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

Introduction

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).