A Method for Target Setting with Share Data

Document Type: research paper

Authors

1 Corresponding Author Departments of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Departments of Mathematics, Qazvin Branch, Islamic Azad University,Qazvin, Iran

Abstract

Data Envelopment Analysis (DEA) is a mathematical programming technique for evaluating
the relative efficiency of a set of Decision Making Units (DMUs) and can also be utilized for
setting target. Target setting is one of the important subjects since according to its results
efficiency can be increased. An important issue to be currently discussed, is to set target
while considering share data. These data for each individual indicate the share of the unit,
which takes part in an activity, from the whole amount which is a predefined constant. It is
obvious that the sum of units’ share is equal to the entire amount. Thus, any changes in the
magnitude of these data has to be dependent on the changes in data of other units. In this
paper a two-stage procedure is developed to find benchmark units where share data exist. The
fact that all DMUs are jointly projected onto the new efficient frontier and simplicity, are the
significant features of the proposed method. With a numerical example we demonstrate how
this method works.

Keywords


Article Title [Persian]

روشی برای الگویابی با داده های سهمی

Authors [Persian]

  • بیژن رحمانی پرچکلایی 1
  • زهره مقدس 2
1 گروه ریاضی، دانشگاه آزاد اسلامی، واحد تهران مرکزی، تهران، ایران
2 گروه ریاضی، دانشگاه آزاد اسلامی، واحد قزوین، قزوین، ایران
Abstract [Persian]

تحلیل پوششی داده­ها روشی بر مبنای برنام ه­ریزی ریاضی است برای ارزیابی کارایی نسبی و الگویابی مجموعه ه­ای از واحد­های تصمیم­ گیرنده. الگویابی و هدف گذاری معقوله بسیار مهمی می ­باشد زیرا به کمک آن می­ توان کارایی را بهبود داد. موضوعی که در این مقاله مورد بررسی قرار گرفته است الگویابی با داده­های سهمی است. داده هر واحد نشان دهنده سهم آن واحد از یک مجموع ثابت است. واضح است که سهم واحد­ها به یکدیگر وابسته است. پس هر تغییری در سهم یک واحد، واحد­های دیگر را تحت تاثیر قرار می­ دهد. در این مقاله یک روش دو مرحله ه­ای تعمیم یافته برای الگویابی در حضور داده­ های سهمی معرفی
می­ شود و با یک مثال مدل پیشنهادی بررسی می­شود

Keywords [Persian]

  • تحلیل پوششی داده ها
  • هدف گذاری
  • داده های سهمی

[1] J. Aparicio, J.L. Ruiz, and I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA, J Prod Anal. 28 (2007), pp.209–218.

[2] C. Baek, and J. Lee, The relevance of DEA benchmarking information and the Least-Distance Measure, Mathematical and Computer Modelling. 49 (2009), pp.265-275.

[3] R.D. Banker, A. Charnes, and W.W. Cooper, Some models for estimating technical and scale efficiencies in data envelopment analysis, Management Sience. 30 (1984), pp.1078-1092.

[4] A. Charnes, W.W. Cooper, and E. Rhodes, Measureing the efficiency of decision making units, European journal of operational reaserch. 2 (1978), pp.429-444.

[5] W.D. Cook, L.M. Seiford, and J. Zhu, Models for performance benchmarking: measuring the efficiect of e-business activities on banking performance, Omega. 32 (2004), pp.313–322.

[6] E. Gonzalez, and A. Alvarez, From efficiency measurement to efficiency improvemenT: The choice of a relevent benchmark, European journal of operational reaserch. 133 (2001), pp.512- 520.

[7] J.L. Hougaard, and H. Keiding, Continuous benchmark selections. Operations Research Letters. 32 (2004), pp.94-98

[8] J.L. Hougaard, and M. Tvede, Benchmark selection: An axiomatic approach, European journal of operational reaserch. 137 (2002), pp.218–228

[9] C.N. Madu, and C. Kuei, Application of data envelop analysis in benchmarking, International Journal of Quality Science. 3 (1998), pp.320-327

[10] A. Post, and J. Spronk, An integrated benchmarking approach to distribution center performance using DEA modeling, Journal of Operations Management. 20 (1999), pp.19-32.