Q1. What are some of the potential benefits of a more formalized approach to forecasting?
Some of the potential benefits of a more formalized approach to forecasting can be based on judgmental forecasts. Since judgmental forecasts relies on opinions from consumer surveys, sales staff, managers, executives, and experts, M&L Manufacturing can get an idea of what is needed at their warehouse and at their supply store. Without accurate data from each store, M&L inventory can be overstock, understock, or no stock. So when a store order supplies, M&L wouldn’t know how much inventory they have, they might have a lot of product 1, but very little of product
2. When using the judgmental forecast, sales staff and managers from other supply store can give M;L Manufacturing what is selling in their store, and ship out more products to fill up their inventory, and they can fill their warehouse on which product is selling faster than the other. Without having the correct amount of inventory in the warehouse, they can lose a lot of money because consumers will purchased other products from a different company. Using the judgmental forecasting, the manager from M;L Manufacturing can get a sense on what is needed at each of their supply store, and get accurate forecasting on each product, and how many products are selling each month.

The potential benefits for M;L manufacturing are:
Proper production planning in future of two of its most valuable and profitable product lines;
Fewer stock-outs in retail stores;
Less uncertainty with regard to unexpected orders and production failures;
Proper inventory management and control over the stock levels;
Better knowledge regarding which products to continue selling and discontinue selling.

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Helps predict the future
Keep the customers happy
Learn from the past
Keep companies looking ahead
Save on labour cost
Remain competitive
Reduce inventory costs
Helps prepare for a drop/increase in sales
Higher profit
Q2. Prepare a weekly forecast for the next four weeks of each product. Briefly explain why you chose the methods you used.

The reason I choose the linear trend equation because it is the most common equation to calculate the weekly forecast, and it is the easiest method to figure out the following four weeks of each product.

The demand for product one has risen over the period of 14 weeks which depicts that demand can be expected to rise further in the coming four weeks. The pattern can be illustrated using a line graph, as shown in figure 1, below.

Based on the shape of the graph, it can be stated that, except for the unusual order of 90 units in the seventh week, the demand has risen over the period in a rising trend. Because of the size of the order the graph gets put off from an otherwise linear pattern of the rising demand.

In order to forecast demand of Product, the following features of the demand of the product need to be noted:
The demand has risen steadily over the period of 14 weeks;
The slight deviation in between has been caused by an unusual order which is not expected in future sales.

The forecasting method most suited to the nature of the demand of Product 1 is ‘Trend Analysis’ using a regression model. Trend analysis is a method of forecasting whereby the data is assumed to show a linear ehavior over a long period of time and based on the linear nature of the growth in sales, a linear equation, obtained through regression analysis is established to make predictions about sales and demand in future and make forecast. The method is suited for long term forecasts as well as short term forecasts.

Using the data obtained from the case study which has been presented in a graph form in Figure 1, regression analysis is conducted to formulate a linear equation based on the existing demand trend. This is done using calculations.

However, rather than manual calculations, MS EXCEL provides a faster mode of calculating and plotting the historic demand figures to develop a regression trend line.. EXCEL allows creating a chart of the demand units against weeks. The chart generates a linear representation of the data which can be further projected for forecasting future sales of the next four weeks using a trend line. EXCEL allows the linear equation to be developed for the trend line as well as produces the figure of R-squared, denoted by r in the above set of formulas.

In the Trend Analysis method of forecasting sales, R-squared value allows estimating the accuracy of the forecast. It represents the deviation that the trend line has from the data. The larger this figure is and the closer it is to 1, the more accurate the forecasts are as they follow the trend in the sales data.

The linear Trend Analysis in the form of a graph is shown in Figure 2, below.

