## Overview and purpose of the report

Throughout Shuzworld’s history, the company has been facing cost minimization challenges. Therefore, it has to choose between outsourcing, reconditioning of its existing equipment, and purchase of new equipment. On the other hand, the production of shoe soles for its sneaker shoes has become the company’s major concern because it is anticipated that it will be at the market if quality will be maintained. To help underpin these needs, numerous processes are supposed to be reviewed.

## Executive summary

As per the request to undertake a survey of the company’s production machine needs, sales forecasting, and machine capacity, I enlisted some of the findings and proposals for your consideration. The sandal manufacturing option that will be the most cost-effective is the reconditioning of the existing equipment. The analysis shows that future costs shall be reduced upon adopting this plan. The company is only required to set aside $75,000 to $350,000 in order to acquire the volume output of readymade sneakers of between 25,000 and 300,000 units.

Concerning sales forecasting, the two methods applicable are the least-squares and exponential smoothing forecasting methods. Lastly, the processes at the production of shoe soles and eye letting are out of control. Therefore, capacity and system specifications are below the expected scope. Frequency in monitoring the process flow is recommended in order to detect early unusual changes in the quality of production. The following detailed scenario assessment that has helped in arriving at the mentioned proposed changes.

- Recommend which method (i.e., using reconditioned equipment, purchasing new equipment, or outsourcing to another manufacturing operation) Shuzworld should use for the manufacturing of its sneakers, utilizing the appropriate decision analysis tool.

The main objective of this question is to undertake a critical analysis of the three different alternatives presented and to establish the most efficient alternative among them. After analyzing the presented situation, it is recommended that Shuzworld should recondition its existing machine in the manufacturing of its sneakers. According to the crossover chart analysis tool, this is the most cost-efficient manufacturing method.

The tool determines the exact volume at which one manufacturing process gets more expensive than another. To calculate volume (V1), the crossover point between outsourcing and reconditioning the existing equipment is obtained. The second volume (V2) is the crossover point between reconditioning and buying new equipment. The equation for V1 is 0 + 3V1= 50,000 + V1. Therefore, V1 is 25,000 units. The equation for V2 is 50,000 + V2= 200,000 + 0.5V2.

Therefore, V2 is 300,000. After the analysis, it is determined that it would cost Shuzworld $75,000 to outsource 0 to 25,000 units of sandals. Additionally, buying new equipment would cost the company $350,000 or more to produce 300,000 units or more. However, reconditioning of the existing equipment would cost the company $75,000 to $350,000 to produce the desired volume of 25,000 to 300,000. Therefore, reconditioning is the most cost-effective means of manufacturing Samba sandals; both outsourcing and buying of new equipment would be the least cost-effective. The above information is supported by the below table:

## Explanation as to the reason for using the chosen analysis tool

The decision analysis tool that I chose to use is a crossover chart. This is because it is one of the best tools that can provide the desired results to this problem. For example, the tool can provide optimal production volumes or crossover points between the three sandal manufacturing options. It does this by identifying the point where the total costs of the manufacturing options change. This way it is possible to solve the costs expected from each option. This means that it can provide the most viable decision while at the same time minimizing costs. This way, the decision-maker can disregard costly options and adopt the least costly options.

### Recommendations

From the theoretical analysis, the Shanghai production plant should recondition the existing equipment for purposes of manufacturing the desired 25,000 to 300,000 units of Samba sandals. This is because such a step would be the least expensive.

From the cross over chart model, reconditioning would the most cost effective for production of the desired 25,000 to 300,000 units while buying of new equipment would be cost effective for production of 300,000 or more units of sandals. Additionally, outsourcing is only cost effective for production of 0 to 25,000 units. This leaves reconditioning as the most financially viable option for production of the desired volume output range (Eiselt & Sandblom, 2010).

- Develop a sales volume forecast using the least squares method and one other forecasting method.

Forecasting using exponential smoothing is used in formulating sales forecasts for Shuzworld. This forecasting will assist in making the following decisions:

- To help make sound decisions in production and supply of its commodities to its retail shop located at four corners retail in Galleria. This will enable it to prepare for the forecasted sales, which equal the amount of sales that would be expected at a particular quarter of the year.
- To help put up the best strategic marketing plan that will enable Shuzworld to position itself better in future with regards to market control in four corners galleria.

To assist accomplish this decision; two methods of sales forecasting have been identified as the most applicable to its situation. They include the least squares method and regression using exponential smoothing with constants.

## Method of least squares

This approach arrives at future forecasts by way of fitting a linear regression line that defines the trend in future business sales. The excel decision analysis tool used in the least squares method is the linear trendline.

