2 Forecasting logistics requirements - John Wiley & Sons · 2 Forecasting logistics requirements...

2 Forecasting logistics requirements

2.1 Introduction2.2 Qualitative methods2.3 Quantitative methods2.4 Data preprocessing2.5 Choice of the forecasting method2.6 Advanced forecasting method2.7 Accuracy measure and forecasting monitoring2.8 Interval forecasts2.9 Case study: Forecasting methods at Adriatica Accumulatori

2.10 Case study: Sales forecasting at Orlea2.11 Questions and problems

G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management © John Wiley & Sons, Ltd 1 / 42

2 Forecasting logistics requirements Questions and problems

Problem 2.1

Groupe Danone is one of the largest food companies in theworld. It is the leading food company in France, Italy and Spain.It is ranked third in Europe and seventh worldwide. In Italy,Danone has invested more in probiotic products, such as Activiaand Actimel. During the first three months of last year, thecompany carried out an opinion poll by launching a campaigncalled ‘Choose the Flavour’ on the Facebook fanpage ActiviaItalia. The goal was to let consumers directly select the newyoghurt flavours. In this way, Facebook was used as a tool tocarry out a market survey. Discuss the limits and opportunitiesoffered by such a qualitative forecasting method.



Problem 2.2

In freight transportation, a typical logistics problem is theallocation of empty containers to depots, in order to satisfyfuture demands of transportation services. How can a carrierpredict demands of containers for the transport of a givencategory of products?



Problem 2.3

To what extent are the forecasting practices different in an MTSand in an MTA system?



Problem 2.4

How would you predict the future demand of a new product?



Problem 2.5 (1/2)

Hot Spot is a firm based in the United States whose corebusiness is the maintenance of home heaters. The companyusually forecasts service requests on the basis of the number ofinstalled heaters. The number of installed home heaters and thenumber of service requests received over past years in NewJersey are reported in Table 1. Forecast the service request p9by using, to this purpose:

- a single regression analysis (service requests versus thetotal number of heaters installed);

- a multiple regression analysis (service requests versus thenumber of heaters installed less than, or equal to, two yearsago and at least two years ago).

Which technique is the most accurate? Why?



Problem 2.5 (2/2)

Heater installations︷︸︸︷

Year ≤ two years ago > two years ago Total Service requests

1 260 000 69 500 329 500 18 6722 265 000 74 200 339 200 19 0763 287 800 82 850 370 650 20 9944 313 750 90 550 404 300 23 2495 345 350 97 150 442 500 25 0256 379 050 105 950 485 000 28 1117 416 950 111 550 528 500 30 9858 459 100 117 000 576 100 33 3979 502 550 123 200 625 750

Table 1: Number of Hot Spot heater installations and servicerequests.



Problem 2.6 (1/2)

Sunshine is one of the world’s leading suppliers of fast-movinggoods in household care and personal product categories.According to the company management, sales of the FacialCleansing Blemish product mostly depend on promotionexpenditure made by the company and its competitor. Table 2reports facial soap sales for the previous 10 quarters, andquarterly levels of sales in Canada for that detergent withrespect to (a) Sunshine promotion expenditure, and (b) thecompetitor’s promotion expenditure divided by the Sunshinepromotion expenditure. Make a sales forecast for the next twotime periods under the hypothesis that Sunshine will increase itspromotion expenditure to CAN$ 14.5 million and thecompetitor’s promotion expenditure will remain the same as inthe actual quarter.



Problem 2.6 (2/2)

Quarter Sunshine promotion Competitor’s promotion Sales of Blemishexpenditure expenditure / Sunshine in Canada

(Millions CAN$) promotion expenditure (Millions CAN$)

1 6.0 1.2 46.82 6.8 1.2 52.73 7.5 1.4 60.54 7.5 1.5 56.65 9.0 1.5 64.46 10.5 1.7 74.17 12.0 1.8 72.28 12.0 1.5 78.09 13.5 1.4 87.8

10 13.5 1.5 95.6

Table 2: Data for the forecasting problem of Sunshine.



Problem 2.7 (1/2)

Carlinek is a Polish company, based in Poznan, which retailsAqua-Floor, a well-known water-resistant laminated floorcovering. The company needs to forecast the demand of thisproduct, by using historical data on the sales of the latest ninemonths, reported in Table 3.After checking the presence of possible outliers in the historicaldatabase, use the weighted moving average method todetermine the one-month-ahead sales forecast.



