Based on the information provided in Table 1, the demand values for "dog ball launcher" for the first quarters of the years for years 2018 and 2019 are 10 and 14 respectively which indicates a fair increase (increased by 4) in the product's demand in the market of 2019. The demand values of the product "dog ball launcher" for the second respective quarters of the years 2018 and 2019 are 29 and 31 respectively which indicates less demand increase (increased by 2) than the previous quarters of the respective years.
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The demand values of the same product for the third respective quarters of the respective years are 26 and 29 respectively, which shows that the demand for the product increased by 3 from the third quarter of 2018 to the third quarter of 2019. The demand values of the product for the last respective quarters of the respective years are 15 and 18 respectively which shows that the demand increased by 3 from the last quarter of 2018 to the last quarter of 2019.
The total demand for the "dog ball launcher" in 2018 is calculated as 80 and the total demand for the same in 2019 is calculated as 92, which shows a total increase of 12 in the product's net demand from 2018 to 2019.
Based on the information provided in Table 2, the demand for the second product "lightweight dog lead" increased by 3 (for January), increased by 59(for February), increased by 41(for March), increased by 24(for April), increased by 15 (for May) and decreased by 1 (for June) from 2020 to 2021. The respective changes in the product's demand are calculated as "increase by 6 for July", "decrease by 4 for August", "decrease by 7 for September", "decrease by 10 for October", "decrease by 11 for November" and "decrease by 8 in December".
The total demand for the second product, "lightweight dog lead" for the year 2020 is calculated as 1037, and the total demand for the same in 2021 is calculated as 1205, which shows an overall increase of 168 in the product's net demand from 2020 to 2021.
2. Explanation of whether the current model of forecasting is appropriate or not
The forecasting model utilized by the procurement department is a "multiplicative seasonal model based on seasonal indices" based on the data from 2018-2019. The seasonal demand variations of the first product are relatively constant, which can be observed in Table 1. The second and third respective quarters of 2020 and 2021 is form the peak demand seasons for the first product. "Multiplicative seasonal model" based on the seasonal indices is a method preferred by analysts when the changes in seasonal demands are in accordance with the changes in the level of the series. This current method of forecasting is not accurate when the seasonal variations are increasing over time. However, the "additive model" derives more accurate results when the seasonal variations in the data, more or less, remain constant. The utilization of the "additive model" for forecasting the quarterly demands of the first product for 2020 and 2021 would be a more appropriate option.
However, the second product shows a large increasing demand trend for which, the utilization of the multiplicative model of forecasting based on seasonal indices would be a better choice for forecasting the demand for the second product for the year 2021.
3. Explanation of recommended forecasting model
Here in this case study, there are several types of functions such as the comparison of the demand for both the products that are been to be sold by the company in the market. However, the company here is to be required for the determination of the value of the demand of both the models for the 2 years based on the products that are to be sold in the trade place of the country. Here the model is been selected to be a simple linear regression model which helps in the identification of the actual demand for both the products of the company. Moreover, it can be seen that the function of the company is to sell different kinds of products that are been related to caring for the pet owned. Therefore, it can be seen that the model which is been currently selected for the identification of the actual demand for the products is been the least square method which helps in the identification of the demand for the first product. The simple linear regression model is been selected as it compares two variables such as demand for both products.
Figure 1: Calculation of simple linear regression of Lightweight dog and Dog ball launcher
From the above mentioned figure, it has been seen that the changes in the demand of both the products are been discussed. However, it can be said that the demand for the first product for the year 2020 and 2021 is been more in terms of the demand computed for the second selected product. However, it has been seen that the company is been trying to compare its demand of first product with the demand of the other commodity that has been produced. Moreover the least square method helps in the evaluation of the values of the company with the help of reducing the squares and evaluating the actual demand for both the products. Moreover, it can be said that the changes in the functions of the company creates a change in the demand for both the products.
Figure 2: Calculation of least square model of Lightweight dog and Dog ball launcher
From the figure mentioned above, it has been seen that the demand for the 1st product is been more than the demand of the second product. This method is already been selected by the company for the identification of the actual change in the demand of the products. It can be said that there are several methods such as the use of regression methods is been used and line charts are been made for the identification of the demand.
5. Determination of the forecasting errors
An additive model of forecasting is best suitable for steady, uniform, and systematic variations in seasonal demands and does not take any sudden changes or threats in market demands into consideration. The sudden changes or shocks in market demands would provide inaccurate forecasted data using the "additive model of forecasting".
The core limitations of using the "multiplicative model of forecasting" are that this model is concerned with simplified results derived from a single observation of data and this method often proves limited in case of forecasting the appropriate measures to reach the expected outcomes.
6. Three key recommendations for the company
In order to understand the seasonal demand trends, it is recommended for the company to acquire customer reviews on various seasons and conduct awareness campaigns or surveys for evaluating the peak demand trends of the two products.
On account of maintaining the inventory size of the first product, it is highly recommended that the company hire "seasonal employees" to maintain the necessary stock supply for the first products.
It is highly recommended that the company reviews its inventory over different seasons to understand the demand variations, demand peaks, and troughs along with evaluating the necessary business strategies to overcome seasonal demand-related issues in the time to come.
Case Study 2
1. Analyzation of the Quality Management
Quality management situations are shown in this study, where line manager Ms. Lionheart is concerned about the quality of the product and services. Here the customers highlighted the problem they encountered at the time of shopping. The complaints focus on two areas which is at the checkout the billing error was made and the variation in the weight of the bags of "pet kingdom branded dried” dog food. In Table 3, the data of the 50 random bills issued per day are shown for the past 30 days and Table 4 shows the 27 random samples of 5 observations from the daily deliveries of the dog food. Ms. Lionheart noticed the error of the billing was increased on the day of the last third of the month.
