Allocating fixed costs and resources via data envelopment analysis

In this paper we first (trivially) show that data envelopment analysis can be viewed as maximising the sum of the efficiencies of the decision-making units (DMU's) in the organisation. Building upon this we present nonlinear models for: (a) allocating fixed costs to DMU's and (b) allocating resources to DMU's. Simultaneous to allocating resources output targets are also decided for each DMU. Numeric results are presented for a small example problem. 1 1. INTRODUCTION Data envelopment analysis (DEA) was first put forward by Charnes, Cooper and Rhodes [10] in 1978 and is used for evaluating the (relative) efficiency of decision-making units (DMU's) in an organisation via weights attached to input/output measures. The standard interpretation of DEA is that each DMU separately chooses those weights that maximise its efficiency. In fact it is trivial to show that an equally valid interpretation of DEA is that weights are chosen simultaneously for all DMU's so as to maximise total organisational efficiency. However this interpretation of DEA as maximising organisational efficiency is a powerful one. Based upon it we develop in this paper models for: (a) allocating fixed costs to DMU's; and (b) allocating resources to DMU's. As will become apparent below the model we develop for allocating resources to DMU's simultaneously decides output targets for each DMU. Numeric results are presented for a small example problem to illustrate our models. We assume throughout this paper some familiarity with DEA. Readers new to DEA are referred to [5,7,9,18,26]. 2 2. REINTERPRETING DEA Let: s be the number of output measures t be the number of input measures n be the number of DMU's which are being evaluated with respect to one another y ip be the value (≥0) of output measure i x jp be the value (≥0) of input measure j (j=1,...,t) for DMU p (p=1,...,n) u ip be the weight (≥0) attached to output measure i v jp be the weight (≥0) attached to input measure j e pq be the (relative) efficiency of DMU q (q=1,...,n) when evaluated using the weights associated with DMU p ε be a very small "non-Archimedean" number (>0) then e pq is defined by: e pq =(u ip y iq)/(v jp x jq) Note here that e pq is the cross-efficiency of DMU q when evaluated using the weights associated with DMU p (see [15,27,31]). The standard DEA approach is to determine the efficiency (e pp) of …