Problem 2.7 (2/2)

Month Quantity Month Quantity

1 450 6 4372 670 7 4563 332 8 –4 123 9 2315 343

Table 3: Aqua-Floor product quantities (in m2) sold by Carlinek inPoznan during the last nine months.



Problem 2.8 (1/2)

Table 4 reports an estimate of the annual mean demand and thecorresponding variance of fruit and vegetable products ofFlanders, Belgium. The products are divided into fivecategories: fall–winter, spring–summer, exotic fruits, citrus fruitsand dried fruits.Verify whether the aggregate forecast is more or less accuratethan the estimated demand for each category.



Problem 2.8 (2/2)

Category Mean Variancet t2

Fall–winter 123 000 24 570Spring–summer 245 000 35 650Exotic fruits 9 860 320Citrus fruits 98 000 2 980Dried fruits 2 450 456

Table 4: Annual mean demand and variance of fruit and vegetableproducts of Flanders.



Problem 2.9 (1/2)

Vaal Engineering is a South African company which producesand distributes industrial slotting machines in Africa. Thenumber of 800xp machines sold during the last 60 months isreported in Table 5.After plotting the data, clean the time series from possibleseasonal and residual variations and then determine the trendcomponent.



Problem 2.9 (2/2)Period Quantity Period Quantity Period Quantity Period Quantity

1 60 16 104 31 32 46 1442 83 17 205 32 81 47 1853 130 18 235 33 149 48 2804 120 19 32 34 141 49 895 187 20 81 35 177 50 736 248 21 149 36 281 51 1377 51 22 141 37 75 52 1468 76 23 177 38 78 53 1919 125 24 281 39 130 54 268

10 134 25 54 40 112 55 3111 196 26 94 41 202 56 6312 262 27 132 42 262 57 12613 54 28 104 43 44 58 13314 94 29 205 44 80 59 21315 132 30 235 45 128 60 281

Table 5: Number of 800xp slotting machines sold by Vaal Engineeringduring the last 60 months.



Problem 2.10 (1/2)

A time series wt , t = 1, . . . ,24, is reported in Table 6. Can the timeseries correspond to a seasonal variation over time, withperiodicity M = 12, obtained through the application of adecomposition method (a multiplicative way to combine thecomponents)? If so, explain the meaning of w1, otherwise whatcan we do?



Problem 2.10 (2/2)

t wt t wt t wt

1 1.012 9 0.876 17 1.1742 1.123 10 0.904 18 1.0553 1.088 11 0.812 19 1.1014 1.122 12 0.714 20 1.0865 1.097 13 1.057 21 0.9096 1.023 14 1.134 22 0.9877 1.001 15 1.099 23 0.8938 0.987 16 1.180 24 0.811

Table 6: Time series wt , t = 1, . . . ,24.



Problem 2.11

The time series decomposition method (additive) into its fourcomponents of trend, cyclical, seasonal and residual variationsis used to estimate monthly sales (in kg) of a product.Characterize the seasonal component st for some t , in terms ofunits, magnitude (can it be positive, negative or zero? Explain itsmeaning) and the average value of M consecutive time periods(M is the periodicity).



Problem 2.12 (1/3)

Mitsumishi is a Korean company whose number of M5 lighttrucks sold during the last 42 months is reported in Table 7. Thecompany invested significant financial resources in promotion,and the M5 sales increased in some months, as shown inTable 8.

(a) Forecast sales for the next six months using an appropriateforecasting method.

(b) Plot a control chart. Are you able to detect any anomalies?



Problem 2.12 (2/3)

Month Quantity Month Quantity Month Quantity

1 22 882 15 20 967 29 28 4142 19 981 16 19 759 30 22 5373 18 811 17 22 200 31 22 8454 19 352 18 24 162 32 9 4515 27 226 19 20 275 33 15 8426 18 932 20 7 949 34 16 4097 18 931 21 14 328 35 13 8818 8 523 22 16 691 36 11 2309 13 064 23 13 784 37 24 765

10 13 733 24 10 986 38 21 73911 12 597 25 24 768 39 25 15312 7 645 26 19 351 40 20 51513 23 478 27 23 953 41 24 03814 17 019 28 18 855 42 25 151

Table 7: Number of M5 trucks sold by Mitsumishi.



