Example $7\mathrm{.}3$ Burger Palace

An innovative drive$-$in$-$only burger chain has established six units in several different cities. Each unit is located in a strip shopping center parking lot. Only a standard meal consisting of a burger, fries, and a drink is available. Management has decided to use DEA to improve productivity by identifying which units are using their resources most efficiently and then sharing their experience and knowledge with the less efficient locations. Table $7\mathrm{.}5$ summarizes data for two inputs: labor$-$hours and material dollars consumed during a typical lunch hour period to generate an output of $100$ meals sold. Normally, output will vary among the service units, but in this example, we have made the outputs equal to allow for a graphical presentation of the units' productivity. As Figure $7\mathrm{.}19$ shows, service units $S_1,S_3,$ and $S_6$ have been joined to form an efficient$-$production frontier of alternative$)$ methods of using labor hours and material resources to generate $100$ meals. As can be seen, these efficient units have defined an envelope that contains all the inefficient units$-$thus the reason for calling the process "data envelopment analysis."

TABLE $7\mathrm{.}5$ Summary of Outputs and Inputs for Burger Palace

$\backslash$table$[[$Service Unit,Meals Sold,Labor$-$Hours,Material Dollars$],[1,100,2,200],[2,100,4,150],[3,100,4,100],[4,100,6,100],[5,100,8,80],[6,100,10,50]]$

Exercises

$7\mathrm{.}1.$ For the Burger Palace kxample, perform a complete analysis of efficiency improvement alternatives for unit $S_2,$ including determination of a composite reference unit.

$7\mathrm{.}2.$ For the Burger Palace example, perform a complete analysis of efficiency improvement alternatives for unit $S_5,$ including determination of a composite reference unit.

$7\mathrm{.}3.$ For the Burger Palace example, what is the effect of removing an inefficient unit from the analysis $($e$.$g$.,S_2)?$

$7\mathrm{.}4.$ For the Burger Palace example, what is the effect of removing an efficient unit from the analysis $($e$.$g$.,S_6)?$Example $7\mathrm{.}3$ Burger Palace

An innovative drive$-$in$-$only burger chain has established six units in several different cities. Each unit is located in a strip shopping center parking lot. Only a standard meal consisting of a burger, fries, and a drink is available. Management has decided to use DEA to improve productivity by identifying which units are using their resources most efficiently and then sharing their experience and knowledge with the less efficient locations. Table $7\mathrm{.}5$ summarizes data for two inputs: labor$-$hours and material dollars consumed during a typical lunch hour period to generate an output of $100$ meals sold. Normally, output will vary among the service units, but in this example, we have made the outputs equal to allow for a graphical presentation of the units' productivity. As Figure $7\mathrm{.}19$ shows, service units $S_1,S_3,$ and $S_6$ have been joined to form an efficient$-$production frontier of alternative$)$ methods of using labor hours and material resources to generate $100$ meals. As can be seen, these efficient units have defined an envelope that contains all the inefficient units$-$thus the reason for calling the process "data envelopment analysis."

TABLE $7\mathrm{.}5$ Summary of Outputs and Inputs for Burger Palace

$\backslash$table$[[$Service Unit,Meals Sold,Labor$-$Hours,Material Dollars$],[1,100,2,200],[2,100,4,150],[3,100,4,100],[4,100,6,100],[5,100,8,80],[6,100,10,50]]$