# Statistical Case Study

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for $19.77 Statistical Case Study: The Possibility

Statistical analysis may be a useful tool in examining the possibilities which are open to a business, and may be used to assist in the decision-making process. This paper will examine the use of the statistical technique known as linear programming in relation to two case studies based in the restaurant business.

The first case-study is based upon the restaurant "The Possibility," a new start-up venture in which two friends, Angela and Zooey, were aiming to provide a French dining experience where there were no other businesses doing so in the area. The problem to be solved in this case study involved determining how many meals to prepare each night in order to maximize their profitability from the venture. Additional parameters which were to be considered included staffing requirements, dietary concerns of customers, and reduction of waste to reduce overheads.

The second case-study also focused on "The Possibility," but centered around a set of slightly more complex decisions, related to changes in the business which may or may not increase profitability. The first of these related to an analysis of the cost-effectiveness of advertising in relation to boosting profits. The second question related to the impact which reducing labor input may have on profitability, and finally the impact of increasing the sale price of their dinners.

It is likely that operational research would be useful to the owners of the Possibility in finding the optimal solution to these problems. There is significant evidence available as to the utility of operations research in the restaurant industry, and a brief summary of that research is provided in the next section.

Operations Research in the Restaurant Industry

The use of 'scientific management' in the restaurant sector is a concept which stemmed originally from Taylor's Principles of Scientific Management, published in 1911. This used scientific and mathematical techniques to demonstrate how the different service elements could measured, predicted and therefore tailored to requirements. It is the application of these techniques from the 1950s onwards which has seen the successful development of many of the fast-food chains, such as McDonalds. This concept was further developed by Sasser in 1976, who described the importance of these scientific techniques for balancing supply and demand (Chase & Apte, 2007).

The use of scientifically-based research into business strategies for improvement of service provision is now more commonly known as 'operations research'. This operations research may be used in many areas of the restaurant business. For example it is may be possible to use these techniques to determine pricing strategies, ways of improving customer satisfaction, how to model staff schedules, and so on. There are many tools which may be used in operations research, although this paper is concerned with one specific tool - linear programming.

Linear programming works as a means of predicting the impact which different decisions will have on the profitability of a particular firm, by assuming that certain inputs are used to create certain outputs. The inputs may be either exogenous (uncontrollable) or controllable factors (Sanjeev, 2007), although it is impact of changes to the controllable factors which are likely to be of most interest. For example in the restaurant industry the input factors which would be considered may include the cost of food which is used for meal preparation and staffing factors, while the outcome is most likely profits generated, but may be customer satisfaction or other such factors of interest.

In particular, it has been shown that linear programming is an effective way to measure the staffing needs of a particular service, particularly where there are different skill levels and different roles to take into account. Evidence from nursing shows that linear programming may be used to take account of these factors and create a far more efficient staff schedule than would be possible through manual allocation alone (Jaumard et al., 1998). A similar situation exists in the restaurant industry, where there are many different roles to schedule, for example chefs, waitresses, kitchen assistants, and so on. Therefore linear programming is likely to be beneficial here also, and in fact Brusco and Johns (1998) show that linear programming not only eases the task of producing a schedule with an adequate skill mix, but also allows for the optimal productivity to be gained.

Data envelopment analysis (DEA) is a technique which has been used since the 1970s, when it was developed by Charnes and colleagues (1978, cited in Chase & Apte, 2007). This technique is aimed at measuring the overall operating efficiency of a service enterprise, although it is usually applied to organizations operating multiple units, for example restaurant chains. A DEA model utilizes linear programming within, but the complexity which is added by considering multiple units means that more complex operations are also included. The end product is a measurement of which units in the organization are operating efficiently and which are not. The analysis also allows for identification of how efficiency may be improved in these units.

There have been numerous studies which have shown that this is an effective method for improvement of overall organizational profitability. Some of these studies have focused on one specific organization, and have been conducted in an attempt to highlight strategies specific to that organization. For example Gimenez-Garc'a et al. (2007) used the linear programming-based DEA approach to determine which units in a Spanish restaurant chain were not performing to the same efficiency standards as the others. Other studies have focused on a much larger sample, for example the study by Sanjeev (2007) examined the efficiency of the entire restaurant and hotel industry in India.

These studies have overall shown that linear programming-based approaches are simpler than many other approaches. They have also been shown to be at least as effective at analyzing business efficiency in the restaurant sector as more traditional financial ratio analysis approaches (Sanjeev, 2007). Aside from the lower complexity in the use of linear programming and DEA, there are also other advantages over financial ratio analysis. This includes the fact that it focuses predominantly on the technical aspects of production, and is not based on assumptions on the cost of inputs and outputs (Banker & Morey, 1986). This basically means that rather than estimating the likely profit which will result from making a change, the estimate is instead of which action is likely to produce the most profit.

