Forecast/forecasting horizon

G. L. Thompson, S. P. Sethi, and Teng. J. T. Strong planning and forecast horizons for a model with simultaneous price and production decisions. Eur J of Operational Research, 16 378-388, 1984. 

Forecasting errors increase with the forecast horizon—Demand forecasts for the next month will be more accurate than those for the next year. 

Step 2 Establish a forecast horizon, namely how far into the future we would like to make prediction. 

Here we assume that the level and trend remain constant over the forecast horizon. Thus, X, = a + bf + e for f = 1,2,..n, where X, is the random variable denoting demand at period t, a, and b are constant level and trend and 8 is the random error. Given the observed values of X, = D, for f = 1,..., n, the forecast for period t is given by... 

The main drawback of the simple linear trend model is that it assumes that the level and trend remain constant throughout the forecast horizon. 

A drawback of the previous approach is that the seasonality indices remain static and are not updated during the forecast horizon. Winters (1960) has extended Holt s method by updating seasonality indices also using exponential smoothing. 

Bias Bias measures whether the forecast is overestimating or underestimating the actual demand over the forecast horizon ... 

All forecasts are prone to error and the further ahead the forecast horizon is, the greater the error. Figure 4.1 shows how forecast error increases more than proportionally over time. 

Here the fulcrum is a long way from demand, i.e. the forecasting horizon is long, necessitating more inventory and capacity to balance against demand. 

As we get closer to real demand then clearly the plan has become much more detailed. Ideally nothing is finally assembled, configured or packaged until we know what the customer s order specifies, To achieve this ideal state clearly requires a high level of agility - a challenge that will be addressed in Chapter 5. Even if the customer s required delivery lead time is less than the time we need to make/source and deliver and we have to make inventory ahead of time, at least the forecast will be more accurate since the forecast horizon is closer. 

Forecast horizon identifies how far in advance of the actual event a forecast is made. 

The forecast horizon must be greater than or equal to the lead time of the decision that is... 

The forecast horizon moves further into the future... 

In comparison, in system dynamics-based simulations, just the initial values are given for all variables while in econometric approaches variables are determined for the whole forecasting horizon (Schwarz Ewaldt, 2002 163). 

Production planning includes considerations on production objectives over a certain time horizon given marketing forecasts for prices and product demands, equipment availability, and inventories. This is a macrolevel problem of the allocation of production capacity, time, product inventories, and labour and energy resources, so as to determine the production goals that maximize the total profit over an extended period of time into the future (e.g. a few months to a few years). 

A particular problem is the number of events that should be simulated before the results are stabilized about a mean value. This problem is comparable to the question of how many runs are required to simulate a Gaussian distribution within a certain precision. Experience shows that at least 1000 sample arrivals should be simulated to obtain reliable simulation results. The sample load (samples/day) therefore determines the time horizon of the simulation, which for low sample loads may be as long as several years. It means also that in practice many laboratories never reach a stationary state which makes forecasting difficult. However, one may assume that on the average the best long term decision will also be the best in the short run. One should be careful to tune a simulator based on results obtained before equilibrium is reached. 

Future capital costs considered in the objective function rely on future capital values - in this scope future inventory values. The planning of future inventory values in all future periods and in all network locations is a complex task. As described in the requirements, future inventory value is determined by the future product values of the products on stock. These product values change, if the included material costs of the product change, which is regularly the case due to volatile raw material prices. The task now is to calculate the future inventory value throughout the value chain network and product steps considering the raw material price forecast for the planning horizon. The problem is illustrated in fig. 57. 

The chosen reference year is 2040. The biomass potential is taken from the Green-X project on the additional renewable potential in the EU (see www.green-x.at/Green-X %20viewer.htm). The time horizon of the Green-X forecasts is 2020. It is assumed that the potential remains constant after 2020. North Africa has the largest additional potential (wind and solar), followed by Turkey (biomass) and Norway (hydro). 

The most influential and determining factors in decision making are the quantitative financial analyses, which are used to declare the winner as the best use of the firm s assets. The criteria used most often are the net present value, NPV, and the internal rate of return, IRR. A financial plan begins with a time horizon, such as 5 years, and the forecast of a number of parameters of expenditures and incomes for each of the years, on ... 

Each operation unit capacity is assumed to be designable within an upper and lower boundary to accommodate for any considered production rate. The product demand forecasts are given for a ten year horizon. The costs are represented by power functions which vary in terms of capacity exponents and hence different investment decisions for the process units are expected. The capacity exponents (c.f Table 1) for the cost functions are taken from Peters and Timmerhaus [5]. For the piecewise linear approximation of the cost function, two time intervals are considered as default. Due to maximum capacity restrictions, the overall capacity of the reactor and the product absorption unit is achieved by an installation of at least three parallel reactors and two... 

In this work, a comparison between proactive and reactive approaches has been carried out in terms of a new proposed evaluation criterion that considers earliness and tardiness, as well as rescheduling costs. This cost takes into account the total deviation from initial starting times and a batch reallocation cost which is proportional to the objective function. According to the presented case studies, the further from initially considered values uncertainty unveils, the better the reactive schedule performs according to the evaluation criterion. On the contrary, if uncertainty unveils as forecasted, and early in the time horizon, the best choice is the proactive approach. Future work will be focused on the validation and further improvement of the proactive-reactive control scheme. 

While MV analysis stiU represents the current paradigm, other approaches to portfolio optimization exist and may eventually displace it. Value-at-risk simulation methodologies may ultimately prove more than tangential. Even so, for many practitioners there is stiU a long way to go before forecasting techniques, asset identification, md time horizon considerations are satisfactorily inte-... 

Forecasts or production schedules should then be used to predict the storage volumes and turnover rates of each category of materieil over the specified planning horizon. Idecilly, these volumes would be stated in terms of the unit loads in which the materials would be stored emd handled. 

The master production schedule (MPS) or some other planning document that specifies how much of each end product is required in each time period r, over some specified planning horizon involving T periods. In most practical applications, the basic time period is a week, although longer periods of a month or so may be used for periods far in the future where there is more uncertainty in the demand process (e.g., the MPS is based more on forecasts than on firm customer orders). The relationship of the MPS to the production plan was discussed in Section 2. 

In reality, the production networks typically consist of more than three sites whereby a time horizon of one or two weeks is reasonable in most cases. The time horizon depends on the forecasting stability of production/consumption estimates as well as the transport times. Hence, the model s complexity increases with increasing numbers of nodes and periods. In cases of very large instances, a heuristical procedure can be. set up like this ... 

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