The tool’s trend line equation is used in estimating future trends and is usually in the form of Y= mx + b where Y is the current sales volume, m is the skype/ slope or the gradient; x is the value of t which represents quarters. B is the value of the y-axis intercept. Y^{t} is the forecasted future sales. In this case, the value of m is 3683.3 while the value of b is 85028. T in quarters has been arranged numerically from 1 to 10 quarters. Therefore, the equation for forecasted sales is Y^{t }=3683.3x + 85028. Therefore, forecasted sales for Shuzworld’s next quarter are 121,861. The above information is portrayed in the below table

The regression line and equation shown below has been plotted using excel trendline tool. The gradient (slope) of the curve is positive meaning that the x-axis figures are directly related with the y-axis figures. Therefore, sales are projected to increase as the years increase. The linear regression equation obtained for forecasting purposes is y^{t}= 3683.3x + 85028. This is used to forecast future sales. Y^{t} represents the forecasted sales volume while x is time. Time (quarters) has been arranged alphabetically from 1 to 10. The points on the curve represent the current sales volumes for different periods.

## Exponential smoothing

Exponential smoothing is a widely accepted forecasting tool in fields such as businesses, hospitals, and politics among others. To demonstrate how Shuzworld can employ this methodology in forecasting future sales, we estimate quarter 3 of 2009 using 0.3 as the smoothing constant for the average and 0.4 as the smoothing constant for the trend. These smoothing constants can also stand for alpha and beta consecutively.

This form of exponential smoothing which allows forecasting for various trends is referred to as Holt’s method. It is also called the trend adjusted exponential smoothing. It involves three processes as follows: smoothing the series levels, smoothing the trend and forecasting sales with the trend. By using this method the forecasted sales volume for the 3^{rd} quarter of 2009 is 121,620. Since the smoothing constant was small, it indicates that the choice of a smoothing constant has an impact on the general outlook of sales forecasts.

The higher the constant, the lower the variation in trend and as it tends towards 100% or 1, the preceding forecasts tends to be almost the same as the previous figure and vice- versa. The estimated figures in the table below illustrate the behavior of this method of forecasting (Eiselt & Sandblom, 2010).

## Comparing the results using exponential smoothing and least squares

Using two different methods yield statistically different results. In order to know the best or most accurate method to use for forecasting the Mean Squared Error (MSE) and the Mean Absolute Deviation (MAD) techniques are used. In the MSE technique, the average of errors of historical data is squared and summed while in the MAD technique the average of the errors of historical data is summed but it is not squared.

The forecasting method that reduces or minimizes the errors is selected as the best forecasting method as it indicates the minimum errors. In this case, the least squares method has the least Mean Squared Error and the least Mean Absolute Deviation. Therefore, it is the most appropriate tool for use in forecasting Shuzworld’s sales. On the other hand exponential smoothing using an alpha of 0.3 and a beta of 0.4 has the highest Mean Squared Error and the highest Mean Absolute Deviation. Therefore, it should be the last option to use for forecasting, as it is the least accurate (Fan & Yao, 2005). The excel sheet named ‘MSE & MAD’ can be used as reference.in order to confirm the MSE and MAD calculations used at arriving at the above conclusions.

### Recommendations

It is recommended that Shuzworld should consider the least squares method of estimating/ forecasting its future sales. This is the most appropriate approach since it minimizes errors because it has the least Mean Squared Error and Mean Absolute Deviation. For example, the least squares method has an MAD of 4,183.92 while the exponential smoothing method using the two constants has an MAD of 5,142.63. Additionally, the least squares method has an MSE of 23,356,172.85 while exponential smoothing has an MSE of 51,038.609.60. Therefore, the least squares method is the recommended method as it has the least errors. This recommendation can be supported by the attached excel sheet.

C. Discuss how to apply control chart metrics to improve quality in the Shuzworld production line.

Historically, the use of control charts has helped organizations to trace variations in quality of production. Samples are taken from the process and quality is measured against the set rubrics or key performance indicators (KPIs). This helps to identify those process points or factors that are contributory to the existing poor quality of a production process (Bouyssou, 2006).

In the case of Shuzworld, the current process limit has been set as 99.73% with process standard deviation of 0.5. From these components, the process mean can be derived from the simple formula that states that the control limit of a given process is always three point’s standard deviation from the process mean. This statement can be summarized in a mathematical representation as follows: ½(UCL + LCL) = ½(10.375+9.625) = 10.00

In assessing the current production risks that arise from the process falling out of control, it is found that the process capacity (CP) is 37.5% out of control; hence, it fails to meet the quality specifications (Ryan, 2011).

Capacity index indicates that the process is way below the expected or set control limits. The Shuzworld Company needs to amend production quality of the soles for its sneakers shoes.