Problem 2.12 (3/3)

Month Sales improvement Month Sales improvement

5 30 19 86 13 29 307 3 30 12

17 20 31 518 15

Table 8: M5 sales improvement (in %) achieved during some monthsby Mitsumishi.



Problem 2.13 (1/3)

Sit is an American company which produces and sellshigh-quality printers. The number of XC2100 printers monthlysold in Berkeley, California, during the last 12 months isreported in Table 9. The company has always forecasted themonthly one-period-ahead demand by using the movingaverage method (r = 2), but the logistician is now evaluating theoption of adopting a new forecasting technique, called Q.Knowing the forecasting errors et , t = 2, . . . ,12, obtained by usingthe Q method for the one-period-ahead forecasts (and reportedin Table 10), determine the value that e8 should take to inducethe logistician to replace the moving average method with Q.



Problem 2.13 (2/3)

Period Quantity Period Quantity

1 835 7 8102 798 8 8143 831 9 8004 772 10 7935 750 11 8056 783 12 829

Table 9: Number of XC2100 printers sold during the last 12 months bySit.



Problem 2.13 (3/3)

Period Error Period Error

1 – 7 162 24 8 x3 −13 9 −84 19 10 415 −35 11 316 27 12 −28

Table 10: Forecasting errors et , t = 2, . . . ,12, generated by using the Qmethod.



Problem 2.14 (1/2)

Aldes is a food and beverage company located in the Republicof Mauritius that is specialized in the export of canned food,such as tuna fish, mainly sold in Africa, the Middle East andWestern Europe, in cartons of 48 cans of 185 g each.The monthly exportation value of tuna fish to Jordan during thelast eight months is summarized in Table 11.Estimate the two-period-ahead exports of tuna fish by using theexponential smoothing method with α= 0.20, α= 0.25 andα= 0.35. By comparing the obtained results, what is the bestvalue of α?If the company decides to promote the product through adiscount policy to increase the sales, how convenient it is tomodify the choice of α? Is it possible to use the selected methodfor six-month-ahead forecasting?



Problem 2.14 (2/2)

Month Sales Month Sales

1 100 000 5 92 0002 98 000 6 87 5003 70 500 7 95 0004 90 000 8 99 500

Table 11: Aldes exports (in $) of tuna fish to Jordan during the lasteight months.



Problem 2.15

Prove that the sum of weights in the equation

pT+1 =α

T−2∑

k=0(1−α)k yT−k + (1−α)T−1y1

(see exponential smoothing method), is equal to 1.



Problem 2.16 (1/2)

Given the time series yt , t = 1, . . . ,12, reported in Table 12, usethe exponential smoothing method to determine the forecastingvalue p13, assuming a time-variable parameterαt =max

t

{

0.24; 3√

35t2

}

t = 2, . . . ,12. Modify Equation

pT+1 =α

T−2∑

k=0(1−α)k yT−k + (1−α)T−1y1,

when the time-variable parameter is used and verify that thesum of weights still remains equal to 1. Determine whether thetime-variable parameter implies a more accurate forecastingthan the value of α= 0.3.



Problem 2.16 (2/2)

t yt t yt

1 1100 7 9202 935 8 9853 1120 9 10704 1040 10 9405 1060 11 11006 1100 12 970

Table 12: Time series yt , t = 1, . . . ,12.



Problem 2.17

Let yt , t = 1, . . . ,T , a time series, characterized by a linear trend,no cyclical and seasonal variations. Prove that the linearregression method corresponds to the elementary techniquewhen r = 2.



Problem 2.18 (1/2)

EuroPack is a leading European firm of packaging products.The plant located in Denmark realizes, in a continuous cycle,more than 150 products in 60 g/m2 polyethylene and nylon film.

(a) Estimate the amount of polyethylene and nylon film neededto ensure daily production in the next week by usinghistorical data related to the last 30 days (shown inTable 13).

(b) Determine the tracking signal (band ±4) at the current timeperiod.

(c) Determine the interval forecast of polyethylene and nylonfilms for one day ahead with respect to T = 30, with a levelof confidence (1−α)= 0.95.



Problem 2.18 (2/2)Period Quantity Period Quantity

1 133 16 1962 155 17 2203 179 18 2074 191 19 2135 176 20 2196 150 21 2197 204 22 1708 145 23 2139 204 24 227

10 209 25 20511 149 26 20312 210 27 18713 185 28 22514 204 29 23515 203 30 194

Table 13: Quantity (in thousands of kg) of kg/m2 polyethylene andnylon films used by EuroPack in the last 30 days.



