Recommend which method (i. e. , using reconditioned equipment, purchasing new equipment in its Shanghai plant, or outsourcing to another manufacturing operation) Shuzworld should use for the manufacturing of its sneakers, utilizing the appropriate decision analysis tool. Shuzworld has decided to produce the Samba Sneaker, a bright colored shoe marketed for teens and pre-teens. The company needs to decide which would be more economical: reconditioning their existing equipment for this production, buying new equipment, or outsourcing the production to China.

Reconditioning has a fixed cost of $50,000 and a variable cost of $1,000 for every 1,000 sneakers produced. Purchasing new equipment has a fixed cost of $200,000 and a variable cost of $500 for every 1,000 sneakers. Outsourcing production to China has no fixed costs, and variable costs of $3,000 for every 1,000 sneakers produced. I have reviewed the figures and have made a recommendation based on my findings. It is my determination that given the data, we should recondition. The data below reflects the outcome of reconditioning old equipment, purchasing new equipment, and outsourcing.

Below is an insert from POM for Windows an operations management tool used to determine best decisions in business operations. Inputting this data into POM for Windows gives the following results: There are two types of costs to consider, fixed and variable. Based upon the information given the relationship between cost and revenues are linear. In order to use the cost volume and breakeven analysis tool, variable costs must be constant. Here we have constant costs but different scenarios which qualify it to be used by this tool.

Using this tool, I created inputs for reconditioning new equipment, buying new equipment, and outsourcing. The figures for fixed and variable costs were used from company research. It was determined that at 1,000 units the variable costs could be determined and that it would be a good place to set our volume for analysis. The total fixed costs for reconditioning is $50,000 with one million dollars spent in variable costs for a total cost of $1. 5 million. To purchase new equipment, the fixed costs are $200,000 and the variable costs are half of the cost of reconditioning the old equipment at $500,000 for a total cost of $700,000.

Finally, to outsource, while there would be no initial or fixed costs, the variable cost would be $3 million, twice as much as it would costs to recondition the old equipment and 4 times as much as simply buying new equipment. According to the data presented to me, Shuzworld will save the most money by buying new equipment. While the fixed costs are more, the variable costs dont compare to that of reconditioning or outsourcing. Below is a copy of the crossover chart showing where each one has its financial advantage over the other.

VOLUME RANGES: The volume (in units) range for each manufacturing option are as follows as shown in the crossover chart above: The breakeven volume for reconditioning vs. outsourcing is 25 units, The volume increases to 80 units under the purchase vs. outsourcing option The recondition vs. purchase option shows a volume of 300 units. When looking at the point of breakeven, the breakeven in reconstructing vs buy is at 300 units and a cost of $350,000. Recondition vs outsource brings us to a breakeven of 25 units and $75,000.

Buy new vs. outsource gives us a breakeven of 80 units for a cost of $240,000. Recondition vs. buy gives us the lowest breakeven point which means that we start making profit at 300 units. The crossover chart tells us at which point we should switch to something else. Based on these figures, it would appear we will save the largest amount of money if we buy new equipment, even though the fixed costs will be higher initially, the variable costs are considerably lower than reconditioning or outsourcing. The crossover chart above shows the points at which each option presents a financial advantage over the other.

According to the calculations: It will cost a total of $1. 5 million dollars to recondition the equipment ($50,000/ fixed and $1 million/variable). Purchasing new equipment will cost $700,000 ($200,000/fixed and $500,000/variable). This is half of what it would cost to recondition old equipment. Outsourcing will cost $3 million ($0/fixed and $3 million/variable), which is twice the amount of reconditioning the old equipment and 4 times the amount of making a new purchase. These calculations can now be used to determine the breakeven volume for Shuzworlds options.

The data above states that the breakeven volume for reconditioning versus buying new equipment is 300 units. The breakeven volume for reconditioning versus outsourcing is 25 units, and the breakeven volume for buying new equipment versus outsourcing is 80 units. Looking at the graph, it becomes apparent that if the demand for Samba Sneakers is between zero and 25 units, that outsourcing would be the best option. If the demand is between 25-300 units, reconditioning the equipment becomes the optimal choice. Buying new equipment becomes the best choice if the company has a demand over 300 units.

