The inventory centralization impacts on sustainability of the blood supply chain

doi:10.1016/j.cor.2016.08.014

Computers & Operations Research

Volume 89, January 2018, Pages 206-212

https://doi.org/10.1016/j.cor.2016.08.014 Get rights and content

Highlights

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Analyzing impacts of centralization in a two-echelon supply chain with perishability.
•
Providing the closed form formulas for performance measures of blood supply chains.
•
Demonstrating that centralization increases the sustainability of the blood supply chain.

Abstract

This paper studies the significance of inventory centralization at the second echelon of a two-echelon supply chain with perishable items when the agents of the second echelon use an ( $S - 1, S$ ) inventory policy. The replenishment at the first echelon is considered to be stochastic. The context in which the studied problem exists is in the blood supply network where the first echelon includes a single blood bank that receives stochastic supply from donors. The second echelon contains hospitals receiving external demands (transfusions). In our proposed structure, some of the hospitals in close proximity of each other maintain centralized inventories to serve their demands in addition to the demands by other neighbour hospitals. The results demonstrate that centralization of hospitals’ inventory is a key factor in the blood supply chain and can increase the sustainability and resilient of the blood supply chain. Using numerical study, it was observed that reducing the number of hospitals that hold inventory from 7 to 3 decreases outdate and shortage in the supply chain by 21% and 40% respectively.

Introduction

The aim of the blood supply chain is supplying adequate safe blood to hospitals. It is paramount that blood is available at hospitals for transfusion purposes since a shortage may endanger the life of patients. In the blood supply chain, replenishment in the blood bank is not fully in control of the decision makers, since replenishment occurs by blood donations. This important property discriminates the blood supply chain from other well-studied supply chains with perishability. The blood supply chain can be modelled as a two-echelon inventory system where the items arrive at the first echelon (the blood bank) stochastically and stochastic demand is realized at the second echelon (the hospitals). The hospitals place orders to the blood bank and there is a lead time for fulfilling the orders. In case of emergencies, the orders are fulfilled immediately with almost zero lead time. Outdates and shortages can occur at the first or second echelon. The outdate in the second echelon is more undesirable (i.e. more costly) than outdate in the first echelon for two reasons: the first reason is that a transportation cost is incurred to an item in the second echelon (the hospitals). The second reason is that an outdated item in hospital “A” could be used in another hospital (hospital “B”) if it was not issued to hospital “A” but if an item is outdated in the blood bank it also became outdated in any hospital that it was issued to. This fact is easy to prove as the blood bank and hospitals use a First In First Out (FIFO) policy. It is very hard to say if the cost of shortages in one of the echelon is greater than the other one. The shortage at hospitals is highly undesirable as it is related to patients’ lives and puts lots of pressure on the system to immediately deliver blood components. Shortage at the blood bank is also very undesirable since the blood bank may fail to satisfy the required emergency deliveries and consequently risk patients’ lives. Furthermore, shortages in the blood bank require calls to external resources or blood banks in other regions that imposes considerable costs to the system. Recent studies show transfusion of fresher red blood cells may lead to better results in some groups of patients. This means not only a blood supply chain should minimize its outdates and shortages, but it also needs to reduce (minimize) the age of transfused items. Therefore, the performance of a blood supply chain can be quantified by the outdate rates, shortage rates and the average age of issues. One way to improve supply chain performance is to reshuffle the structure of the supply chain by centralization of hospitals’ inventory in the second echelon as much as possible. For example, assume that there are four hospitals H¹, H², H³ and H⁴ at the second echelon of the supply chain; i.e. there are four hospitals that hold the inventory in the second echelon. All of them receive items from the blood bank. We show that if H¹ can receive items from H² within a negligible amount of time and H³ can receive items from H⁴ within a negligible amount of time; keeping inventories only in H² and H⁴ will significantly improve performance of the supply chain. Note that H² and H⁴ are two hospitals that hold the inventory in the second echelon.

Here we present four examples to verify the assumption that some of the hospitals are close proximity from each other and it is pragmatic to centralize their inventory:

Example 1: There are three nearby hospitals in Heidelberg, Melbourne, Australia. The Mercy Hospital is located in the same building as Austin Hospital. In addition, The Warringal Private Hospital is located only 400 m away from Austin Hospital.

