1. What type of company was studied? What kind of product did they sell? What is their geographic reach? Why is demand forecasting in this business?
2. What types of models did the author use? Please give a brief summary of each.

1.1 The Company PR Companyr already has more than halfa century ofhistory, presenting itself today as a reference company in the production and distribution of delicatessen. From its foundation to the present PR has speCialized and nansformed itself into a modern organization with a professmnal management and equipped With the latest technologies, thus managing to anticipate the challenges and specicnies of competitiveness and globalization Without never losing its roots in Portugal, It should also be mentioned that PR is a highly certied company by seval standards that attest Quality Management Systems (ISO 9001' 2008); Environmmtal Management System (ISO 14001: 2004) and Food Safety Management Systems (ISO 22000: 200 S). It is also internationally recognized by specic standards by the food industry, such as IFS 7 international Featured Standard, which strengthens its competitiveness in the global market The company's strategyr is essentially sustained business growth, always guaranteeing a quahty of excellence to the consumer, assuming quality and safety as a business priority. In order to respond to market demand. PR presents a diverse portfolio of products, which can be grouped into six different product families as shown in Fig. 1. Fig. 1. Bacons Charcuterie Hams Smoked Mortadella Fats Product families. Currently, PR is present in the most diverse sectors ofthe national distribution retail; cash & carry, modern dlSlIllJlJtlU, and professional channels. In addition to the domestic market, where it has been gaining strength and holding leading positions, PR has already achieved strong internationalization of its brand in countries such as: Angola, BraZiL France: Germany, Holland: Luxembourg, Mozambique= United Kingdom, Russia, South Africa and Sweden (Fig. _). fig. 2. PR company's markets. Full size image 1.2 The Importance of Demand Forecasting in the Food industry Due to the increasing level ofcompetitiveness among companies; forecasting plays an important role in supply chain management, and the viability of a company is often dependent on the eftiCiency and accuracy offorecasts []. Demand forecasts are behind all strategic andplanning decisions in any retail business as they directly a'ect the company's protability and competitive position. For these reasons= the use ofdemand forecasting techniques is a fundamental support in planning and managing a company's supply chain [1]. Its importance becomes patent, since its outcome is used for many rnctions Within the organization. they allow the nancial department to estimate costs, levels of profit and capital needs; they enable the sales departmart to obtain knoiwhow of each product's sales volume; the purchasing department may plan short, and longiterm acquisitions; the marketing department can plan their actions and evaluate the impact of dierent markehng strategies on the sales volume and brand awareness; the logistics department Will be able to dene the specttic logistics needs and finally, the operations department that can manage and plan in advance the purchase of machinery and materials; as well as the hiring of labor It is therefore consensual that forecasts are very useful, and even essential for most companies. Accurate demand forecasts have the potential to increase profitability, nnprovtng the chain's efciency and reducing waste. This paper describes various demand forecasting models for products made by a food company. In the food business, gm management of inventories involves numerous articles whose particular characteristics; namely perishability, are relevant. Bad decisions in this area can lead to large losses related to excess stock. 2 Demand Forecasting 2.1 Demand Forecasting Methods Predicting demand is a mndamental activity as it can reveal market trends and contribute to the strategic planrung ofthe company. According to [14]; danand forecasting is an essential tool for a faster and safer decision-making process. There are several techniques available to support analysts in forecasting demand. Although these techniques have substantial differences, there are common characteristics: - They generally assume that the causes that have inuenced danand in the past Will continue to act in the m - Forecast accuracy decreases as the forecasting horizonm - Aggregated forecasts for product groups are more accurate than individual product forecasts. Forecasting methods may be divided into quantitative and qualitative methods Quantitative methods require the construction of mathematical models: using historical data, that describe demand variation over time. These methods include decomposition, moving averages, exponential smoothing, ARIMA, etc. In general. qualitative methods result from the opinion ofprocess specialists to predict demand. They are frequently questioned as the systematic approach provided by quantitative techniques presents a better performance concerning future estimates. However. in cases of information scarcity; for example in the launching of new products; the expenence and knowehow of managers may be useful. 