Although linear programming-based approaches have been an integral part of the operational research toolbox for a number of years now, there are still many researchers attempting to develop the capabilities of the technique further. This is evident in the vast amount of literature which appears regularly in the major peer-reviewed journals related to operations management (Gattoufi et al., 2004). Therefore it is likely that in time there will become ever more sophisticated tools available for managers in the restaurant industry, to assist them in making complex business decisions. However for many small restaurants, it is possible that the simplest linear programming techniques which are already available would provide a sufficient tool to allow them to better judge the outcomes of their business options.

Given the application which linear programming may have for the restaurant industry, it may be seen that each of these problems detailed in the introduction lends itself well to analysis with a linear programming model. This technique is therefore demonstrated in this paper using Microsoft Excel, and is used to model and solve the problems in the case studies.

Determining the Number of Meals to Prepare

The problem in the first case study relates to the number of meals which should be prepared each night at the restaurant if the profitability is to be maximized. The first step is to establish the constraints on the linear programming problem. It was already determined that there would be only two types of dishes served at the restaurant - beef dishes and fish dishes. Therefore the beef dishes are labeled as the first variable, X1, and the fish dishes are labeled as the second variable, X2. Now the profit from each fish dinner sold is around $12, and the profit from each beef dinner sold is around $16. This means that the overall profits which are made, which will be termed Z, would be given by:

16X1 + 12X2

The first constraint which must be taken into account in this decision is the labor requirements for the dishes. It is estimated that each beef dish requires 1/2 an hour to prepare, while each fish dish requires 1/4 an hour to prepare. Therefore the total labor required is given by:

Labour = 1/2 X1 + 1/4 X2

As there are only 20 hours of labor available for all the food preparation each day, this therefore gives the constraint:

X1 + 1/4 X2 ? 20

It has also been determined that the total number of dinners prepared each night will be less than 60, which gives:

X1 + X2 ? 60

However it has also been identified that at least 10% of… [END OF PREVIEW] . . . READ MORE

for $19.77 Statistical Case Study: The Possibility

Statistical analysis may be a useful tool in examining the possibilities which are open to a business, and may be used to assist in the decision-making process. This paper will examine the use of the statistical technique known as linear programming in relation to two case studies based in the restaurant business.

The first case-study is based upon the restaurant "The Possibility," a new start-up venture in which two friends, Angela and Zooey, were aiming to provide a French dining experience where there were no other businesses doing so in the area. The problem to be solved in this case study involved determining how many meals to prepare each night in order to maximize their profitability from the venture. Additional parameters which were to be considered included staffing requirements, dietary concerns of customers, and reduction of waste to reduce overheads.

The second case-study also focused on "The Possibility," but centered around a set of slightly more complex decisions, related to changes in the business which may or may not increase profitability. The first of these related to an analysis of the cost-effectiveness of advertising in relation to boosting profits. The second question related to the impact which reducing labor input may have on profitability, and finally the impact of increasing the sale price of their dinners.

It is likely that operational research would be useful to the owners of the Possibility in finding the optimal solution to these problems. There is significant evidence available as to the utility of operations research in the restaurant industry, and a brief summary of that research is provided in the next section.

Operations Research in the Restaurant Industry

The use of 'scientific management' in the restaurant sector is a concept which stemmed originally from Taylor's Principles of Scientific Management, published in 1911. This used scientific and mathematical techniques to demonstrate how the different service elements could measured, predicted and therefore tailored to requirements. It is the application of these techniques from the 1950s onwards which has seen the successful development of many of the fast-food chains, such as McDonalds. This concept was further developed by Sasser in 1976, who described the importance of these scientific techniques for balancing supply and demand (Chase & Apte, 2007).

The use of scientifically-based research into business strategies for improvement of service provision is now more commonly known as 'operations research'. This operations research may be used in many areas of the restaurant business. For example it is may be possible to use these techniques to determine pricing strategies, ways of improving customer satisfaction, how to model staff schedules, and so on. There are many tools which may be used in operations research, although this paper is concerned with one specific tool - linear programming.

Linear programming works as a means of predicting the impact which different decisions will have on the profitability of a particular firm, by assuming that certain inputs are used to create certain outputs. The inputs may be either exogenous (uncontrollable) or controllable factors (Sanjeev, 2007), although it is impact of changes to the controllable factors which are likely to be of most interest. For example in the restaurant industry the input factors which would be considered may include the cost of food which is used for meal preparation and staffing factors, while the outcome is most likely profits generated, but may be customer satisfaction or other such factors of interest.