The trend line equation generated by EXCEL is y = 3.457x + 48.28, were y represents the units of the product and x represents the week. This equation shows the total demand never falls below 48 units and the company can expect this much minimum demand to exist in the coming weeks even in the hard times. The r-squared is 0.889 which is highly close to 1 depicting that the trend line follows the pattern of the demand data. This figure is mainly due to the unusual order placed by a customer of 90 units. Therefore, it can be concluded that the Trend Analysis is suitable for the forecasting of the future demand of Product 1 produced by the company as it shows strong accuracy. There are different ways of dealing with outliers. A simple and intuitive way is to replace the demand for the week in question with the average demand from the previous week and the next week in the time-series. Therefore in this case, the demand of 90 in week 7 will be replaced with 71.5 ((67 + 76)/21.
Linear trends show a steady, straight-line increase
It has an upward sloping trend
Predicts short-term demand for products
The data present in the case study is used to create a graph using EXCEL, which is shown in Figure 3, below.

Based on the nature of the spread of the data, it can be safely said that the data shows variations and seldom progresses in a linear fashion.

The exponential smoothening method of forecasting is most suitable to determine the future demand of the product because it would allow ‘smoothening’ these variations. It is a simple method compared with the regression model and places value in the most recent values of the demand of the product to predict the future demand values.

EXCEL is used to generate the exponential smoothening graph and equation necessary to forecast the future demand of Product 2. The findings are shown in Figure 4, below.

The exponential equation drawn by EXCEL for the data is y + 40.04e0.008x.

time series is seasonal (fluctuating)
cheap and widely used approach to forecasting
quick and easy to prepare
it isn’t time consuming
it is easily understandable
applicable for short term decision making
The forecasted values of Product 1 using linear Trend Analysis and Product 2 using Exponential Smoothening method are shown below in Table 1.

T Y t*Y T2
1 50 50 1
2 54 108 4
3 57 171 9
4 60 240 16
5 64 320 25
6 67 402 36
7 71.5 500.5 49
8 76 608 64
9 79 711 81
10 82 820 100
11 85 935 121
12 87 1044 144
13 92 1196 169
14 96 1344 196
105 1020.5 8449.50 1015

Period Forecast (T=46.64 + 3.50t)
15 T = 46.64 + 3.50 (15) = 99.14
16 T = 46.64 + 3.50 (16) = 102.64
17 T = 46.64 + 3.50 (17) = 106.14
18 T = 46.64 + 3.50 (18) = 109.64
Table 1: Forecasted Demand of Product 1 and Product 2
Week Product 1 Product 2
15 100 45
16 103 46
17 107 46.5
18 110 47
The use of both forecasting methods allows the manager to make decision on which product to place emphasis on. Use of a formalized forecasting method results in a ore sufficient production allows M&L to purchase enough raw materials for future demands orders from customers will be fulfilled.
Highline Financial Services, Ltd.Highline Financial Services provides three categories of service to its clients. Managing partner Freddie Mack is getting ready to prepare financial and personnel hiring (or layoff) plans for the coming year. He is a bit perplexed by the following printout he obtained, which seems to show oscillating demand for the three categories of services over the past eight quarters:
Year Quarter A B C
1 1 60 95 93
2 45 85 90
3 100 92 110
4 75 65 90
Year Quarter A B C
2 1 72 85 102
2 51 75 75 3 112 85 110
4 85 50 100
Examine the demand that this company has experienced for the three categories of service it offers over the preceding two years .Assuming nothing changes in terms of advertising or promotion, and competition doesn’t change, predict demand for the services the company offers for the next four quarters. Note that there are not enough data to develop seasonal relatives. Nonetheless, you should be able to make reasonably good, approximate intuitive estimates of demand. What general observations can you market regarding demand? Should Freddie have any concerns? Explain.

These data can be used to give a forecast of the future market trend (demand) of the services that the company provides to its clients. With the predictions of the future i.e. the next whole year or the next four quarters, the company can now plan for its operations and how to improve its current situation and also increase its revenue. The forecasting or prediction of future market trend is done using quantitative techniques such as time series:it comprises forecasting using the least square methods, regression, moving averages, exponential smoothing, hybrid forecasting models, spectral analysis, custom forecasting models, and decomposition forecasting methods among many other techniques. Least square method is a statistical method used to determine the best the best line that suits a model. It is specified with an equation with particular parameters to observed data. The most appropriate model that will suit in this example provided here is the least square method because it can give a forecast even to the next infinity period to come. The other methods are mostly limited to one or two periods. Here we want to give a forecast of the next four quarters for the coming year. This makes the least square method the most ideal technique to use here.
The data presented in the two tables above illustrate the data from the past two periods. The table has the demand data of the services of the company for the most recent years. This market trend/demand implies that a lot of considerations have to be made by the company to stabilize with the best form ever.The company’s management has an option of reducing on its prices to avoid the risk of losing out to its competitor given the rise in competition in the sector (Stevenson, 2015). The reduction in prices for the services offered is meant to stimulate sales to increase revenue from the current. The company has to improve on the quality of services and service delivery to attract more clients hence a stimulationof its sales or also risk losing out to the other competitors. In the instances where the trend persists, then the company’s management may be forced to lay off most of its workers and in severe cases it may even be forced to close business in future.