This means that the best option for the company will be determined by their demand. The company has given no indication of the amount of demand they expect to see, so a best guess scenario will have to be applied. It is unlikely that they will see a very low demand (less than 25 units), because the Samba Sneaker is an exciting new product. It is quite likely that the company will see a demand of 25-300 units. Further points to recommend reconditioning would be that the operating director of the plant, Alistair Wu, does not like outsourcing.

The company states that he is very particular about any production that is not in-house. Also, buying new equipment for this new product would be unwise, as it is unsure how it will perform in the future market of consumers as well as the project only planned for one quarter. The numerical data and points taken from the case study all point towards the optimal choice to be reconditioning the existing equipment. This data was calculated using POM for Windows. The Breakeven/Cost-Volume Analysis module was used because it had the option for the cost-volume analysis.

This was appropriate because there was no given data for revenue or sales projections. The cost-volume analysis needed only the fixed and variable costs, and the volumes associated with those costs. I chose the decision analysis tool breakeven cost volume analysis because the tool allowed for ease of use and also had parameters set up to account for the different types of costs and the number of options. In this case, we had 2 costs, fixed and variable, and 3 different options, reconstructing old equipment, purchasing new equipment, and outsourcing.

This decision analysis tool allowed me to construct a crossover chart which showed the points at which the costs of the options demonstrated an advantage over the other. A1. Submit a copy of the output from your decision analysis tool of choice. a. Explain why you chose the decision analysis tool you used. The decision analysis tool I chose to solve this specific issue was the breakeven cost volume analysis tool, because it was easy to use and had specific parameters already in place to account for each type of cost and the number of options available.

Since there are two costs (fixed and variable) and three different options (reconstructing, purchasing, or outsourcing), the decision analysis tool allowed me to graph a crossover chart that detailed the points at which the cost of each option became advantageous over the other. A review of the breakeven analysis shows that the breakeven points for each option are as follows: Option Breakeven Point Cost Recondition vs. Outsource 25 units $75,000 Purchase vs. Outsource 80 units $240,000 Recondition vs. Purchase 300 units $350,000

The lowest breakeven point at which we start to earn a profit is at 350 units for the Recondition vs. Purchase option and the crossover chart above shows us at which breakeven point each option becomes more viable. In addition to the recommendation above, the volume (in units) range for each manufacturing option are as follows (see chart above): The breakeven volume for reconditioning vs. outsourcing is 25 units, the volume increases to 80 units under the purchase vs. outsourcing option, while the recondition vs. purchase option shows a volume of 350 units.

Since we are attempting to save money on this project the best option would be to purchase new equipment because, it is highly likely that the demand for the new item will exceed 80 units, outsourcing is frowned upon by the plants Operating Director, and the quality of the product will be more easily managed by in-house production. It is also fair to say that, if demand exceeds 80 units, then it would obviously surpass the 25 unit demand mark, rendering both outsourcing and reconditioning useless and a waste of company funds that can best serve the company in other investments.

Furthermore, implementing the product focused operation strategy which I used to assist me in making the best possible decision, proved that a high fixed cost and low variable cost combination is the most beneficial option to select. Using the product focused operation strategy allowed me to a specific standard and maintain a specific set of qualities for the new Line. This strategy also allows for a high volume of products with low variety, takes into consideration production equipment solely used for specific tasks, low skilled workers, and production standardization.

Develop a sales volume forecast using the least squares method and one other forecasting method. 1. Submit a copy of the output from the decision analysis tools you used. 2. Compare the results between the two methods you used. In order to improve the performance of our retail mall stores, a sales forecast can be created using previous sales trends to develop future sales goals by implementing a process known as forecasting. Using the least squares(LS) forecasting method I will attempt to project future sales using a straight line regression series.

The LS method uses X and Y intercepts with the changes in the series is being referred to as the slope. Using the LS method, a sale forecast can be determined by changes in the line of its slope. The data to be used is found in the Four Corners Sales chart below. Four Corners Shuzworld Sales Quarter Sales 2Q 2007 90,000 3Q 2007 95,000 4Q 2007 98,000 1Q 2008 96,000 2Q 2008 102,000 3Q 2008 99,000 4Q 2008 118,000 1Q 2009 109,000 2Q 2009 124,000 I computed the data using the Excel OM v4 software and the charts below reflects the data output generated by using the least squares method as requested by the task instructions.