Example 2: There are four neighbour hospitals in Parkville, Melbourne, Australia. The distance between Royal Children's Hospital (H1) and Melbourne Women's Hospital (H2) is less than 900 m and the distance between Melbourne Women's Hospital (H2) and Melbourne Private Hospital (H3) and Royal Melbourne Hospital (H4) is less than 250 m (according to Google Map).

Example 3: The Women's and Children's Hospital in Adelaide, Australia is located about 350 m away from The Memorial Hospital.

Example 4: The Wellington Hospital in Wellington, New Zealand is located about 650 m away from The Ewart Hospital.

In this paper we systematically consider such centralization in the blood supply chain. The main focus of this study is to shed some lights on the impacts of centralization of blood inventories at the hospitals. One particular issue of interest is to examine how the number of hospitals and variability in the size of hospitals could influence the blood supply chain performance. The insights from our analysis will help to identify those hospitals which should keep their inventory management system intact and those which need to keep zero base stock inventory while satisfying their demands using other nearby hospitals. To the best of our knowledge there is no research on the inventory centralization issue in a two-echelon inventory system with uncontrollable replenishment and perishable items, hence our paper is a novel work in this field.

The rest of the paper is organized as follows. Section two reviews the related literature. Section three provides approximation formulas for the performance measures of a blood supply chain. Section four investigates the optimal value of base-stock level (S) as the decision variable in a blood supply chain. Section five discusses how the number and configuration of the hospitals could influence the performance of a blood supply chain. Section six offers conclusions and some directions for future research.

Section snippets

Literature review

The research on the perishable supply chain with focus on ordering policies is copious. For a few examples refer to Yu et al. [32]; van Donselaar and Broekmeulen [30] and Herbon et al. [15]. However, there is little research considering the situation of the blood service with stochastic replenishment. There is a literature survey of the blood supply chain by Belien and Force [6] that reviews and classifies 98 papers published in the area of the blood supply chain in last three decades.

Performance approximation

We first review the configuration and assumptions under the studied system. We assume that items arrive at the blood bank from a stationary Poisson process with rate λ and demand occurs at the hospitals by a stationary Poisson processes. The demand rate at hospital i is represented by μ_i. Items have a fixed shelf life (m) and it starts at the donation time (the time that the item arrives at the blood bank). An item is outdated after m units of time (e.g. days) of the donation time. There is a

Optimal S's at hospitals

The levels of the inventory at the hospitals (S's) are the decision variables in the supply chain. These are conventionally obtained by minimizing a cost function reflecting the effects of outdate and shortage rates at hospitals and the blood bank. Let's introduce the following notations:

n is the number of hospitals.

S=( $S_{1}, S_{2}, \dots, S_{n}$ ) is base-stock level at hospitals (hospitals use an (S-1,S) policy and S_i is the base-stock level at hospital i.

μ_i is the original demand rate at hospital i.

$μ_{i}^{c}$ is

Sensitivity analysis – centralizing impacts

This section analyses the centralization impacts on the performance measures and furthers the analysis on a network perspective.

Conclusion

Stochastic behaviour of demand is a challenging aspect in many supply chains but it is more crucial for the supply chain with perishability. Moreover, in the blood supply chain the input to the inventory of the blood bank that is located at the first echelon occurs by donations that has a stochastic behaviour itself and imposes extra complexity and uncertainty to the supply chain issues. Minimizing both outdates and shortages as well as reducing the age of the items patients receive are targets

Acknowledgments

The authors are grateful to the anonymous reviewers and the guest editor for their numerous constructive and thoughtful comments throughout the submission process.

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View full text

The inventory centralization impacts on sustainability of the blood supply chain

Highlights

Abstract

Introduction

Section snippets

Literature review

Performance approximation

Optimal S's at hospitals

Sensitivity analysis – centralizing impacts

Conclusion

Acknowledgments

Int J Prod Econ

Eur J Oper Res

Eur J Oper Res

Comput Oper Res

Int J Prod Econ

Eur J Oper Res

Int J Prod Econ

Omega

Int J Prod Econ

Int J Prod Econ

On the issuing policies for perishable items such as red blood cells and platelets in blood service

Decis Sci

A novel allocation strategy for blood transfusions: investigating the trade between the age and availability of transfused blood

Transfusion

Déjà-vu all over again: using simulation to evaluate the impact of shorter shelf life for red blood cells at Héma-Québec

Transfusion

Analysis of ordering and Allocation Policies for multiechelon, Age-differentiated Inventory Systems