M.Z. Babai

Demand categorisation in a European spare parts logistics network

Purpose – Spare parts have become ubiquitous in modern societies and managing their requirements is an important and challenging task with tremendous cost implications for the organisations that are holding relevant inventories. An important operational issue involved in the management of spare parts is that of categorising the relevant stock keeping units (SKUs) in order to facilitate decision-making with respect to forecasting and stock control and to enable managers to focus their attention on the most “important” SKUs. This issue has been overlooked in the academic literature although it constitutes a significant opportunity for increasing spare parts availability and/or reducing inventory costs. Moreover, and despite the huge literature developed since the 1970s on issues related to stock control for spare parts, very few studies actually consider empirical solution implementation and with few exceptions, case studies are lacking. Such a case study is described in this paper, the purpose of which is to offer insight into relevant business practices. Design/methodology/approach – The issue of demand categorisation (including forecasting and stock control) for spare parts management is addressed and details reported of a project undertaken by an international business machine manufacturer for the purpose of improving its European spare parts logistics operations. The paper describes the actual intervention within the organisation in question, as well as the empirical benefits and the lessons learned from such a project. Findings – This paper demonstrates the considerable scope that exists for improving relevant real word practices. It shows that simple well-informed solutions result in substantial organisational savings. Originality/value – This paper provides insight into the empirical utilisation of demand categorisation theory for forecasting and stock control and provides some very much needed empirical evidence on pertinent issues. In that respect, it should be of interest to both academics and practitioners.

Determining order-up-to levels under periodic review for compound binomial (intermittent) demand

We propose a new method for determining order-up-to levels for intermittent demand items in a periodic review system. Contrary to existing methods, we exploit the intermittent character of demand by modelling lead time demand as a compound binomial process. In an extensive numerical study using Royal Air Force (RAF) data, we show that the proposed method is much better than existing methods at approximating target service levels and also improves inventory-service efficiency. Furthermore, the proposed method can be applied for both cost and service oriented systems, and is easy to implement.

On the demand distributions of spare parts

Spare parts have become ubiquitous in modern societies, and managing their requirements is an important and challenging task with tremendous cost implications for the organisations that are holding relevant inventories. Demand for spare parts arises whenever a component fails or requires replacement, and as such the relevant patterns are different from those associated with ‘typical’ stock keeping units. Such demand patterns are most often intermittent in nature, meaning that demand arrives infrequently and is interspersed by time periods with no demand at all. A number of distributions have been discussed in the literature for representing these patterns, but empirical evidence is lacking. In this paper, we address the issue of demand distributional assumptions for spare-parts management, conducting a detailed empirical investigation on the goodness-of-fit of various distributions and their stock-control implications in terms of inventories held and service levels achieved. This is an important contribution from a methodological perspective, since the validity of demand distributional assumptions (i.e. their goodness-of-fit) is distinguished from their utility (i.e. their real-world implications). Three empirical datasets are used for the purposes of our research that collectively consist of the individual demand histories of approximately 13,000 SKUs from the military sector (UK and USA) and the Electronics Industry (Europe). Our investigation provides evidence in support of certain demand distributions in a real-world context. The natural next steps of research are also discussed, and these should facilitate further developments in this area from an academic perspective.

Analysis of order-up-to-level inventory systems with compound Poisson demand

We analyse a single echelon single item inventory system where the demand and the lead time are stochastic. Demand is modelled as a compound Poisson process and the stock is controlled according to a continuous time order-up-to (OUT) level policy. We propose a method for determining the optimal OUT level for cost oriented inventory systems where unfilled demands are backordered. We first establish an analytical characterization of the optimal OUT level. The actual calculation is based on a numerical procedure the accuracy of which can be set as highly as desired. By means of a numerical investigation, we show that the method is very efficient in calculating the optimal OUT level. We compare our results with those obtained using an approximation proposed in the literature and we show that there is a significant difference in accuracy for slow moving items. Our work allows insights to be gained on stock control related issues for both fast and slow moving Stock Keeping Units (SKUs).

On the inventory performance of multi-criteria classification methods: empirical investigation

A number of multi-criteria inventory classification (MCIC) methods have been proposed in the academic literature. However, most of this literature focuses on the development and the comparison of ranking methods of stock keeping units (SKUs) in an inventory system without any interest in the original and most important goal of this exercise which is the combined service-cost inventory performance. Moreover, to the best of our knowledge these MCIC methods have never been compared in an empirical study. Such an investigation constitutes the objective of this paper. We first present the inventory performance evaluation method that we illustrate based on an example commonly used in the relevant literature which consists of 47 SKUs. Then, we present the empirical investigation that is conducted by means of a large data-set consisting of more than 9086 SKUs and coming from a retailer in the Netherlands that sells do-it-yourself products. The results of the empirical investigation show that the MCIC methods that impose a descending ranking of the criteria, with a dominance of the annual dollar usage and the unit cost criteria, have the lowest combined cost-service performance efficiency.