Period Demand (y) Period(x) Period 1 90,000 1 Period 2 95,000 2 Period 3 98,000 3 Period 4 96,000 4 Period 5 102,000 5 Period 6 99,000 6 Period 7 118,000 7 Period 8 109,000 8 Period 9 124,000 9 Forecast 121861. 111 10 On the chart above, the time periods (in quarters) are represented by X. You can see that in the third quarter of 2009, our projected sales forecast starts at $121,861. 11, using the least squares method as requested by the task instructions. The least squares method is appropriate because I only needed to project sales for one future quarter and the data provided was a series of numbers with even intervals.

Another forecasting method that can be used is exponential smoothing, as it is used as a smoothing constraint to determine future numbers. An accurate forecast is given when trends are taken into consideration since the exponential smoothing becomes trend adjusted (Heizer ; Render, 2010). Using the Excel OM software to determine the results for the trend adjusted exponential smoothing forecast generated the following data: Alpha 0. 3 Beta 0. 4 Data Forecasts and Error Analysis Period Demand Smoothed Forecast, Ft Smoothed Trend, Tt

Forecast Including Trend, FITt 2Q 2007 90,000 90000 90000 3Q 2007 95,000 90000 0 90000 4Q 2007 98,000 91500 600 92100 1Q 2008 96,000 93870 1308 95178 2Q 2008 102,000 95424. 6 1406. 64 96831. 24 3Q 2008 99,000 98381. 87 2026. 891 100408. 8 4Q 2008 118,000 99986. 13 1857. 84 101844 1Q 2009 109,000 106690. 8 3796. 564 110487. 3 2Q 2009 124,000 110041. 1 3618. 082 113659. 2 Next 116761. 5 4858. 976 121620. 4 The given smoothing constraint of 0. 3 and the trend adjustment of 0. 4 generates a prediction for Qtr 3 of 2009 as $121,620.

The Excel OM v4 software and forecasting module was selected with the option for Trend Adjusting Exponential Smoothing because the trend adjusting exponential smoothing forecast was best calculated using this method to determine an accurate forecast for the upcoming period. In comparison, the least squares method forecasted a 2009 Qtr 3 sales amount of $121,861. 11, while the trend adjusted exponential smoothing method generated a sales forecast of $121,620. 40. A noticeable difference of $240.

71 is realized between the two methods, however, the numbers are very close in relation since forecasting methods consider trends when calculating figures. Do to the similarities in the calculation methods, it is difficult to determine which forecast method is most accurate. In order to determine the accuracy of each method the actual 2009 Qtr 3 results would be needed. However, since this information is unavailable, it is safe to assume that both forecasts are correct. Error measurements included in the results provided using the decision analysis tool, can be calculated by the MAD and the MSE methods.

The MAD is the first measure of forecast error for the least squares method. The MAD is calculated by adding the absolute values of each individual forecast error and dividing by the number of data periods, while the MSE is a method of measuring the overall forecast error and is calculated by taking the average squared differences between the forecasted and the observed values. The main disadvantage to MSE is that it accentuates the larger deviations due to the squared term. The MAPE is calculated as the average of the absolute difference between the forecasted values and the actual values, then expressed as a percentage of the actual values.

The exponential smoothing with trend adjustment forecasts our 10th qtr sales at $121,620. 40 and has the following error output of MAD 5785. 459, MSE 57418436 and a MAPE of 5. 25%. Also, the mean average deviation is 4183. 51, the average mean square error is 23356173 and the mean absolute percent error is 3. 95%. We can use either method because calculations in both forecasts are very close. C. Discuss how to apply control chart metrics to improve quality in the Shuzworld production line. Applying the use of control chart metrics to improve the quality in Shuzworlds production line can be easily implemented.

Control charts are graphical representations of process data over time and are used to separate natural and assignable causes to variations in production (Heizer ; Render, 2010). Natural causes are the variations typically seen by a company and are caused by chance. If the variations remain within a normal distribution pattern, then production will remain in control. Likewise, assignable causes are traceable variations that can be traced to a source, such as, broken machinery or unskilled workers, which causes decreases in the quality of production (Heizer ; Render, 2010).