Problem 2.19 (1/2)

Oasis is a pineapple soft drink sold in Germany. The monthlysales data over the past 44 months are reported in Table 14.

(a) Plot the data on a graph. What important observations canyou make about the demand pattern? Which data arerelevant and should be used for forecasting purposes?

(b) Use two different forecasting methods to predict sales overthe next four months.

(c) Estimate MAPD of both methods using the data of the lastsix months. Which approach seems to work best?

(d) Select the most accurate method (see Problem 2.19(c)) andthen determine, with a level of confidence (1−α)= 0.90, theinterval forecast for the one-month-ahead sales at T = 44.



Problem 2.19 (2/2)

Month Quantity Month Quantity Month Quantity Month Quantity

1 9 050 13 10 000 25 9 150 37 8 9002 8 050 14 9 750 26 8 750 38 9 4503 7 000 15 9 300 27 8 800 39 8 7504 6 120 16 10 100 28 9 400 40 9 5005 8 250 17 10 400 29 12 000 41 13 4006 11 450 18 15 650 30 13 450 42 14 0007 10 900 19 16 350 31 14 900 43 16 8508 12 850 20 17 000 32 18 760 44 21 0009 10 650 21 13 600 33 12 250

10 11 000 22 11 250 34 11 00011 9 200 23 9 500 35 9 60012 8 900 24 9 200 36 9 100

Table 14: Sales (in kl) of Oasis soft drink in Germany over the last 44months.



Problem 2.20 (1/2)

Hollaflowers is a Dutch cut-flowers company with its owndistribution network that covers five European countries. Inorder to maintain a product quality control in the last phase ofthe distribution system, the company uses its resources fortimely delivery to customers. To this end, it is required todetermine the necessary resources to satisfy future demands ofcustomers. Based on daily data over the last five weeks, whichare reported in Table 15, forecast the number of vans for theone-week-ahead deliveries.



Problem 2.20 (2/2)

Week︷︸︸︷

Day 1 2 3 4 5

Monday 3 24 21 25 24Tuesday 8 16 25 23 16

Wednesday 10 12 12 19 8Thursday 2 18 15 12 22

Friday 6 6 26 12 14

Table 15: Number of vans daily used over the last five weeks byHollaflowers.



Problem 2.21 (1/2)

The National Health Service of Belgium is responsible for thedistribution of Neurozam to all national hospitals. Neurozam is adrug used to fight a rare neurological disease. Its high cost andperishability forced the National Health Service to have smallamount of stocks, used to satisfy demand of not more than threedays. Plan the supply of the drug of the National Health Servicetaking into account the number of packages of the drugdistributed in the last 20 days (see Table 16).



Problem 2.21 (2/2)

Day Quantity Day Quantity

1 23 11 02 25 12 03 19 13 04 0 14 165 14 15 146 0 16 67 0 17 08 13 18 09 16 19 12

10 0 20 0

Table 16: Number of packages (three vials each) of Neurozamdistributed over the last 20 days from the Belgian National HealthService.G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management © John Wiley & Sons, Ltd 38 / 42


Problem 2.22

A company is planning to add extra capacity to a plant currentlymanufacturing 110000 items per year. After an accurate salesforecast over the next few years, one is quite sure that the mostlikely value of the annual demand is 140000 items and that theMSE is equal to 108. It is known that the company loses $ 3 foreach unit of unused capacity and $ 7 for each unit of unsatisfieddemand. How much capacity should the company buy? (Hint:the forecasting error can be assumed to be normallydistributed.)



Problem 2.23

Given the time series yt , t = 1, . . . ,42, reported in Table 7, it isassumed that yt = 0, for t = 4, 5, 6, 16, 17, 18, 28, 29, 30, 40, 41,42. Determine p42(τ),τ= 1, . . . ,6, using, if it is necessary, thesame forecasting method selected in Problem 2.12.



Problem 2.23

Monitor the forecasts for the monthly sales of sportswear of thePlaza supermarkets by using, as an accuracy measure, thetracking signal instead of MAD.



Problem 2.24

To control a one-period-ahead forecasting process determinedwith the exponential smoothing method (α= 0.3) on the timeseries reported in Table 6 (see Problem 2.14), use a ‘3-σ’control chart. What you can say about the accuracy of theforecasting method? Construct a 95% level of confidence for theone-period-ahead forecast.


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