The proposed research focuses on the food production industry. More specifically, we are interested in evaluating the performance of this industry at firm-level. This will provide us the possibility to identify high performing firms, use them as reference units and analyze their common policies and characteristics. Since this study deals with evaluating the relative performance of one unit compared to others, the most appropriate method to be used is Data Envelopment Analysis (DEA). A major benefit of the DEA methodology is that, it supports the manager in order to take decisions in difficult cases, where complex relations exist between the multiple inputs and outputs involved in the activities of his/her company. This chapter presents an extensive case study involving the use of a well known Decision Support System (DSS) entitled DEA-Solver. For the purposes of this research, the most recent data available at the time of writing have been chosen, published by the Joint Research Centre (JRC) of the European Commission. Such a choice ensures the credibility, as well as the conformity of the sampled data. The proposed model uses several variables as inputs and outputs, i.e. the number of employees, capital expenditure, R&D investment, net sales, and operating profit. Furthermore, this research aims to identify key factors / policies, which play an important role in the success of a food producer. We believe that, these findings will be of great interest to all companies in the food production industry.
TopIntroduction
The disciplines of mathematics and informatics provide a number of tools essential for obtaining ‘good’ decisions in many sciences; the combination and implementation of these tools leads to what is generally referred to as DSS. As the sustainable use of resources is becoming due to various, very often unpredictable, factors more and more a necessity, the role of DSS will gradually increase, especially in key aspects of sustainability like the food sector and agricultural. DSS can be applied to various levels of these sectors, from local and national level to international level of organizations, like the European Union (EU). DSS in food industries and agriculture are fast evolving scientific disciplines with much to offer in key issues like sustainability of resources (Manos et al., 2004; Bournaris et al., 2002). The aim of this chapter is to present an extensive case study involving the use of a well known (DSS) entitled DEA-Solver. More specifically, this case study focuses on the evaluation of food production industry at firm-level. Since this study deals with evaluating the relative performance of one unit compared to others, the most appropriate method to be used is DEA. A major benefit of the DEA methodology is that, it supports the manager in order to take decisions in difficult cases, where complex relations exist between the multiple inputs and outputs involved in the activities of his/her company.
DEA method, initially proposed by Charnes et al. (1978), involves the use of linear programming tools to construct a non-parametric surface over the available data. Performance (or efficiency) measures are then calculated in relation to this surface. A brief outline of the DEA methodology, having an input orientation and assuming constant returns to scale (CRS), follows: suppose we have data on n inputs and m outputs for each of k firms. Thus, the data for all k firms, referred to as Decision Making Units (DMUs), are represented in the nxk input matrix X and the mxk output matrix Y. An efficiency measure of a DMU, for example the unit 1, is given by the ratio of all outputs over all inputs, such as u´∙y1 / v´∙x1, where u is an mx1 vector of output weights and v is an nx1 vector of input weights. The DEA problem is formulated as follows (Coelli et al., 2005; Talluri, 2000): find optimal values for u and v, such that the efficiency measure for the firm 1 to be maximized, subject to the constraints that the efficiency measures for each DMU must be less than or equal to unity. The optimal values are obtained by the solution of the mathematical programming problem (P.1):
subject to
∀
i = 1, 2, …,
kur, vj ≥ 0 (P.1)
Since this problem has an infinite number of solutions, a reformulation of the DEA model is required aiming to convert the objective function to a linear function. Hence, we can arbitrarily consider that the sum of inputs for the decision making unit 1 equals to one:
The DEA model is reformed to a linear programming problem, known as the “multiplier form”:
subject to
∀
i = 1, 2, …,
kpr, qj ≥ 0 (P.2)