2.2 Demand Forecasting Process at PR The data available consisted ofweekly sales from the rst week of20|3 through week 1? of 2016 (Fig. g). Fig. 3. cu as rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 7777777777 2. .................... ' .............................................................................................. 2; ............ - I.. .. .. . .................... . ....................... ,. ...._..,.tl,.._ .. __t l li- Il \"WW "" ..i. .u. .m.li u... ....m.. .ilu. H. ..i. mil\" .i an]: an" znls ems Sales from week 1 of 2013 to week 17 of 2016. We start by Whow the company predicts its sales in orda to optimize processes and reduce unnecessary stocks or avoid lost sales. The demand forecast pforrned by PR is based on a tired: mov1ng at'age. Ihll in week i, a demand forecast for week 9+2 is made for each product based on the actual sales concerning weeks 04, 03, 0-2 and 01. Fig. 5 shows the actual sales (black) and the forecasts obtained with the 4-week moving average model (red). fig. 4. PE- mu zais ms Actual sales vs Forecasts using the 44veek MA model. (Color gure online) The mat autocorrelation function for this model is illustrated in Fig. i. fig. 5. u \"awn1- -I.I 4-week MA Em automrrelation function. We evaluated the normality of the errors using MSmimov test, which reveals that the errors could be considered normally distributed (9:200). This result is illustrated in Fig. g (a and 1)). fig. 5. Norm-l on anfnlrrnu i-mm m E-meneNm-i om ..- .n v M x m'. mi tum 0mm: VII]! (21] Hinlugt'all] Ur MA I'I'I'UTb' (b) QC! Pint of MA i'rl'ut'h. Normality assumption for MA errors. Currently, and as a form of support, the company has a le inExcel format, which is updated weekly With the actual sales These base forecasts may be adjusted according to qualitative information obtained from its sales force, Salespeople play a key role in obtaining information for forecasts as they work very closely to customers and to the market. It is up to the task manager to generate forecasts, informally collect information from the sales team in order to adjust the base forecasts obtained orn the method above described, The m collected from the commercial team can he oft-'arious nature For example, a sales campaign for a particular product for a particular customer, or the exit from the market ofa competing product. In this case= the sensitivity and experience of the task manager comes into play, which can increase or decrease orders to a reasonably weighted value Accordingly, the value ofe'xpected sales {in kg), calculated on the basis ofthe 4-week moving average, is adjusted by the person responsible for the forecasts, which includes the input that he collects from both past sales and future sales, The aim is mainly to try to decode the danand peaks of certain products and-"or their low demand in certain weeks. In summary, after the calculation ofthe base forecasts based on the 4-week moving averages (MA), in order to include all the relevant information, it becomes necessary to receive inputs orn the marketing area (promotion of llE\\\\' products and promotional plans), the commercial area (customer and market data) and operational planning (capacity constraints, logistics, etc.) in order to adjust the values against these inputs. After collection, processing and analysis phases, the nal values obtained are validated once more and communicated to the production planning department. 