Determining the Efficiency and Optimal Use of Inputs under Uncertainty Conditions for Production of Edible Mushrooms in Iran

The cultivation of edible mushrooms is expanding rapidly due to its nutritional and medicinal values as well as its economic benefits. However, lack of knowledge and principled management may cause many problems for producers or even bring them closer to the bankruptcy brink. The first step to improve the efficiency of units is finding an appropriate method to measure it. Data Envelopment Analysis (DEA) is one of the methods that is widely used to evaluate the relative efficiency of a homogenous set of DMUs. Despite the many advantages of this model, the high sensitivity of DEA to even a small change in the data reduces the validity of its results. In fact the conventional DEA assumes that input and output data are without any deviation. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. So In this paper, to deal with uncertainty in data the linear robust optimization framework of Bertsimas and Sim (2004) was used to compare technical efficiency of Iranian mushroom-producing provinces and determine the optimum use of inputs.
According to the purpose of this study, a robust data envelopment analysis (RDEA) model with imprecise inputs and outputs was used. The method is based on the robust optimization approach of Bertsimas and Sim (2004) which with the introduction of the conservative parameter (Γ) for each constraint, adjusts robustness in an optimisation model against the level of conservatism of the solution. The value of Γ is dependent on the maximum probability of constraint violation (p) and numbers of uncertain data in every constraint (n). So this RDEA model allows adjustment of level of robustness of the solution to trade-off between protection against constraint violation and conservatism of efficiency scores. In order to estimate the models, the GAMS software was used and related data was gathered from Statistical Center of Iran.
In this paper to distinguish the causes of technical inefficiency, pure technical efficiency and scale efficiency were measured. According to the results of this model, at all levels of P, the pure technical efficiency was higher than the scale efficiency and technical efficiency, and its value was higher than 98% in all cases. This indicates that mushroom producers have a high level of knowledge and skills in this field and shows that the cause of low technical efficiency of the producers is their non-optimal scale. In addition, according to the results of both RDEA and DEA models, the most important input that has caused the inefficiency of the units is the "seed cost" input and with optimal use of this input, the cost of that can be reduced by about 70% (in ε=0.1 and P=1). Another result of this study is that with the reduction of the Probability of constraint violation, the rate of technical efficiency has decreased. For example in ε=0.1, if P is reclined from 1 (no protection against uncertainty) to 0.8 and 0.1, the average technical efficiency is reduced from 93% to 89% and 85% respectively. Also when ε is increased from 10 to 20 and 30 percent (in P=0.1) the average technical efficiency is reduced from 85 to 83 and 82 percent. On the contrary by reducing P, the percentages of reduction compare to the actual value is increased. For instance by reducing P from 1 to 0.8 and 0.1 the percentages of reduction of "seed cost" are decreased from 70% to 78% and 80% respectively. This results highlights the importance of using RDEA models to more conformity of the results to the real world.
Based on the results the low technical efficiency of the producers is because of their non-optimal scale. Therefore, it is recommended to consider the optimal size unit for those who want to enter this activity. On the other hand, the policymakers should improve access to facilities so the small units could enlarge their unit if it's necessary. Also considering the experience of successful mushroom farms, self-reliance in production of mushroom seeds can greatly reduce inefficiency of the units. Eventually considering that the level of uncertainty has a great impact on the efficiency results and the optimal level of inputs, future researches on the appropriate level of uncertainty according to the real conditions of production can improve the results of the RDEA model.