Elsevier

Omega

Volume 76, April 2018, Pages 1-17
Omega

Finite time horizon fill rate analysis for multiple customer cases

https://doi.org/10.1016/j.omega.2017.03.004Get rights and content

Highlights

  • Investigates the fill rate behavior in multiple customer cases for three demand fulfillment policies.

  • Analyzes the impact of performance review period length on the fill rate in multiple customer scenarios.

  • Studies the impact of correlated demands on the fill rate.

  • Examines the impact of size of customer in realized fill rate in multiple customer cases.

Abstract

The item fill rate – defined as the fraction of demand that is immediately satisfied from on-hand stock – is commonly used as a performance measure in service level agreements between customers and suppliers. Under such agreements, the fill rate is measured over a finite horizon (the performance review period) and the supplier faces a financial penalty if an agreed target is not met. The distribution of the item fill rate (fill rate) determines the probability of exceeding the agreed target, it is therefore a point of interest in SLA coordination. The average finite horizon fill rate decreases with an increase in performance review period length. However, the impact of performance review period length on the shape of the fill rate distribution is not well understood. Past studies of finite horizon fill rate only consider a single customer in the supply chain. In this study, we analyze fill rate distributions for a supplier that has multiple customers each with their own service level agreement. We examine the effects of performance review period length, choice of demand fulfillment (service) policy and correlation between customers’ demands on both the average fill rate and the probability of achieving the target fill rate. This study provides new insights into service level agreement coordination between suppliers and customers. For instance, the results show that a supplier with multiple customers must take care with choosing a service policy, as rationing will affect the fill rate distribution and hence the realized service level.

Introduction

In an increasingly globalized business environment, companies need strong inventory management strategies to remain competitive [33]. One such strategy is the use of a service level agreement (SLA) as a mechanism to manage and evaluate supplier performance. An SLA is an agreement between a service provider and a client that specifies the required quality or degree of service [13]. An SLA is one of the most common types of contracts used to manage supplier relationships [24]. A survey by Oblicore [31] found that 91% of organizations use SLAs to manage their suppliers. Thonemann et al. [37] found that in Germany 70% of retailers use service levels to measure the performance of their suppliers.

Giant Eagle, a popular US supermarket chain, uses SLAs and associated penalties to manage the performance of its suppliers over time [19]. In 1997 a late delivery by an aircraft manufacturer violated the terms of the service level agreement and resulted in a large financial penalty and the subsequent loss of customers [16]. These are just two examples of the widespread use of SLAs to manage supply level and on-time delivery.

In a standard SLA the partners agree on a target service level that should be achieved by the supplier in each defined performance review period. If the supplier fails to meet this target, they typically face some kind of financial penalty. There is also scope for the use of service level performance measures to promote competition between multiple suppliers. Dyer et al. [10] reported that it was common in Japan for companies to apply a “two-vendor policy” to promote competition and thus improve supplier performance. An empirical study by Bensaou [4], found that Japanese companies often divided their purchases between multiple suppliers and then subsequently used service level measures to evaluate and select which suppliers to maintain relations with.

In inventory theory, inventory management mechanisms and related service levels have been an active area of study since the 1950s [14]. Lee and Billington [23] and Johnson and Scudder [15] reported that item fill rate is a popular and preferred service level measurement used by many firms. The item fill rate is defined as “the long run average fraction of demand satisfied immediately using on-hand stock” [40]. A survey undertaken by Kay [18] showed that 70% of manufacturing firms believed that supplier performance, especially fill rate and on time delivery, are critical to their business.

In some cases, an alternative service level measure, known as the “ready rate”, is employed. The ready rate is defined by Axsäter [2] as “the fraction of time that the net inventory level is positive”. Cesaro [7] defined yet another service level measure as “the expected number of back orders outstanding at a random point in time”. Schneider [32] provided a comprehensive classification and evaluation of various service level measures. In this paper, we study the item fill rate, also referred to as the “fill rate”, as our service level measure. The fill rate is a random variable across a finite time horizon, the incentive for studying this random variable derives from the extensive practical use of fill rates as the performance measure in SLAs.

In practice, a supplier will often replenish the inventory to a base stock level at a specified time interval, called the “replenishment period”, for example on a weekly, monthly, or daily basis. Supplier performance is then evaluated at a regular interval, the performance review period, which may be monthly, quarterly, or six-monthly, for example. In a given performance review period, a supplier failing to meet the target fill rate specified in the SLA may incur a financial penalty, while in some SLAs the supplier may receive a bonus for exceeding the target fill rate. Thus, under a typical SLA the supplier is responsible for achieving a target fill rate in each performance review period.

In a finite period, inventory level and supplier performance can be monitored and the resultant information can be used to assist a supplier in meeting or exceeding the terms of an SLA. Regrettably, it is not simple to calculate the probability of reaching a particular fill rate target for a given base stock level and performance review period length. In practice, some suppliers with SLAs use an infinite horizon model, then “overshoot” to improve their probabilities of success. For example, if a supplier must exceed a 90% fill rate, they might establish their stock level based on a 93% long-run fill rate. This overshooting is done to improve their probability of success and hence avoid any related penalties.