Spare parts management: Linking distributional assumptions to demand classification

Spare parts are known to be associated with intermittent demand patterns and such patterns cause considerable problems with regards to forecasting and stock control due to their compound nature that renders the normality assumption invalid. Compound distributions have been used to model intermittent demand patterns; there is however a lack of theoretical analysis and little relevant empirical evidence in support of these distributions. In this paper, we conduct a detailed empirical investigation on the goodness of fit of various compound Poisson distributions and we develop a distribution-based demand classification scheme the validity of which is also assessed in empirical terms. Our empirical investigation provides evidence in support of certain demand distributions and the work described in this paper should facilitate the task of selecting such distributions in a real world spare parts inventory context. An extensive discussion on parameter estimation related difficulties in this area is also provided.

Supply chain forecasting when information is not shared

The operations management literature is abundant in discussions on the benefits of information sharing in supply chains. However, there are many supply chains where information may not be shared due to constraints such as compatibility of information systems, information quality, trust and confidentiality. Furthermore, a steady stream of papers has explored a phenomenon known as Downstream Demand Inference (DDI) where the upstream member in a supply chain can infer the downstream demand without the need for a formal information sharing mechanism. Recent research has shown that, under more realistic circumstances, DDI is not possible with optimal forecasting methods or Single Exponential Smoothing but is possible when supply chains use a Simple Moving Average (SMA) method. In this paper, we evaluate a simple DDI strategy based on SMA for supply chains where information cannot be shared. This strategy allows the upstream member in the supply chain to infer the consumer demand mathematically rather than it being shared. We compare the DDI strategy with the No Information Sharing (NIS) strategy and an optimal Forecast Information Sharing (FIS) strategy in the supply chain. The comparison is made analytically and by experimentation on real sales data from a major European supermarket located in Germany. We show that using the DDI strategy improves on NIS by reducing the Mean Square Error (MSE) of the forecasts, and cutting inventory costs in the supply chain.

Modelling and solution approaches for the interconnected city logistics

Achieving a sustainable delivery of goods in urban areas has become a challenging task for service providers and logistics managers. Under this context, the physical internet (PI) Manifesto offers through its emergent concept of interconnected city logistics (ICL) a solution toward a more sustainable transportation of PI containers within cities. In this article, we explore the operational urban transportation problem of PI containers under ICL considerations. For this variant, built on the multiplicity of urban logistics centres and their interconnection, a comprehensive modelling approach is proposed to include key features such as multiple time periods, multi-zone urban coverage, heterogeneous fleets, multi-trip and multi-hub pickups, and delivery constraints. In order to deal with solvability issues encountered with realistic instances of the problem, a heuristic solution approach is developed. This is done with the objective to come up with solutions offering the best trade-offs between economic and ecological attributes within a short computational time. To validate the approach, a realistic set of instances is built with data inspired from city freight movements in an urban area in France. Using these experiments, the solvability of the model and the performance of our heuristic approach are discussed and managerial insights are derived.

A note on the demand distributions of spare parts

In a recent paper published by the International Journal of Production Research (Syntetos, Babai, and Altay 2012), we undertook a detailed empirical investigation of the validity and utility of various statistical distributions in a spare parts demand context. Spare parts are typically characterised by intermittent demand structures and, as such, the findings presented in that paper safely also extend to other inventory settings (like those comprising slow-moving items, etc.). The choice of a statistical distribution constitutes an important input into a stock control system since parametric decisions about replenishments are influenced directly by the hypothesised demand distribution. When reflecting on the paper’s methodology, an error was identified. The goodness-of-fit of the various distributions considered in that study was assessed by employing the Kolmogorov–Smirmov (K–S) test. When calculating the relevant statistic, the number of categories should be derived based on the empirical sample size. However, in the paper under discussion, the number of categories was derived based on the (maximum) demand size rather than the sample size. The purpose of this note is to point out the drawback associated with this analysis and its implications for the results presented in the paper. Suppose that the N observations in a demand series are ordered from the smallest to largest, i.e.

On the performance of the base-stock inventory system under a compound Erlang demand distribution

In this paper, we propose a new method for determining the optimal base-stock level in a single echelon inventory system where the demand is a compound Erlang process and the lead-time is constant. The demand inter-arrival follows an Erlang distribution and the demand size follows a Gamma distribution. The stock is controlled according to a continuous review base-stock policy where unfilled demands are backordered. The optimal base-stock level is derived based on a minimization of the total expected inventory cost. A numerical investigation is conducted to analyze the performance of the inventory system with respect to the different system parameters and also to show the outperformance of the approach that is based on the compound Erlang demand assumption as compared to the classical Newsboy approach. This work allows insights to be gained on stock control related issues for both slow and fast moving stock keeping units.