In order to implement the use of control charts, we must first develop a control chart, by pulling a random sampling of our shoes. We must then compare the shoes to each other and inspect them to determine their quality and detect variations. Doing this will allow us determine the distribution pattern. This process must be done over several periods of time in order to determine if an assignable cause exists that needs to be corrected in order to improve production (Heizer ; Render, 2010).

It is suggested that the implementation of control chart metrics be considered, because it will provide us with a visual representation of whether or not our production is in control. If production is found to be out of control, then it means that there are high variations in the quality of our product. The indication of a steady pattern of bell curves in the distribution pattern means that we are in control of our production (Heizer ; Render, 2010), which is exactly what we want to achieve.

The image below is a control chart for our dual-density rubber foam molding machine that makes soles for most of our shoes. The chart shows a random hourly selection of 15 soles taken over a 16-hour timeframe. We have set a control limit of 99. 73% for this process, with the standard population deviation at 0. 5 inches. I have also set an upper control limit (UCL) of 10. 375 inches and a lower control limit (LCL) of 9. 625 inches. You can see that two samples on the chart have fallen outside of these limits, and are considered to be out of control. Additionally, the samples that fall between the UCL and LCL are considered to have natural variations.

However, the out of control samples have caused the entire process to become erratic and considered out of control. This means that we detected an assignable cause that must be investigated and discovered, in order to regain control of the process (Heizer ; Render, 2010). It is possible that the assignable cause may be attributed to a single machine that may require more frequent service, since the erratic samples occurred near the end of the 16-hour sampling timeframe. The chart below displays the control limits and sample fraction defectives for 20 operators of the eyeleting machines.

These employees use the machines to create eyelets in both, our boots and mens shoes. We reviewed 100 items for each worker and counted the errors. The control limit is 99. 73%. In this chart, there is a UCLp of 0. 125 and a LCLp of 0. These attributes are measured on a P-chart, which means that the measurements are in terms of defects. Looking at the chart above, we see that two of our employees have fallen outside of the preset limits. Specifically, Operators 13 and 20 are out of control and need to have their work examined closely to determine if a serious problem exists (Heizer & Render, 2010).

Reconditioning has a fixed cost of $50,000 and a variable cost of $1,000 for every 1,000 sneakers produced. Purchasing new equipment has a fixed cost of $200,000 and a variable cost of $500 for every 1,000 sneakers. Outsourcing production to China has no fixed costs, and variable costs of $3,000 for every 1,000 sneakers produced. I have reviewed the figures and have made a recommendation based on my findings. It is my determination that given the data, we should recondition. The data below reflects the outcome of reconditioning old equipment, purchasing new equipment, and outsourcing.

Below is an insert from POM for Windows an operations management tool used to determine best decisions in business operations. Inputting this data into POM for Windows gives the following results: There are two types of costs to consider, fixed and variable. Based upon the information given the relationship between cost and revenues are linear. In order to use the cost volume and breakeven analysis tool, variable costs must be constant. Here we have constant costs but different scenarios which qualify it to be used by this tool.

Using this tool, I created inputs for reconditioning new equipment, buying new equipment, and outsourcing. The figures for fixed and variable costs were used from company research. It was determined that at 1,000 units the variable costs could be determined and that it would be a good place to set our volume for analysis. The total fixed costs for reconditioning is $50,000 with one million dollars spent in variable costs for a total cost of $1. 5 million. To purchase new equipment, the fixed costs are $200,000 and the variable costs are half of the cost of reconditioning the old equipment at $500,000 for a total cost of $700,000.

Finally, to outsource, while there would be no initial or fixed costs, the variable cost would be $3 million, twice as much as it would costs to recondition the old equipment and 4 times as much as simply buying new equipment. According to the data presented to me, Shuzworld will save the most money by buying new equipment. While the fixed costs are more, the variable costs dont compare to that of reconditioning or outsourcing. Below is a copy of the crossover chart showing where each one has its financial advantage over the other.

