Fuzzy Nonlinear Optimization Model to Improve Intermittent Demand Forecasting

Fuzzy Nonlinear Optimization Model to Improve Intermittent Demand Forecasting

Raúl Poler (Universitat Politècnica de València, Spain), Josefa Mula (Universitat Politècnica de València, Spain), Manuel Díaz-Madroñero (Universitat Politècnica de València, Spain) and Mariano Jiménez (Universidad del País Vasco (UPV/EHU), Spain)
Copyright: © 2014 |Pages: 18
DOI: 10.4018/978-1-4666-4785-5.ch010
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This chapter proposes a fuzzy nonlinear programming model for intermittent demand forecasting purposes. The authors formulated the Syntetos and Boylan (SB) forecasting method as a crisp nonlinear programming model. They also attempted to improve it with a new fuzzy nonlinear programming formulation. This fuzzy model is based on fuzzy decision variables, which represent fuzzy triangular numbers. The authors applied fuzzy arithmetic operations, such as addition and subtraction of fuzzy numbers, fuzzy decision variables. They carried out the defuzzification of the fuzzy decision variables through the possibilistic mean value of fuzzy numbers. Finally, the authors validated and tested it by comparing it with the deterministic nonlinear programming model that they adopted as the basis of this work. The computational studies show that fuzzy model performance is consistently better than the SB nonlinear programming model, especially when intermittency is high.
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Forecasting is an estimation of future demand (Blackstone, 2010). Forecasting demand plays a key role in decision-making processes within the business management activities framework. Due to the relation among the various business areas, an incorrect forecast could have substantially adverse effects on the firm as a whole. Forecasting future demand is central for planning and executing business processes in industrial firms at both the macro and micro levels. At the organizational level, forecasting sales are required as essential inputs for many decision activities in several functional areas; e.g., marketing, sales, production, purchases, accountancy and finances (Mentzer & Bienstock, 1998). Demand forecasting is also relevant for managing inventories (Buffa & Miller, 1979; Hax & Candea, 1984; Silver, Pyke, & Peterson, 1998).

Various forecasting methods exist, but a vast variety of problems in this field also abound which require all type of treatments. Selecting a model depends on a wide range of considerations; e.g., time horizons, objectives, data properties, and many other aspects (Poler & Mula, 2011). Furthermore, the forecasting model must be manageable and should produce reliable results that are easy to interpret.

Demand forecasting methods can be classified into three main categories: qualitative methods, causal methods and quantitative methods (Makridakis, Wheelwright, & Hyndman, 1998). On the one hand, qualitative methods are helpful when there is little or no quantitative information available, but there is enough qualitative information or knowledge. Essentially, they are based on expert opinions (the Delphi Method), on studies into customer opinions, etc. The objective of causal or econometric methods is to develop models that relate demand with a set of independent variables. Selecting independent variables depends on the availability of the data and their relation with the demand to be forecasted. Building these forecast models implies employing trial-and-error techniques. For this purpose, we select explanatory variables, which logically influence demand requirements, and we carry out regression and, finally, we do statistical verifications. While developing the model, we test alternative equation forms to see which better fits the historical data and/or fulfills some statistical standards and scenarios. The model that best fits the historical data may provide more reliable forecasts. Thus, we can deal with the problem by developing several models, followed by a careful analysis before reaching a forecast. On the other hand, quantitative methods require sufficient quantitative information. These methods have two main classes: a) time series, which forecast the continuation of historical data patterns; b) explanatory series, which attempt to explain how certain variables affect the forecast (simple regression, multiple regression, regression with ARIMA (autoregressive-integrated-moving-average), dynamic regression, an analysis of intervention, multivariate autoregressive models, etc-). The traditional quantitative analysis approaches of available time series include heuristic methods, such as decomposition of time series, exponential smoothing, and the regression of time series and ARIMA models with formal statistical bases. A set of advanced methods also exists, which attempt to face certain constraints that are inherent to traditional models. This chapter analyzes quantitative forecasting methods based on the use of time series in an intermittent demand context.

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