A bargaining game model for efficiency decomposition in the centralized model of two-stage systems

A network DEA approach for series multi-stage processes

“…*** Insert Table 6 about here *** *** Insert Table 7 about here *** As shown in Table 7, in all units except one (namely the unit 24) the second phase program (23) did not alter the efficiency scores obtained by model (22). For unit 24, the second phase program increased the stage-1 efficiency score from 0.9623 to 1 without decreasing the efficiency score of stage-2 (0.8658).…”

“…If ‫̂ݏ‬ଵ = ‫̂ݏ‬ଶ = 0, then the optimal solution of (22) is already Pareto optimal, and model (23) does not alter the efficiency scores obtained by (22).…”

“…Liang et al [20] and Cook et al [6] studied the efficiency decomposition in two-stage processes using game theoretic concepts. Zhou et al [22] approached the efficiency decomposition in simple two-stage processes as a Nash bargaining game. Li et al [19] used a parametric approach to assess the efficiency of DMUs with extra inputs in the second stage, in the frame of the multiplicative approach.…”

Two-stage DEA models with undesirable input-intermediate-outputs

“…As in [13] If we adopt radial measure for initial inputs, which means that all initial inputs can be proportionally reduced without reducing the final outputs, we can construct the following model for DMU 0 : Here, the optimal value * θ is the maximal proportionate reduction of inputs allowed by the production possibility set (8).…”

“…Under the Nash bargaining theory, Du et al treated the two stages as two players and then constructed a game model to evaluate the overall and individual efficiencies [7]. Zhou et al developed a Nash bargaining game model to obtain fair efficiency decompositions for the centralized model while keeping the system efficiency unchanged [8]. The above models can only deal with the assumption of constant returns to scale (CRS).…”