# Spec target setting using DEA Employs `inverse DEA` to estimate specifications(in/out-puts) to achieve a predetermined efficiency. ```r target.spec.dea(xdata, ydata, date=NULL, t=NULL, dt=NULL, dmu, et="c", alpha=NULL, beta=NULL, wv=NULL, rts="crs", sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex", bound=TRUE, pin=TRUE) ``` ## Arguments - `xdata`: Input(s) vector (**n** by **m**) - `ydata`: Output(s) vector (**n** by **s**) - `date`: Production date (**n** by **1**) - `t`: A vantage point from which the RoC is captured - `dt`: Delta **t** i.e., specs are estimated within PPS at **t+dt** - `dmu`: DMU whose inputs(or outputs) are to be estimated - `et`: Efficiency target; default value ("c") retains the current efficiency - `alpha`: Perturbed input(s) of designated DMU (**1** by **m**) - `beta`: Perturbed output(s) of designated DMU (**1** by **s**) - `wv`: Weight vector for scalarization (**1** by **m** or **s**) - `rts`: Returns to scale assumption `"crs"`Constant RTS (default) `"vrs"`Variable RTS `"irs"`Increasing RTS `"drs"`Decreasing RTS - `sg`: Employs second-stage optimization `"ssm"`Slack-sum maximization (default) `"max"`Date-sum maximization `"min"`Date-sum minimization - `ftype`: Frontier type `"d"`Dynamic frontier (default) `"s"`Static frontier - `ncv`: Non-controllable variable index(binary) for internal NDF (**1** by **(m+s)**) - `env`: Environment index for external NDF (**n** by **1**) - `cv`: Convexity assumption `"convex"`Convexity holds (default) `"fdh"`Free disposal hull (this will override `rts`) - `bound`: Puts upper/lower bounds on alpha/beta if `TRUE`(default) - `pin`: Includes the perturbed DMU in the PPS if `TRUE`(default) ## Returns - **`$alpha`**: Estimated input(s) - **`$beta`**: Estimated output(s) - **`$lambda`**: Intensity vector - **`$xslack`**: Input slack - **`$yslack`**: Output slack ## References Lim, Dong-Joon, "Inverse DEA with frontier changes for new product target setting." **European Journal of Operational Research** 254.2 (2016): 510~516. Wei, Quanling, Jianzhong Zhang, and Xiangsun Zhang. "An inverse DEA model for inputs/outputs estimate." **European Journal of Operational Research** 121.1 (2000): 151~163. ## Author(s) Dong-Joon Lim, PhD ## See Also `dm.dea` Distance measure using DEA `roc.dea` RoC calculation using DEA `target.arrival.dea` Arrival target setting using DEA ## Examples ```r # Reproduce Example 2 in Wei, Q. et al.(2000) # ready x <- matrix(c(1, 1, 1), 3) y <- matrix(c(4, 8, 5, 8, 4, 5), 3) a <- matrix(1.8, 1) w <- matrix(c(0.5, 0.5), 1) # go target.spec.dea(x, y, dmu = 3, alpha = a, wv = w, rts = "crs")$beta # Reproduce Table 4 in Lim, D-J. (2016) # Load engine dataset df <- dataset.engine.2015 # Subset for forced induction systems fis <- subset(df, grepl("^.C..", df[, 8])) # ready # Suppose one wants to estimate Porsche 911 turbo s' engine specs # to retain its current competitiveness with downsized 3.5 litre engine in 2018. # What might be the minimum specs to achieve this goal # considering the technological changes we've seen so far? # Plus, the CEO wants to put more emphasis on the torque improvement over HP. d <- subset(fis, select = 2) x <- subset(fis, select = 4) y <- subset(fis, select = 6 : 7) a <- as.matrix(3.5) w <- matrix(c(0.3, 0.7), 1) # go target.spec.dea(x, y, d, 2015, 3, 262, alpha = a, wv = w, rts = "vrs", sg = "min")$beta ```

target.spec.dea function