Economic Order Quantity Estimation with Uncertain External Information on Product Demand Quantile

Economic Order Quantity Estimation with Uncertain External Information on Product Demand Quantile

Copyright: © 2023 |Pages: 13
DOI: 10.4018/978-1-6684-8474-6.ch008
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In this chapter, a more accurate method for estimating economic order quantity (EOQ) is suggested. This method improves accuracy by using uncertain external additional information about market demand. External additional information can be available in form of summary statistics (sample means, sample quantiles) and their uncertainty measures (confidence intervals, widths of confidence intervals, standard errors, sample variances, or sample standard deviations). Annual demand was estimated by average sales and improved with the use of uncertain quantile information. It is shown that uncertain additional information can reduce variance of the estimator. This new approach is illustrated using sales data of midsize retail company.
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For many years one of the key problems in logistics and supply chain management is the problem of inventory management (Muller, 2011). Optimization of inventory management is mostly focused on cost minimization and profit maximization, while better meeting the consumers’ demand (Davis, 2016). Economic order quantity (EOQ) is an important inventory management system parameter widely used in logistics and supply chain management. EOQ suggests a balance between costs and profits related to inventory management of a product. Traditionally, EOQ is based on product demand forecasting and minimized total costs of ordering and holding of the product. EOQ indicates how much and how often to make orders while fully satisfying customer demand (Raju, 2022). Moreover, careful choice of EOQ reduces risks of deficit and overstock, and improves quality of logistical service (Setiawan, 2018; Agada & Ogwuche, 2019) and degree of customer satisfaction (Hu et al., 2010; Mishra & Venkataraman, 2022) in the B2C, as well as B2B and B2G markets. Accurate assessment of the EOQ is especially important in inventory management as it directly affects cost, sales price and overall profit (Ladany & Sternlieb, 1974; Huang & Wu, 2020).

Literature suggests many different approaches for improving EOQ tailored to different settings. For example, traditionally, the holding cost is assumed to be constant, but in real life settings this assumption may not hold. This setting of variable holding cost needs specific approaches for calculating EOQ. Alfares and Ghaithan (2019) reviewed EOQ production-inventory models with variable holding cost. Many authors suggested different estimators of EOQ for different types of demand. Some deterministic EOQ models rely on ordinary differential equations. Piunovskiy and Zhang (2011) reviewed deterministic EOQ models and analyzed accuracy of EOQ where the demand was modeled by a stochastic jump process. Other EOQ models are tailored for specific types of products (Hegedűs & Longauer, 2023). Çalışkan (2022) considered EOQ of deteriorating items with planned backorders. Bankole et al. (2022) considered estimation of EOQ of perishable goods which demand distributions were described by Weibull distributions proportional to their prices.

Note, that the above methods typically require specialized software, additional personnel trained to work with this software, which is often cost-prohibitive for small and midsize businesses.

The true demand has to be estimated on previously collected data. This estimation requires accurate selection of appropriate statistical methods. Tasks of increasing accuracy of statistical estimation has long been in the focus of statistical research (Lehmann & Casella, 2011) and has been recently recognized in logistics (Zenkova & Kabanova, 2018; Zenkova et al., 2020a; Pranav et al., 2021; Kabanova et al., 2022; Umasarulatha, 2022). The methods on the use of additional information allow to go beyond the limitations of a single sample and incorporate external to sample information in statistical inference. This article extends ideas and methods described earlier in Tarima and Pavlov (2006), Tarima and Zenkova (2022), Zenkova and Musoni (2020) and Zenkova et al. (2021).

Key Terms in this Chapter

Accuracy of a Statistical Estimator: A population quantity describing quality of estimation provided by the estimator. Examples of accuracy measures are variance, mean square error, and bias.

Inventory Management System: Software designed to work with various databases to record, process, and order products with the goal of having the right products, at the right time, in the right place, and at the right cost. Inventory management systems expediate inventory related optimal decision making to minimize risks and maximize profit.

Inventory Management: A company level activity to manage product in stock as well as supply chains, which includes order, store, and sell of companies’ products. This definition applies to both retail and production of goods.

Statistical Estimation: A group of methods in mathematical statistics to use available data for point and interval estimation of statistical characteristics of random variables. Examples of popular statistical characteristics to be estimated include cumulative distributions functions, mathematical expectations, and standard deviations.

Additional Information: When used in statistical estimation is external to the main sample information relevant to a characteristic of a random variable. The sources of additional information include expert opinions, experimental settings, and external to the main sample sources of additional observations. Examples of additional information: exact knowledge of a distributional quantile, symmetry of a distribution, ranges of possibly values of random variables, a quantile estimate from an external data source available with its standard error.

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