Previous studies of SLAs often assume there is a single customer in the supply chain, however in practice a supplier usually deals with multiple customers. To address this gap, our study is focused on fill rate behavior and related management insights in the multiple customer case. For instance, a supplier dealing with multiple customers' needs to understand the impact of demand fulfillment policy choice on the fill rate realized for each customer. Likewise, understanding the impact of performance review period length on the fill rate assists the supplier in negotiating SLA terms with multiple customers. Similarly, understanding how the correlation between demand from customers impacts the fill rate helps a supplier in deciding required stock levels and in setting related production and marketing strategies.

The aim of this study is to systematically investigate finite horizon fill rate behavior when there are multiple customers for a supplier that uses a base stock policy. In this setting, there are S items of pooled inventory available in each replenishment period to fulfill the demand of all customers. We alter the performance review period length, the demand fulfillment policy (referred to as the “service policy”) and the correlation between demand from customers to examine the changes in the average fill rate and the probability of exceeding the target fill rate of each customer. Three service policies are considered in this study: first come first served (FCFS), prioritized lowest fill rate (PLFR) and a linear programming (LP) approach. Each policy is explained in detail in Section 3.

Our analysis sheds some light on how suppliers might approach negotiating SLAs and determine how they will best manage their inventories. In summary, the research questions in this study are:

  • How do the average fill rate and the probability of success (i.e. probability of exceeding the target fill rate) change in the multiple customer case when the performance review period length is increased? In the literature, this question has been answered by Chen et al. [8] and Thomas [36] for the single customer case.

  • How does the base stock level required to achieve a given probability of success change when a supplier deals with multiple customers, rather than one customer?

  • How does the choice of demand fulfillment policy (service policy) affect the fill rate of each customer?

  • How does the correlation structure of demand affect the fill rate of each customer?

  • In the multiple customer case, who receives better service (i.e. a higher average fill rate and higher probability of exceeding the target fill rate), the customer with larger demand or the customer with smaller demand?

The key findings of this study for a supplier with multiple customers are as follows:

  • If demands from customers are independent, the average fill rate is the same as in the single customer case. Average fill rate decreases when the performance review period length increases. This was observed for all three service policies.

  • If demands from customers are independent and the LP service policy is employed, the probability of success is the same as in the single customer case. However, when either the FCFS or PLFR polices are used, the probability of success is higher than the single customer case for short performance review periods, and lower for long performance review periods.

  • If demands from customers are independent and the LP service policy is employed, the base stock level required to achieve a given probability of success is the same as in the single customer case. Whereas when either the FCFS or PLFR policies are employed, the required base stock level is lower than the single customer case for short performance review periods, and higher for long performance review periods.

  • When demands from customers are negatively correlated, but the aggregated variance of demand is fixed, both the average fill rate and the probability of success are lower than in the single customer case. This holds for all three service policies.

  • When demands from customers are positively correlated, but the aggregated variance of demand is fixed, the average fill rate is the same as in the single customer case for all three service policies. When the LP policy is used the probability of success is the same as in the single customer case. However, under either the FCFS or PLFR policy, the probability of success is higher than in the single customer case for short performance review periods, and lower for long performance review periods.

  • When either the FCFS or PLFR policy is employed both the average fill rate and the probability of success are higher for customers with larger demand than for customers with smaller demand. Whereas for the LP policy the average fill rate and the probability of success of all customers is the same regardless of demand size.

In summary, the above findings indicate that a supplier with multiple customers must take care with the choice of service policy, as rationing will affect the fill rate distribution and therefore the realized service level.

The rest of the paper is organized as follows. The next section provides a review of the related literature. Section 3 introduces the notations and the modeling framework. Section 4 presents the results, analysis and discussion for different scenarios and Section 5 concludes.

Section snippets

Literature review

There are numerous studies investigating inventory service level measures for a supplier in a supply chain [1], [26], [39]. Service level measures, such as the fill rate or ready rate, can be measured over an infinite or finite horizon. Published research to date has been dominated by studies that employ an infinite horizon. However, as described in the introduction, in a typical SLA the inventory service level is measured and monitored periodically. Chen et al. [8] showed that for an inventory

Definitions and notations

The notations used in this study are as follows:

    T

    the length of the performance review period measured by the number of replenishment periods. For example, when T=5 the performance is reviewed after 5 replenishment periods

    S

    the base stock level in the base stock policy

    I

    the set of customers. The cardinality of set I is n (i.e. n is the number of customers)

    βi(S, T)

    the fill rate for customer i in a performance review period. Where T is the performance review period length and S is the base stock

Analysis

Because of the complexity arising from the numerous parameters in the model, we use a simulation approach, similar to Thomas [36], to analyze the fill rate in a supply chain with multiple customers. In this section of the paper analysis of fill rate distributions and stocking decisions is undertaken for various scenarios with accompanying insights and remarks.

Scenarios differ in terms of the number of customers, the service policy (FCFS, PLFR or LP) and the length of the performance review

Conclusions

This work has explored the behavior of the item fill rate when there are multiple customers in the supply chain. The findings provide insights that can assist suppliers in the design and negotiation of SLAs. Our experiments were designed such that the aggregated demand distribution for the multiple customer case was equivalent to the demand in a corresponding single customer case. We considered three different policies for demand fulfillment for the multiple customer case: a first come first

Acknowledgment

The authors are grateful to the anonymous reviewers and the Area Editor for their insightful and helpful comments that helped us to significantly improve this paper.

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    This manuscript was processed by Associate Editor Q. Wang.

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