In particular, it has been shown that linear programming is an effective way to measure the staffing needs of a particular service, particularly where there are different skill levels and different roles to take into account. Evidence from nursing shows that linear programming may be used to take account of these factors and create a far more efficient staff schedule than would be possible through manual allocation alone (Jaumard et al., 1998). A similar situation exists in the restaurant industry, where there are many different roles to schedule, for example chefs, waitresses, kitchen assistants, and so on. Therefore linear programming is likely to be beneficial here also, and in fact Brusco and Johns (1998) show that linear programming not only eases the task of producing a schedule with an adequate skill mix, but also allows for the optimal productivity to be gained.

Data envelopment analysis (DEA) is a technique which has been used since the 1970s, when it was developed by Charnes and colleagues (1978, cited in Chase & Apte, 2007). This technique is aimed at measuring the overall operating efficiency of a service enterprise, although it is usually applied to organizations operating multiple units, for example restaurant chains. A DEA model utilizes linear programming within, but the complexity which is added by considering multiple units means that more complex operations are also included. The end product is a measurement of which units in the organization are operating efficiently and which are not. The analysis also allows for identification of how efficiency may be improved in these units.

There have been numerous studies which have shown that this is an effective method for improvement of overall organizational profitability. Some of these studies have focused on one specific organization, and have been conducted in an attempt to highlight strategies specific to that organization. For example Gimenez-Garc'a et al. (2007) used the linear programming-based DEA approach to determine which units in a Spanish restaurant chain were not performing to the same efficiency standards as the others. Other studies have focused on a much larger sample, for example the study by Sanjeev (2007) examined the efficiency of the entire restaurant and hotel industry in India.

These studies have overall shown that linear programming-based approaches are simpler than many other approaches. They have also been shown to be at least as effective at analyzing business efficiency in the restaurant sector as more traditional financial ratio analysis approaches (Sanjeev, 2007). Aside from the lower complexity in the use of linear programming and DEA, there are also other advantages over financial ratio analysis. This includes the fact that it focuses predominantly on the technical aspects of production, and is not based on assumptions on the cost of inputs and outputs (Banker & Morey, 1986). This basically means that rather than estimating the likely profit which will result from making a change, the estimate is instead of which action is likely to produce the most profit.

Although linear programming-based approaches have been an integral part of the operational research toolbox for a number of years now, there are still many researchers attempting to develop the capabilities of the technique further. This is evident in the vast amount of literature which appears regularly in the major peer-reviewed journals related to operations management (Gattoufi et al., 2004). Therefore it is likely that in time there will become ever more sophisticated tools available for managers in the restaurant industry, to assist them in making complex business decisions. However for many small restaurants, it is possible that the simplest linear programming techniques which are already available would provide a sufficient tool to allow them to better judge the outcomes of their business options.

Given the application which linear programming may have for the restaurant industry, it may be seen that each of these problems detailed in the introduction lends itself well to analysis with a linear programming model. This technique is therefore demonstrated in this paper using Microsoft Excel, and is used to model and solve the problems in the case studies.

Determining the Number of Meals to Prepare

The problem in the first case study relates to the number of meals which should be prepared each night at the restaurant if the profitability is to be maximized. The first step is to establish the constraints on the linear programming problem. It was already determined that there would be only two types of dishes served at the restaurant - beef dishes and fish dishes. Therefore the beef dishes are labeled as the first variable, X1, and the fish dishes are labeled as the second variable, X2. Now the profit from each fish dinner sold is around $12, and the profit from each beef dinner sold is around $16. This means that the overall profits which are made, which will be termed Z, would be given by:

16X1 + 12X2

The first constraint which must be taken into account in this decision is the labor requirements for the dishes. It is estimated that each beef dish requires 1/2 an hour to prepare, while each fish dish requires 1/4 an hour to prepare. Therefore the total labor required is given by:

Labour = 1/2 X1 + 1/4 X2

As there are only 20 hours of labor available for all the food preparation each day, this therefore gives the constraint:

X1 + 1/4 X2 ? 20

It has also been determined that the total number of dinners prepared each night will be less than 60, which gives:

X1 + X2 ? 60

However it has also been identified that at least 10% of… [END OF PREVIEW] . . . READ MORE

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Statistical. (2008, August 6). Retrieved January 25, 2020, from https://www.essaytown.com/subjects/paper/statistical-case-study/8229229MLA Format

"Statistical." 6 August 2008. Web. 25 January 2020. <https://www.essaytown.com/subjects/paper/statistical-case-study/8229229>.Chicago Format

"Statistical." Essaytown.com. August 6, 2008. Accessed January 25, 2020.https://www.essaytown.com/subjects/paper/statistical-case-study/8229229.