Reference no: EM13241508

Performance Analysis Corporation, founded in 1979, is a management consulting company that specializes in the use of management science to design more efficient and effective operations for a wide variety of chain stores. Performance Analysis Corporation has evaluated the operation of banks, savings and loans, and grocery chains. Recently, the company has been involved in evaluating the efficiency of fast-food outlets. In the following application, we describe how linear programming methodology has been used to provide an evaluation model for a chain of fast-food restaurants.

Fast-Food Business

The fast-food business for a chain such as Mc-Donald's or Kentucky Fried Chicken is characterized by hundreds, or even thousands, of individual restaurants, some of which are company owned and some of which are franchised. A typical restaurant may gross close to a million dollars annually, thus the impact of relatively minor improvements at a large proportion of the restaurants can have a substantial effect on a chain's profitability and market share.

Although each individual restaurant in a given chain usually offers the same type of menu (with some minor geographical variations), they must often deal with vastly different environments and competition. In addition, the age of the restaurant, facade used, ease of access and egress, hours of operation, scale of operation and so on can vary substantially from restaurant to restaurant.

A major objective of company management in the fast-food industry involves the performance evaluations of managers of individual restaurants in the chain. These evaluations are the basis for awarding year-end bonuses and for personal advancement purposes. Unfortunately, there is not a single measure of performance such as profit that can be used as the basis for the evaluation since other measures such as market share and rate of growth are also important.

A Linear Programming Evaluation Model
Once approach to the store evaluation problem utilizes the concept of Pareto optimality. According to this concept, a restaurant in a given chain is relatively inefficient if there are other restaurants in the same chain that have the following characteristics:

1. Have the same or worse environment

2. Produce at least the same levels of all outputs

3. Utilize no more of any resource and less of at least one of the resources.

The mechanism for discovering which of the restaurants are Pareto inefficient involves the development and solution of a linear programming model. **Constraints on the problem involve requirements concerning the minimum acceptable levels of output (e.g, profit and market share) and conditions imposed by uncontrollable elements in the environment). The objective function calls for the minimization of the resources necessary to produce the output. Solution of the model produces the following output for each restaurant:

1. A score that assesses the level of so-called relative technical efficiency achieved by the particular restaurant over the time period in question.

2. The reduction in controllable resources and/or the augmentation of outputs over the time period in question for an inefficient restaurants to have been rated as efficient.

3. A per group of other restaurants with which each restaurant can be compared in the future.

Sensitivity analysis, especially that concerning the dual prices, provides important managerial information. For each constraint concerning a minimum acceptable output level, the dual price tells the manager how much one more unit of output would increase his/her efficiency measure. Analysis of the ranges for each of the constraint coefficients (the aij values) provides information concerning how much outputs could be reduced or inputs increased before the restaurant would become inefficient.

Types of factors Utilized

The approach is capable of handling three types of factors: quantitative controllable factors, such as salaries paid or local advertising expenditures; noncontrollable quantitative factors, such as the median income in the geographic are served by the restaurant or the unemployment rate; and qualitative factors, such as the degree of competition or appearance of restaurant. The outputs include total sales of various types (e.g., by time of day), profits, market share, rate of growth of sales, and so forth.

Benefits

The analysis typically identifies 40-50% of the restaurants as underperforming, given the previously stated conditions concerning the inpiuts available and outputs produced. Performance Analysis Corporation has found that if all of the relative inefficiencies identified are eliminated simultaneously, the resulting increase in corporate profits is typically in the neighborhood of 5-10%. This is truly a substantial increase given the large scale of operations involved.
The district manager has an objective score card for each restaurant manager that indicates areas (e.g, overtime salary) where improvements may be in order. The efficient restaurants can be used to generate a set of best practices that can be models for other restaurants. Of primary benefits are the reactions of restaurant managers who appreciate that the evaluation process they are subject to recognizes the environment they are forced to operate within; deals with noncommensurability of outputs involved is theory based and nonpolitical; and is defensible understandable and equitable.

Questions

1. State in your own words what it means for one restaurant in a chain to be relatively inefficient when compared to another restaurant in the same chain.

2. Suppose the evaluation model showed that for a particular restaurant the resource mix necessary to produce a given output mix was 90% of what another restaurant was using to produce that same mix of output. Would you conclude that the restaurant was relatively efficient or inefficient? Why?