With the data from the previous section I will use the least square method technique of forecasting to give a prediction of the future market sales. This will help the industry make good the use of the information to ensure that they are successful in marketing their services. Using the least square method, the trend equation will be in the form of: y= a+ bxWhere: a = ?y – b?x while b= n?xy – ?x?ynn?x2 – (?x)2
n in the equation is the period or number quarters in a year for our case here.

To forecast the demand trend for the services for the following year3, we will have to get the values for XY (xvalueis multiplied by y value to get it), X2 (the xvalue is squared to get it) this is gotten from what we already have in the data of presented in the table above in table 1. This will be presented for all the quarters in the year in tabular format as shown in table 2. The X value for the following quarters will be 9, 10, 11, 12 this is the period n, and the yvalue to be computed will be the sales forecast of the next periods.

year Quarter A B C
1 1 60 95 93
2 45 85 90
3 100 92 110
4 75 65 90
2 1 75 85 102
2 51 75 75
3 112 85 110
4 85 50 100
3 1 The future trend/forecast of the market can be forecasted just as shown above and this will help the company to put in place good marketing strategies that will help them win the market from competitors. This will increase the demand for the services. I recommend that the company adjusts to the above stated strategies as mentioned above like price reduction, improving on the quality of services and reducing the labor force as a way of reducing the company costs. Forecasting is an essential technique which industries are to use in assessing the trend of the market. Forecasting gives the industry company clues on how business is fairing and the best way that they can adjust to the predictions in future.

For this case, the forecast for the first, second, third and the forth quarter for the three services demanded will be corresponding to the values in 9, 10, 11, and 12 respectively as shown in the table in the forecast column. Having substituted the summations in the formula above, the forecasts in red above in the table are derived. For instance when substituted:
For service A
b = (8×2895) – (36×602)
(8×204) – (362)
= 4.429
a = 602 – (4.429×36)
= 55.32
Therefore y= 55.32 + (4.43x)
For service B
b = (8×2671) – (36×632)
(8×204) – (362)
= -4.12
a = 632 – (-4.12 × 36)
= 97.54
Therefore y = 93.25 + (0.666x)
For service C
b = (8 × 3493) – (36 × 770)
(8×204) – (362)
= 93.25
a = 770 – (0.67 × 36)
= 93.25
year quarter X x2 A(y) XY B(y) (XY) C(y) (XY)
1 1 1 1 60 60 95 95 93 93
2 2 4 45 90 85 170 90 180
3 3 9 100 300 92 276 110 330
4 4 16 75 300 65 260 90 360
2 1 5 25 75 375 85 425 102 510
2 6 36 51 306 75 450 75 450
3 7 49 112 784 85 595 110 770
4 8 64 85 680 50 400 100 800
? 36 204 602 2895 632 2671 770 3493
3 1 9 95.2 60.5 99.1 2 10 99.6 56.3 100 3 11 104.1 52.2 101 4 12 108.5 48.1 101.3 From the demand, I can observe that the demand for service A is increasing steadily. This therefore means that the manager needs not make changes to the department. This is according to the forecasted demand for the next four quarters using the least square method. The demand for service B seems to be reducing and the manager should make changes immediately. This is seen in the forecasted demand for the following year that reflects a drastic drop in the demand for the services. Forecast for C shows that the demand is set to remain the same with very insignificant fluctuations. Forecasting is ideal for the manager because he can plan for the future.
Stevenson, W. J. (2015). Operations management. New York: McGraw-Hill Education.


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