Generalized Returns To Scale has been introduced to compute the rate of variation in outputs to the variation in inputs up to the Most Productive Scale Size pattern. In this paper, we address the generalized RTS in the multiplicative models and we propose an algorithm to calculate the rate of variations in different intervals. We also demonstrate that the non-discretionary factors can be easily taken into account in the algorithm. Manuscript profile

Identification of various sources of inefficiency plays an important role in the performance analysis aimed at developing plans for the improvement of decision making. In this regard, not only technical, cost, and allocative efficiency can be estimated by information on inputs and outputs and their prices, but losses due to the lack of profit and revenue and optimal cost can also be calculated based on the relevant inefficiency. The present paper aimed at providing new estimation of cost efficiency and sources of losses in the total efficiency in a non-competitive environment where there is the possibility of change in prices of inputs and outputs from one DMU to another. In line with studies (Tone .K, "A Strange Case of the Cost and Allocative Efficiencies in DEA". Journal of the Operational Research Society 53, (2002), pp.1225-1231) and (Tone. K., Tsutsui, M. "Decomposition of Cost Efficiency and its Application to Japanese-Us Electric Utility Comparisons". Socio-Economic Planning Sciences 47 (2007), pp.91-106), the present study sought to introduce new sources of inefficiency and related losses by presenting new price-based and cost-based production possibility sets. Manuscript profile

Cross efficiency is a method with the idea of peer evaluation instead of self-evaluation, and is used for evaluation and ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA). Unlike most existing DEA ranking models which can only rank a subset of DMUs, for example non-efficient or extreme efficient DMUs, cross efficiency can rank all DMUs, even non-extreme ones. However, since DEA weights are generally not unique, cross-efficiency which uses optimal weights corresponding to evaluation of DMUs may not be unique either. This deficiency renders the cross efficiency method useless. However, the secondary goals proposed to deal with this deficiency of cross efficiency have such drawbacks themselves as well. In this paper we present a new secondary goal for cross efficiency method based on the lexicographic method. The main advantage of the proposed method is that with the possibility of existence of alternative optimal weights at the end of the secondary goal problem, the performance and the rank of DMUs will be constant, while the previous secondary goal methods don't offer any suggestions to deal with their alternative optimal weights. Manuscript profile