Order Quantity Distributions: Estimating an Adequate Aggregation Horizon

Abstract

Accepted: 1 September 2016In this paper an investigation into the demand, faced by a company in the form of customer orders, is performed both from an explorative numerical and analytical perspective. The aim of the research is to establish the behavior of customer orders in first-come-first-serve (FCFS) systems and the impact of order quantity variation on the planning environment. A discussion of assumptions regarding demand from various planning and control perspectives underlines that most planning methods are based on the assumption that demand in the form of customer orders are independently identically distributed and stem from symmetrical distributions. To investigate and illustrate the need to aggregate demand to live up to these assumptions, a simple methodological framework to investigate the validity of the assumptions and for analyzing the behavior of orders is developed. The paper also presents an analytical approach to identify the aggregation horizon needed to achieve a stable demand. Furthermore, a case study application of the presented framework is presented and concluded on. KeywordsDemand distribution, Poisson processes, order quantities, Coefficient of Variation, Planning&Control. IntroductionTo achieve good customer service, companies aim at delivering products on time at competitive prices. One aspect in achieving competitive performances is companies' abilities to match customer expectations. In many situations resources are dedicated prior to knowing actual customer demand. This makes forecasting customers' ordering behavior of critical importance. Most research on this topic has been dedicated to either forecasting demand [1] or how to react in a quick robust manner to customer demand through e.g. better planning [2]. The research presented in this paper focuses on another aspect that has received limit research attention, namely the fact that demand is composed of individual customer orders. The fact that the demand a company faces is actually composed of a large number of presumed i.i.d. customer orders that can be aggregated is challenged in this research through an investigation of actual behavior and modelling of what to do when customer orders are in fact not i.i.d. This paper expands on the work reported in [3] through adding a framework, extending the complexity of the model, elaborating on the current state and adding more numerical examples. This paper focuses on customer order quantity distributions, analyses their behavior and investigates the consequence of transforming these into demand rates that are used for planning purposes. It also presents an analytical model to calculate the aggregation horizon necessary to ensure a stable distribution of demand for operational planning purposes. In this research main aim is to establish the specific need for aggregation in 39 Unauthenticated Download Date | 5/9/18 8:28 PM Management and Production Engineering Reviewthe form of the number of customer orders needed to aggregate to achieve a system-wide desired stability. In...

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