Is the model at PAC fairer than a more basic KPI $($such as gross revenue$)?$ What roles do efficiency and fairness play as a manager when considering all stakeholders? Give an example of how sensitivity analysis is used or could be used at your current organization or a company you would like to work forEVALUATING EFFICIENCY AT PERFORMANCE ANALYSIS CORPORATION$*$

Performance Analysis Corporation specializes in

the use of management science to design more

efficient and effective operations for a wide variety

of chain stores. One such application uses linear

programming methodology to provide an evalua$-$

tion model for a chain of fast$-$food outlets.

According to the concept of Pareto optimality,

a restaurant in a given chain is relatively inefficient

if other restaurants in the same chain exhibit the

following characteristics:

Operate in the same or worse environment

Produce at least the same level of all outputs

Utilize no more of any resource and less of at

least one of the resources

To determine which of the restaurants are Pareto

inefficient, Performance Analysis Corporation de$-$

veloped and solved a linear programming model.

Model constraints involve requirements concern$-$

ing the minimum acceptable levels of output and

conditions imposed by uncontrollable elements in

the environment, and the objective function calls

for the minimization of the resources necessary to

produce the output. Solving the model produces

the following output for each restaurant:

A score that assesses the level of so$-$called

relative technical efficiency achieved by the

particular restaurant over the time period in

question

The reduction in controllable resources or the

increase of outputs over the time period in ques$-$

tion needed for an inefficient restaurant to be

rated as efficient

A peer group of other restaurants with which

each restaurant can be compared in the future

Sensitivity analysis provides important manage$-$

rial information. For example, for each constraint

concerning a minimum acceptable output level,

the dual value tells the manager how much one

more unit of output would change the efficiency

measure.

The analysis typically identifies $40\%$ to

$50\%$ of the restaurants as underperforming,

given the previously stated conditions concern$-$

ing the inputs available and outputs produced.

Performance Analysis Corporation finds that if

all the relative inefficiencies identified are elimi$-$

nated simultaneously, corporate profits typically

increase approximately from $5\%$ to $10\%.$ This

increase is truly substantial given the large scale

of operations involved.

$*$Based on information provided by Richard C$.$ Morey

of Performance Analysis Corporation.