a nonparametric way for measuring the efficiency of a set of decision making units. This method first was presented for measuring the efficiency of units that included one input-one output. Later on, this idea developed and a model was presented that could measure efficiency of systems with some inputs-some outputs.
Proposed model was called CCR. Then a model called BCC that has variable return to scale. Over time DEA models developed and were presented in more specialized areas. But the base of all of them is CCR and BCC models. Therefore for introduction of CCR model assume that "n" decision making unit is available as DMUj,{j=1,…,n}, so that input vector Xj=(X1j,…,Xmj) produce output vector Yj=(Y1j,…,Ysj). Furthermore, it is assumed that xj≥0 & xj≠0 and yj≥0 and yj≠0 that is at least one of components of input
vector and output vector is opposite of zero. We define matrix x=(x1,…,xn) which is an (m×n) matrix as
inputs matrix and matrix Y=(Y1,….,Yn) which is an (s×n) matrix as outputs matrix. We use following models for evaluation of DMUo in which o ∈{1,…..,n}:
� θ
. . � , (2.1)
,
.
�� �
. . , (2.2)
� ,
.
Model (2.1) is CCR model in input oriented and model (2.2) is CCR model in output oriented. If we add
condition ∑ −1 = to conditions of models (2.1) and (2.2), BCC model obtain in input and output oriented
min � (2.3)
. . ∑ =1 ≠
� ,
∑ =1 ≠
, k = , … , n.
According to this model, for grading of DMUo, delete it from a set of decision maker units (reference set)
and carryout it for rest of DMUs. Calculated efficiency scores of DEA standard models are bounded from
above to number one when as super efficiency scores of one efficient unit, after performing of this model, is greater or equal to one [4]. In continue, we will evaluate the efficiency of eight decision making unit and will use the BCC input-oriented model and a super efficient model in the case of variable return to scale.
3 Data initial and analysis
Consider 8 decision independent making units of a centralized organization (fire department). By done studies, we divide performance of these units into two general categories that are executive performance (relief and rescue) and services performance (prevention). Proportional to this performance, we will have two BCC input-oriented models that call them executive model and services model respectively. Based on studies we consider the number of the personnel of every performance as only input for every model and also allocate an output to every model. Output of operational model is the number of people who have been saved after accidence, and output of service model is the number of people who have been saved before
accidence category. Set Q includes 8 independent decision making units (DMUs). For every one of two
models assume that xkt amount of consumed input DMUo, (o=1,….,8) for Implementation of model t,(t=1,2). Also assume that ykt is produced outputs in each model and μ t is number of outputs of model t. BCC input-
oriented model is formulated as follow:
′� = min (3.4)
. . ∑ �
∈�
� � ,
∑ � ∈�
� � , = , … , ,
∑ � ∈�
= ,
� , ∀ ∈ � .
Table1: Input and outputs values, efficiency and inefficiency scores � − � � − � 0 1.00 60 12 -3.96 0.56 67 9 DMU1 0 1.00 139 19 -2.96 0.63 73 8 DMU2 -11.76 0.72 225 42 -2.03 0.71 75 7 DMU3 -0.75 0.95 90 15 -3.96 0.56 70 9 DMU4 -10.80 0.76 253 45 -1.02 0.83 75 6 DMU5 -0.76 0.96 132 19 0 1.00 83 17 DMU6 0 1.00 305 41 -5 0.5 72 10 DMU7 0 1.00 100 15 0 1.00 78 5 DMU8
According to efficiency scores illustrated in table1, in model (2.1) two units are efficient and six units inefficient and in model (2.2), four units are efficient and two units are inefficient.
4 Increasing of efficient units based on super efficiency scores
For decreasing inefficiency of inefficient units, first of all, we calculate super efficiency scores of efficient units. Anderson–Peterson super efficient model [1] in the case variable return to scale formulated as follow:
′�
= min (4.5)
. . ∑ � ∈� �≠ � , � ∑ � ∈� �≠ � � , = , … , , ∑ � ∈��≠ = , � , ≠ .
Calculation of super efficiency scores related to efficient unit o shows how mach the inputs of unit o in model t can increase without being inefficient of unit o. It should be noticed that often super efficiency scores in BCC models can not be defined. Because these scores are not bounded from above and this is necessary and enough condition for infeasible super efficiency. Thus, after carrying out of super efficient model, unbounded super efficient scores with highest bounded value observed from super efficiency scores for every model is replaced separately. These scores are shown in table 2 with index b.
Table 2: Input values, supper efficiency and inefficiency Scores
Now by assuming that all organization personnel are able to service in both performances, a design was presented and its aim was to make efficient all inefficient units, after carrying out of design. This aim can be achieved by decreasing input (personnel) for inefficient units and increasing input(personnel) for efficient units, so that produced output value doesn’t change.
Design: Recognition of number of surplus people inefficient units with the aim of reallocation of them, firstly among performance of a unit and then among units of one performance.
Implementation process design: Firstly, The units are grouped into three categories.
Group (A): units of this group are inefficient in both own performances. Therefore for increasing own
efficiency, it is necessary to dismissnumber of surplus people of both own performance.
Group (B): units of this group are super efficient in both own performance, thus units of this group don’t
need reallocation.
Group (C): Units of this group are efficient in one own performance and are super efficient in other own
performance. In this case, it is necessary that the number of people from own inefficient performance be reallocated to own super efficient performance.
According to table 2, DMUs 3,4 and 5 are inefficient in both own performance, so they belong to group(A). DMU8 also are super efficient in both own performances, so they belong to group (B). Thus DMUs that belong to group(C) are DMUs 1,2,6 and 7 because these DMUs are efficient in one own performance and are super efficient in another. Now, after grouping of units, steps are carried out as follow:
Step1: We recognize minimum score, among performances of all units that belong to group(C).
Step2: Number of surplus people of that recognized performance is reallocated once more to super efficient
performance of the same unit. Amount of possible reallocation is limited by absolute value
ABS[αtxt− xt] and amount of super efficiency[α′txt− xt].
Step3: Amount of super efficiency available from Step2, is decreased by reallocated people.
Step4: Steps1 to 3 is repeated again until any reallocation among performance of every unit become
impossible.
Step5: when it is impossible to reallocate among performances of every unit, remainder of minimum
inefficient score between two performances of inefficient units is recognized.
Step6: Number of surplus people of that unit in that recognized performance is reallocated to a unit with
maximum score of super efficiency available in the same performance. Amount of reallocation is calculated like step2.
Step7: steps5 and 6 are repeated until any reallocation is possible or is needed. Now we carry out presented
Table 3: Input values, efficiency and inefficiency scores after implementation of design
According to table 3, all available inefficiencies have been deleted, and inefficient units become efficient without any need to dismiss people (workforce). It should be considered that if after finishing reallocation, a unit remains super efficient; we can solve this problem by employment of new workforce.
5 Conclusion
In this article, first of all, performance of 8 independent units of a centralized fire department was studied and then by BCC input-oriented model, efficiency and inefficiency of these units was evaluated and then a design in form of reallocation of inefficient units inputs to efficient units was presented and its aim was deleting inefficiency rate of all inefficient units, based on super efficiency scores. By carrying out of this design all inefficient units become efficient and also volume of work divided among all units become more fairly. Therefore carrying out of this
Design causes increasing of Organizations efficiency and also causes entrepreneurship in society.
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