3 Exponential Smoothing Models In the moving average method described in the previous section, the forecast is determined by aSSigning the same weight to each of the last 4- obsen'ations available {0-1, 0-2, 6-; and 64) and ignoring all the older observations (prior to week (94)). However, it is reasonable to assume that the most recent observations contain more relevant information about what might happen in the future and therefore should have a greater weight in forecasting than the older observations. Exponential smoothing methods are based on this principle, Exponential smoothmg is one ofthe most popular forecasting methods This method applies a weighted average to the observations ofa time series, m'th greater weights being given to the most recent information. Single exponential smoothing is based on the Eq. 1 Mewchow (1) Error Autocorrelation Function where @ @+1 is the forecast for period +1, @ is the smoothing constant and ? ? is the observed value for period t. Since the smoothing constant varies between 0 and 1, more weight is given to the most recent observations in determining forecasts. Its application in forecasting appears to have been pioneered in 1956 by Robert Brown. In 1957, Holt described double exponential smoothing and, in 1960, Peter R. Winters improved the algorithm by adding seasonality. This algorithm became known as triple exponential smoothing or the Holt-Winters method [10, 13]. Using data from 2013, 2014 and 2015 and the Forecast Pro software, we developed exponential smoothing models to forecast the first 17 weeks of 2016. The model selection criterion was the Mean Absolute Deviation (MAD), defined in Eq- 2. 40 0= 10= 1010 0-0010 (2) where @ @ and @ @ represent, respectively, the actual sales in week { and sales forecast for week i. 4.ol Exponential smoothing error autocorrelation function. The model that minimized within sample MAD is described in Table 1. Table 1. Exponential smoothing model selected. Figure 7 shows the actual sales (black) and the forecasts obtained with the selected model (red). In addition, we evaluated the normality of the errors using Kolmogorov-Smirnov test, which Fig. 7. reveals that the errors could be considered normally distributed (?=.058). This result is 26. illustrated in Fig. 9 (a and b). Fig. 9. Normal Q-Q Plot of ES errors Percent (36) Expected Normal 2013 2014 2015 2016 Actual sales vs Forecasts using Exponential smoothing model. (Color figure online) 50.000 75 060 Errors Observed Value The error autocorrelation function for this exponential smoothing model is illustrated in Fig. 8. (a) Histogram of ES errors. (b) QQ Plot of ES errors. Fig. 8. Normality assumption for ES errors. 4 ARIMA Models 8In 1970 George Box and Gwilym Jenkins popularized ARIMA (Autoregressive Integrated "Partial Autocorrelation Function Moving Average) models in their seminal textbook, Time Series Analysis: Forecasting and Control. ARIMA models generated a lot of interest in the academic community, due mostly to their theoretical foundations, which proved that, under certain assumptions, the models would produce optimal forecasts. However, the Box-Jenkins methodology apparently hasn't been widespread adopted among the business community. This was mostly due to the difficult, time consuming and subjective procedure described by Box and Jenkins to identify the proper form of the model for a given dataset. Furthermore, empirical studies showed that despite the ARIMA model's theoretical superiority over other forecasting methods, in practice the models did not regularly outperform other time series methods. Differenting Generically, a non-seasonal easonal Box-Jenkins model is represented as ARIMA (p. d, q). where p indicates the number of AR terms, d indicates the order of differencing, and q indicates Single the number of MA terms. A seasonal Box-Jenkins model is symbolized as ARIMA (9.0.9)*(@:0.@), where the pad.q indicate the model orders for the short-term components of the model, and P,D.@ indicate the model orders for the seasonal components of Partial Autocorrelation Function (PACF) after a simple and a seasonal difference. the model. We used Forecast Pro to build the ARIMA models. After transforming data in order to remove trend (using a simple difference) and seasonality (using a seasonal difference) we analysed the Autocorrelation function (ACF) and the Partial Autocorrelation function (PACF), presented in This analysis led to an ARIMA(0, 1, 1)*(0,1,1)52 that minimized within Figs. 10 and 11 Fig. 10. sample @=9772 and is summarized in Table 2. Autocorrelation Function Table 2. ARIMA model selected. Model coefficients are significant and the Error Autocorrelation function (Fig. 12) shows that errors are random. Figure 13 shows the actual sales (black) and the forecasts obtained with the selected model (red). Fig. 12. 1.0 Error Autocorrelation Function Difference Simple Automatic Apply 45 4 Autocorrelation Function (ACF) after a simple and a seasonal difference. Fig. 11. -.ol 9 10Error Autocori'elation Function (ACF) for ARIMAEo.i_.i)x(o,1,i)52. F'_13. 26 .. .. .. . .. . .. .. . .. . .. . .. .. .. . .. .......... 22 77777 ' 20 . 18 II; II xlom ------ 2m! 20H 2M5 2M6 Actual sales vs Forecasts using ARI)-LA(D,1,1) >