Whole blood or apheresis donations? A multi-objective stochastic optimization approach

Highlights

• A novel methodology for the stochastic multi-objective optimization problem.

• Evaluation of the optimality gap for each non-dominated solution.

• Consideration of several important characteristics of the blood supply chain.

• Discussion of several solution methods for the Sample Average Approximation problem.

Abstract

In the blood supply chain, several alternative technologies are available for collection and processing. These technologies differ in cost and efficiency: for example, collection by apheresis requires very expensive machines but the yield of blood products is considerably greater than whole blood collection. Blood centre managers are faced with the difficult strategic problem of choosing the best combination of technologies, as well as the equally difficult operational problem of assigning donors to collection methods. These decisions are complex since so many factors have to be taken into account, including stochastic demand, blood group compatibilities, donor availability, the proportions of blood types in both donor and recipient populations, fixed and variable costs, and process efficiencies. The use of deterministic demand forecasts is rarely adequate and a robust decision must consider uncertainty and variability in demand as well as trade-offs between several potentially conflicting objectives. This paper presents a multi-objective stochastic integer linear programming model to support such decisions. The model treats demand as stochastic and seeks to optimize two objectives: the total cost and the number of donors required. To solve this problem, we apply a novel combination of Sample Average Approximation and the Augmented Epsilon-Constraint algorithm. This approach is illustrated using real data from Bogota, Colombia.

Introduction

The blood supply chain comprises the processes of collecting, testing, processing and distributing blood and blood products, from donor to recipient. Blood products are transfused to patients as part of routine medical treatments or surgical operations, and also in emergency situations. However, the increasing demand for blood products as well as the decreasing population of donors makes decision-making for the blood supply chain challenging (Seifried et al., 2011), and this is particularly the case in developing countries with limited resources. On the other hand, shelf-life constraints, multiple products, compatibilities and blood proportions make the problem complex, limiting the set of methodologies suitable.

Different configurations of the blood supply chain can be found in developed and developing countries. Developed countries tend to have centralized systems, while, in developing countries, the systems are often more decentralized. For example, in the UK there are five large production centres that supply blood for England and Wales (Woodget, 2014); in contrast, in Colombia there are 82 production centres of different sizes that provide blood products for the whole country. Another important difference between developed and developing countries is the availability of resources. According to the World Health Organization, the blood donation rate in high-income countries is 36.8 donors per 1000 population, while in middle-income and low-income countries it is 11.7 and 3.9 donations per 1000 population respectively (WHO, 2014). Hence, blood supply chain management is challenging in general; however, features such as economic resources, donor behavior and decentralization of the system have made these kinds of decisions even more challenging in developing countries.

A recent review (Osorio, Brailsford, & Smith, 2015) of quantitative models in the blood supply chain identifies several gaps in the literature. One of the gaps identified is the necessity to study the different collection and production alternatives, given that blood products can be obtained in ways that differ in terms of cost and efficiency. Decisions about strategies to fulfil demand considering whole blood and apheresis donations have been rarely studied in general.

This paper contributes in two different ways. Firstly, the model proposed in this paper includes several characteristics that have not been taken into account in previous research in quantitative models for the blood supply chain, for example, the combination of uncertainty and multiple objectives simultaneously. Furthermore, the model includes other aspects that are rarely considered in blood supply chain literature such as multiple collection methods and multiple products simultaneously. Given a stochastic annual demand for blood products, the model supports strategic decisions such as technology selection and donor allocation and the use of substitute products in order to meet demand while minimizing both cost and the number of donors required. Secondly, in order to deal with uncertainty and multiple objectives, this work proposes a novel methodology that integrates two other approaches, namely Sample Average Approximation (SAA) and the Augmented Epsilon-Constraint algorithm. The model and the proposed methodology are evaluated using actual data in the public domain from Bogota, Colombia (INS, 2013).

This paper proceeds as follows: Section 2 presents the literature review of the main concepts used in this paper. Section 3 describes the problem and the type of decisions to be studied while Section 4 describes the data used. Section 5 introduces the mathematical formulation of the problem studied, with both a deterministic and a stochastic version of the model. Section 6 presents the integrated methodology proposed. Finally, in Section 7, the results of the application of the proposed model and methodology to a case study are presented, while Section 8 presents the main conclusions and extensions of this work.