VOLUME RANGES: The volume (in units) range for each manufacturing option are as follows as shown in the crossover chart above: The breakeven volume for reconditioning vs. outsourcing is 25 units, The volume increases to 80 units under the purchase vs. outsourcing option The recondition vs. purchase option shows a volume of 300 units. When looking at the point of breakeven, the breakeven in reconstructing vs buy is at 300 units and a cost of $350,000. Recondition vs outsource brings us to a breakeven of 25 units and $75,000.

Buy new vs. outsource gives us a breakeven of 80 units for a cost of $240,000. Recondition vs. buy gives us the lowest breakeven point which means that we start making profit at 300 units. The crossover chart tells us at which point we should switch to something else. Based on these figures, it would appear we will save the largest amount of money if we buy new equipment, even though the fixed costs will be higher initially, the variable costs are considerably lower than reconditioning or outsourcing. The crossover chart above shows the points at which each option presents a financial advantage over the other.

According to the calculations: It will cost a total of $1. 5 million dollars to recondition the equipment ($50,000/ fixed and $1 million/variable). Purchasing new equipment will cost $700,000 ($200,000/fixed and $500,000/variable). This is half of what it would cost to recondition old equipment. Outsourcing will cost $3 million ($0/fixed and $3 million/variable), which is twice the amount of reconditioning the old equipment and 4 times the amount of making a new purchase. These calculations can now be used to determine the breakeven volume for Shuzworlds options.

The data above states that the breakeven volume for reconditioning versus buying new equipment is 300 units. The breakeven volume for reconditioning versus outsourcing is 25 units, and the breakeven volume for buying new equipment versus outsourcing is 80 units. Looking at the graph, it becomes apparent that if the demand for Samba Sneakers is between zero and 25 units, that outsourcing would be the best option. If the demand is between 25-300 units, reconditioning the equipment becomes the optimal choice. Buying new equipment becomes the best choice if the company has a demand over 300 units.

This means that the best option for the company will be determined by their demand. The company has given no indication of the amount of demand they expect to see, so a best guess scenario will have to be applied. It is unlikely that they will see a very low demand (less than 25 units), because the Samba Sneaker is an exciting new product. It is quite likely that the company will see a demand of 25-300 units. Further points to recommend reconditioning would be that the operating director of the plant, Alistair Wu, does not like outsourcing.

The company states that he is very particular about any production that is not in-house. Also, buying new equipment for this new product would be unwise, as it is unsure how it will perform in the future market of consumers as well as the project only planned for one quarter. The numerical data and points taken from the case study all point towards the optimal choice to be reconditioning the existing equipment. This data was calculated using POM for Windows. The Breakeven/Cost-Volume Analysis module was used because it had the option for the cost-volume analysis.

This was appropriate because there was no given data for revenue or sales projections. The cost-volume analysis needed only the fixed and variable costs, and the volumes associated with those costs. I chose the decision analysis tool breakeven cost volume analysis because the tool allowed for ease of use and also had parameters set up to account for the different types of costs and the number of options. In this case, we had 2 costs, fixed and variable, and 3 different options, reconstructing old equipment, purchasing new equipment, and outsourcing.

This decision analysis tool allowed me to construct a crossover chart which showed the points at which the costs of the options demonstrated an advantage over the other. A1. Submit a copy of the output from your decision analysis tool of choice. a. Explain why you chose the decision analysis tool you used. The decision analysis tool I chose to solve this specific issue was the breakeven cost volume analysis tool, because it was easy to use and had specific parameters already in place to account for each type of cost and the number of options available.

Since there are two costs (fixed and variable) and three different options (reconstructing, purchasing, or outsourcing), the decision analysis tool allowed me to graph a crossover chart that detailed the points at which the cost of each option became advantageous over the other. A review of the breakeven analysis shows that the breakeven points for each option are as follows: Option Breakeven Point Cost Recondition vs. Outsource 25 units $75,000 Purchase vs. Outsource 80 units $240,000 Recondition vs. Purchase 300 units $350,000

The lowest breakeven point at which we start to earn a profit is at 350 units for the Recondition vs. Purchase option and the crossover chart above shows us at which breakeven point each option becomes more viable. In addition to the recommendation above, the volume (in units) range for each manufacturing option are as follows (see chart above): The breakeven volume for reconditioning vs. outsourcing is 25 units, the volume increases to 80 units under the purchase vs. outsourcing option, while the recondition vs. purchase option shows a volume of 350 units.