Studying the control chart on production of soles, a six-sigma rule is applied adequately during this process.

There are 2 out of 3 consecutive points that fall beyond the area above and below the 2 standard deviations from the mean. These points are observable on the thirteenth and fourteenth hour of production process. However, most of the process flow is observed to be in-control since only two out of the fifteen sampled points exhibit unusual process behavior (Ragsdale, 2010).

Although the process is somewhat in control, its capacity analysis reveals that it is still not capable of satisfying process specifications as set out in the production policies and processes. It follows therefore that the production team should move in to identify those cause actions that have rendered the process out of control in order to realize quality that meets the desired specifications.

To improve the process capacity in production of soles, it is recommended that the sampling of process outcomes be increased. This is because a large sample is always a better way of representing a situation. The interval or the frequency of data sampling during the production process should be stepped up to allow early detection of process variations. In doing this, the production variations will notify those involved in the process (say machine operators) that remedial or process action change is necessary for quality production.

## Reason for using the tool

Since the process variations in the production process have a huge bearing on the quality of products and services, the concept of using control charts becomes necessary. This tool allows very simple but effective identification of events that indicate process change (Ryan, 2011). This will be of great help to Shuzworld since it offers objective criteria for implementation of change. Generally, when the tool is applied in future, notable changes in the process can be used to detect either bad cause or good cause. Where good cause is seen to be eminent, it shall provide a better ground for new working methodology whereas bad causes are eliminated (Ryan, 2011). The figure below shows a copy of the excel decision tool used to evaluate the quality of the production plant at Shuzworld company.

## Analysis of the eye letting machine

The eye letting chart is used to evaluate an organization’s efficiency and effectiveness in the production process. Samples are taken from the process and trend performance is measured against the set rubrics or key performance indicators (KPIs) like in the control chart. This helps to identify those process points or factors that are outside the set boundaries.

The analysis of the eye letting chart reveals that the process is still not in control. This is because just like the control chart, there are two process points that are above the control boundaries. These points are 10.8 and 10.6 which are observed during the thirteenth and the fourteenth hour consecutively. They are above the set upper boundaries of 10.4. These points may represent production volume. They indicate that the production process was above the average during that particular production period.

Therefore, the available production resources were being over utilized. However, the other 12 points are within both the upper and the lower boundaries. Therefore, it is clear that the chart has not yet met the required specifications meaning that there is abnormality in the production process. The two stray points exist when production is beyond or below the desired levels. In this case, production is beyond the desired levels. The situation needs to be improved in order for Shuzworld to minimize wastage and to ensure efficient use of its resources.

In order to improve the situation the sampling size or production process/ volume can be slowed down in order to be able to identify errors. If the sample is reduced to 10 points, then it is easier to identify the specific issues that are affecting Shuzworld’s overall production process.

Additionally, the production engineers can change the upper boundaries in order to increase tolerance level and to reduce errors. For example, they can be set it at 11 or 12 so that many points can fall within the set boundaries. It is also important to change the production components and to conduct market research in order to identify the desirable production components. Obtaining knowledge from experienced engineers can help in identifying the ideal or optimal production levels rather than using trial and error techniques.

## Conclusion

The discussed recommendations to the situations at Shuzworld retail shop would be most welcome in helping the managerial group in designing the best supply chain.

Shuzworld would be the most efficient company if it reconditions its existing manufacturing equipment for production of Samba sneakers. Additionally, the production of shoe soles can be stepped up by increasing the process capacity and improving the few observed conditions that render the process to be slightly out of control (Rausand & Arnljot, 2004). The production department should institute a policy of regularly monitoring system output that would help in detecting early variations in quality for reduced defective products. The various decision making tools that have been used to obtain profit maximization, cost minimization, regression and charting analysis are attached here in.

## References

Bouyssou, D. (2006). *Evaluation and Decision Models with Multiple Criteria: Stepping Stones for the Analyst*. University of Bruxelles: Birkhäuse.

Eiselt, H. A., & Sandblom, C. (2010). *Operations Research: A Model-Based Approach*. New York, NY: Springer.

Fan,J., & Yao, Q. (2005). *Nonlinear Time Series: Nonparametric and Parametric Methods*. New York: Springer.

Ragsdale, C. (2010). *Spreadsheet Modeling & Decision Analysis*. New York: Cengage Learning.

Rausand, M., & Arnljot, H. (2004). *System Reliability Theory: Models, Statistical Methods, and Applications*. Hoboken: John Willey & Sons.

Ryan, T. P. (2011). *Statistical Methods for Quality Improvement*. New York: John Wiley and Sons.