New slack model based efficiency assessment of public sector hospitals of Uttarakhand: state of India

Abstract

The total potentials for improvement in the efficiency of a DMU frequently remain unrevealed by calculating radial efficiency measure by basic data envelopment analysis (DEA) models. This paper, therefore, applies a new slack model (NSM) of DEA, which directly deals with input and output slacks, to assess the efficiency of 27 public sector hospitals of State of Uttarakhand (India) for the calendar year 2011. The study is undertaken with three inputs: number of beds, number of doctors and number of paramedical staff (PMS) and four outputs: number of outdoor-patients and number of indoor-patients including two case-mix outputs: number of major surgery and number of minor surgery received. The data for the study have been collected from the Directorate of Medical Health and Family Welfare, Government of Uttarakhand, Dehradun, India. The paper concludes that overall technical efficiency of average hospitals in the State is only 55.90 % which indicates that the hospitals have a high potential for improvement. Region-wise efficiency analysis reveals that the hospitals of Garhwal region are found to achieve relatively better efficiency score than their counterparts of Kumaon region. To examine the robustness of the results, sensitivity analysis is also conducted.

Appendices

Appendix 1: Some definitions

• (1) Overall Technical Efficiency (OTE): The efficiency score evaluated from CCR model is defined as OTE. It reflects the ability of a hospital to obtain the maximum outputs from the given set of inputs.

• (2) Pure Technical Efficiency (PTE): The efficiency score evaluated from BCC model is defined as PTE. It refers to the proportion of OTE which is attributed to the efficient conversion of inputs into outputs given the scale size.

• (3) Scale Efficiency (SE): The SE is defined as the ratio of OTE to PTE. It measures the impact of scale size on the efficiency of a hospital.

• (4) Efficient Hospital: A hospital is said to be efficient if and only if $\theta^{*}\,=\,1$ and slacks $s_{i}^{ - *}\,=\,s_{r}^{ + *}=0\, \forall \,i,\,\,r;$ otherwise it is called inefficient.

• (5) Peer: A peer is an efficient hospital which acts as a reference point for inefficient hospitals.

• (6) Peer Count: The frequency of an efficient hospital H occurring in all reference sets except the reference set of H is called the peer count.

• (7) Peer Weight: The multiplier value ($\lambda$-value) of an efficient hospital H which makes a reference set for an inefficient hospital is called the peer weight.

• (8) Reference Set: A set of efficient hospitals whose combination makes an inefficient hospital efficient is called the reference Set.

• (9) Slacks: The quantity of excess resources used and deficient outputs produced by an inefficient hospital to become efficient after radial change to reach the efficiency frontier are known as input slacks and output slacks respectively.

Appendix 2

See Table 8

Table 8 List of selected hospitals of Uttarakhand State