Since we are attempting to save money on this project the best option would be to purchase new equipment because, it is highly likely that the demand for the new item will exceed 80 units, outsourcing is frowned upon by the plants Operating Director, and the quality of the product will be more easily managed by in-house production. It is also fair to say that, if demand exceeds 80 units, then it would obviously surpass the 25 unit demand mark, rendering both outsourcing and reconditioning useless and a waste of company funds that can best serve the company in other investments.

Furthermore, implementing the product focused operation strategy which I used to assist me in making the best possible decision, proved that a high fixed cost and low variable cost combination is the most beneficial option to select. Using the product focused operation strategy allowed me to a specific standard and maintain a specific set of qualities for the new Line. This strategy also allows for a high volume of products with low variety, takes into consideration production equipment solely used for specific tasks, low skilled workers, and production standardization.

Develop a sales volume forecast using the least squares method and one other forecasting method. 1. Submit a copy of the output from the decision analysis tools you used. 2. Compare the results between the two methods you used. In order to improve the performance of our retail mall stores, a sales forecast can be created using previous sales trends to develop future sales goals by implementing a process known as forecasting. Using the least squares(LS) forecasting method I will attempt to project future sales using a straight line regression series.

The LS method uses X and Y intercepts with the changes in the series is being referred to as the slope. Using the LS method, a sale forecast can be determined by changes in the line of its slope. The data to be used is found in the Four Corners Sales chart below. Four Corners Shuzworld Sales Quarter Sales 2Q 2007 90,000 3Q 2007 95,000 4Q 2007 98,000 1Q 2008 96,000 2Q 2008 102,000 3Q 2008 99,000 4Q 2008 118,000 1Q 2009 109,000 2Q 2009 124,000 I computed the data using the Excel OM v4 software and the charts below reflects the data output generated by using the least squares method as requested by the task instructions.

Period Demand (y) Period(x) Period 1 90,000 1 Period 2 95,000 2 Period 3 98,000 3 Period 4 96,000 4 Period 5 102,000 5 Period 6 99,000 6 Period 7 118,000 7 Period 8 109,000 8 Period 9 124,000 9 Forecast 121861. 111 10 On the chart above, the time periods (in quarters) are represented by X. You can see that in the third quarter of 2009, our projected sales forecast starts at $121,861. 11, using the least squares method as requested by the task instructions. The least squares method is appropriate because I only needed to project sales for one future quarter and the data provided was a series of numbers with even intervals.

Another forecasting method that can be used is exponential smoothing, as it is used as a smoothing constraint to determine future numbers. An accurate forecast is given when trends are taken into consideration since the exponential smoothing becomes trend adjusted (Heizer ; Render, 2010). Using the Excel OM software to determine the results for the trend adjusted exponential smoothing forecast generated the following data: Alpha 0. 3 Beta 0. 4 Data Forecasts and Error Analysis Period Demand Smoothed Forecast, Ft Smoothed Trend, Tt

Forecast Including Trend, FITt 2Q 2007 90,000 90000 90000 3Q 2007 95,000 90000 0 90000 4Q 2007 98,000 91500 600 92100 1Q 2008 96,000 93870 1308 95178 2Q 2008 102,000 95424. 6 1406. 64 96831. 24 3Q 2008 99,000 98381. 87 2026. 891 100408. 8 4Q 2008 118,000 99986. 13 1857. 84 101844 1Q 2009 109,000 106690. 8 3796. 564 110487. 3 2Q 2009 124,000 110041. 1 3618. 082 113659. 2 Next 116761. 5 4858. 976 121620. 4 The given smoothing constraint of 0. 3 and the trend adjustment of 0. 4 generates a prediction for Qtr 3 of 2009 as $121,620.

The Excel OM v4 software and forecasting module was selected with the option for Trend Adjusting Exponential Smoothing because the trend adjusting exponential smoothing forecast was best calculated using this method to determine an accurate forecast for the upcoming period. In comparison, the least squares method forecasted a 2009 Qtr 3 sales amount of $121,861. 11, while the trend adjusted exponential smoothing method generated a sales forecast of $121,620. 40. A noticeable difference of $240.