In the given Table 3 it is shown that from day one today tenth the number of incorrect billing was between 1 to 2 and the 6th-day incorrect billing was 3. After the observation from the 11th to the 20th day, it was found that the data was increased and the number of incorrect billing was increased which was 1 incorrect bill made on day 11th and it increased to 3 on the 20th day. The third column shows days 21st to 30th where incorrect billing made was increased. The number of incorrect bills was 3 on the day 21st and it was increased on the 30th day by 5. On the other hand, the data on the weight of the dog food are shown in Table 4, where the data shows the mean and the range change of the sample with the help of five observations.
2. Three sigma control limits and the control chart showing acceptability quality
"Three-sigma control" is made in the statistical chart to determine and then set the limit of the upper control and the lower control limit. The data which lie above the average and also below the three-sigma line show below 1 percent of all data points through the bell curve. It is a statistical calculation in which the data of three standard deviations are taken from the mean and the business applies three sigma for refereeing the efficiency of operation process and produces a high-quality product. Here 50 random bills per day for limiting the incorrect bill and 27 samples were randomly taken from the five observations to determine the limit of the variation of the weight of the dog food bag.
Indication of the three sigma for acceptable quality shoes the Quality standard of the company and the limits which can be determined for the quality standards. The measurement understanding the sigma control limit shows the average with the help of the bell curve which represents the normal distribution. The data on the left or right points to the record of the product on the bell curve. It can be higher or lower than the mean data. On the other hand, the lower value represents that the data fall point to the mean and the high value shows widespread data and is not close to the average.
Figure 3: Preparation of the X chart
Figure 4: Preparation of the P chart
Figure 5: Preparation of the X chart
The control chart here is been made for the identification of the different kinds of functions such as the use of dog ball food for the dogs which is been helpful for the identification of the demand of the products in respect to the 3 sigma model.
3. Explanation of the process of control
Figure 6: 3 Sigma chart
There is data on the error made in the billing and the weight of the dog food shown with the help of the table. The 3- sigma control and the control chart are helpful to analyses the limits in the quality standards. The mean of all the observations is shown with the help of the given data, and the data shows the average as a mean of the weight of the food bag. It can be calculated with the help of dividing the total sum of the product by the total number of bags of dog food. here the data shows the average of the weight which was incorrectly made. The data shows that sample 1 has 44.96 means and it is increased from sample 5 to 45.02, the variance in the range are also can be seen here. The mean in averagely increased by 45.03 which shows the variation made in the whole month in the weight of the food of the dog. Control of the processing system is taken in the industrial process to carry the business efficiently with consistency and make the variation less as possible. In this process, "Quantity management" is taken by the company to make the quality of the goods and services and this process of control also helps in maintaining throughput efficiency and practices of earning profit.
4. Explanation of the findings and the consequences
Figure 7: Standard deviation of the incorrect bills
Here, in the given figure, the measurement of dispersion and its relation with the mean is shown with the help of the given. The low standard deviation represents the clustered data around the value of the mean and when the standard deviation is high it indicates the data are spread out more.SD value is 0.299168708 and the mean is 2.9333333 which represent the positive effect (McGrath et al. 2020). It means some measurements can be adopted to eliminate the risk from error in billing at the time of checkout.
Figure 8: Standard deviation of variation in weight of Dog food
Here, the standard deviation is 0.069940 which is less than the mean value, this represents the riskiness of the measures of the company and the mean of the company is 44.99074. This shows the relation of the SD is positive with the mean.
5. Implementation of the “TQM” in the Quantity Management
The summarization of the TQM (Total Quality Management) is the system of the management system focuses on the customer of the organization in which all the employees with continual improvement are included (Calvo-Mora et al. 2020). The implementation of the "TQM " model, in this case, is helpful as it can help to improve the quality of the goods and services (Kuwayama and Olmstead, 2020). In quantity management, there should be clarity of the vision and the mission of the business which can be formed with the TQM model. On the other hand, this model sets the measure for the development and it improves the tool to survey each group of consumers and to solicit the feedback of the customer. This implementation helps in the organize on define the map processes of the ideas, quality policy, objectives, defects, and findings, which are needed to known by the organization.
6. Recommendation
In the following case, the company can implement the TQM mode as it helps to make the strategy from the given data and creates effective communication which helps integrate disciplined quality into the activities and the culture of the organization.
"Quantity management" is necessary to adopt in the business to understand the consumer loyalty, satisfy employees and make a healthy workplace.
It is recommended that different kinds of methods should be taken in the management to rectify past mistakes.
Reference
Lin, Z., Müller, H.G. and Park, B.U., 2022. Additive models for symmetric positive-definite matrices and Lie groups. Biometrika.
Pedersen, E.J., Miller, D.L., Simpson, G.L. and Ross, N., 2019. Hierarchical generalized additive models in ecology: an introduction with mgcv. PeerJ, 7, p.e6876.
Calvo-Mora, A., Blanco-Oliver, A., Roldán, J.L. and Periáñez-Cristóbal, R., 2020. TQM factors and organisational results in the EFQM excellence model framework: an explanatory and predictive analysis. Industrial Management & Data Systems.
Kuwayama, Y. and Olmstead, S.M., 2020. Hydroeconomic modeling of resource recovery from wastewater: Implications for water quality and quantity management. Journal of Environmental Quality, 49(3), pp.593-602.
McGrath, S., Zhao, X., Steele, R., Thombs, B.D., Benedetti, A. and DEPRESsion Screening Data (DEPRESSD) Collaboration, 2020. Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis. Statistical methods in medical research, 29(9), pp.2520-2537.