71 is realized between the two methods, however, the numbers are very close in relation since forecasting methods consider trends when calculating figures. Do to the similarities in the calculation methods, it is difficult to determine which forecast method is most accurate. In order to determine the accuracy of each method the actual 2009 Qtr 3 results would be needed. However, since this information is unavailable, it is safe to assume that both forecasts are correct. Error measurements included in the results provided using the decision analysis tool, can be calculated by the MAD and the MSE methods.

The MAD is the first measure of forecast error for the least squares method. The MAD is calculated by adding the absolute values of each individual forecast error and dividing by the number of data periods, while the MSE is a method of measuring the overall forecast error and is calculated by taking the average squared differences between the forecasted and the observed values. The main disadvantage to MSE is that it accentuates the larger deviations due to the squared term. The MAPE is calculated as the average of the absolute difference between the forecasted values and the actual values, then expressed as a percentage of the actual values.

The exponential smoothing with trend adjustment forecasts our 10th qtr sales at $121,620. 40 and has the following error output of MAD 5785. 459, MSE 57418436 and a MAPE of 5. 25%. Also, the mean average deviation is 4183. 51, the average mean square error is 23356173 and the mean absolute percent error is 3. 95%. We can use either method because calculations in both forecasts are very close. C. Discuss how to apply control chart metrics to improve quality in the Shuzworld production line. Applying the use of control chart metrics to improve the quality in Shuzworlds production line can be easily implemented.

Control charts are graphical representations of process data over time and are used to separate natural and assignable causes to variations in production (Heizer ; Render, 2010). Natural causes are the variations typically seen by a company and are caused by chance. If the variations remain within a normal distribution pattern, then production will remain in control. Likewise, assignable causes are traceable variations that can be traced to a source, such as, broken machinery or unskilled workers, which causes decreases in the quality of production (Heizer ; Render, 2010).

In order to implement the use of control charts, we must first develop a control chart, by pulling a random sampling of our shoes. We must then compare the shoes to each other and inspect them to determine their quality and detect variations. Doing this will allow us determine the distribution pattern. This process must be done over several periods of time in order to determine if an assignable cause exists that needs to be corrected in order to improve production (Heizer ; Render, 2010).

It is suggested that the implementation of control chart metrics be considered, because it will provide us with a visual representation of whether or not our production is in control. If production is found to be out of control, then it means that there are high variations in the quality of our product. The indication of a steady pattern of bell curves in the distribution pattern means that we are in control of our production (Heizer ; Render, 2010), which is exactly what we want to achieve.

The image below is a control chart for our dual-density rubber foam molding machine that makes soles for most of our shoes. The chart shows a random hourly selection of 15 soles taken over a 16-hour timeframe. We have set a control limit of 99. 73% for this process, with the standard population deviation at 0. 5 inches. I have also set an upper control limit (UCL) of 10. 375 inches and a lower control limit (LCL) of 9. 625 inches. You can see that two samples on the chart have fallen outside of these limits, and are considered to be out of control. Additionally, the samples that fall between the UCL and LCL are considered to have natural variations.

However, the out of control samples have caused the entire process to become erratic and considered out of control. This means that we detected an assignable cause that must be investigated and discovered, in order to regain control of the process (Heizer ; Render, 2010). It is possible that the assignable cause may be attributed to a single machine that may require more frequent service, since the erratic samples occurred near the end of the 16-hour sampling timeframe. The chart below displays the control limits and sample fraction defectives for 20 operators of the eyeleting machines.

These employees use the machines to create eyelets in both, our boots and mens shoes. We reviewed 100 items for each worker and counted the errors. The control limit is 99. 73%. In this chart, there is a UCLp of 0. 125 and a LCLp of 0. These attributes are measured on a P-chart, which means that the measurements are in terms of defects. Looking at the chart above, we see that two of our employees have fallen outside of the preset limits. Specifically, Operators 13 and 20 are out of control and need to have their work examined closely to determine if a serious problem exists (Heizer & Render, 2010).