A robust mathematical model for platelet supply chain considering social announcements and blood extraction technologies

Highlights

• Presenting social announcement in collection facilities to promote the number of available donors.

• Assessing hospitals’ efficiency as suppliers for allocating BET regarding to different types of available donors.

• Developing the donor appointment reservation including, booked and non-booked donors within and after working hours.

• Considering donors’ priority and incorporating it into the model as first-time, experienced and regular donor.

• Applying a robust stochastic optimization approach to cope with natural input uncertainty in an platelet supply chain.

Abstract

Since the only source of supplying platelets is available donors, evaluating donors’ treatments plays a vital role in the supply chain. According to the investigation of a real study, four main issues have directly affect the quantity of platelet donation in the supply chain, namely, (1) different types of donors as first-time secondary polycythemia donors, experienced secondary polycythemia donors and regular donors, (2) number of booked and non-booked donors within and after working hours, (3) submitting social announcements such as banner ads, social media, and newspapers, and (4) allocating blood extraction technologies to hospitals. Moreover, dealing with demand fluctuation and short lifespan of platelets is also a critical point. Noteworthy, since the technology allocation in hospitals is expensive, the hospitals’ efficiency is determined by a fuzzy analytic hierarchy process approach. Therefore, to address these issues, firstly, we create a balance between hospitals’ efficiency as suppliers and costs in a bi-objective mixed-integer programming model. Then, a robust-stochastic approach is considered to tackle the uncertainty in input data. The results validate in a real case study to facilitate practitioners making proper decisions.

Introduction

Platelet (PLT), plasma and red blood cell are the most critical derivatives of whole blood in which, PLT has the least lifespan and expires between 5 and 7 days. Platelet supply chain (PSC) is an essential system for patients requiring PLTs. Shortage of PLT puts patient lives at risk and leads to high expenses for the supply chain (Haijema, van der Wal, & van Dijk, 2007). Four echelons in PSC for dealing with patient consumption are dedicated, including (1) collection, (2) test and analysis, (3) production and (4) distribution to public treatment centers (see Fig. 1). At the echelons, decisions are associated with donor assigning in blood collection centers, suppliers’ effectiveness, social announcement, production planning, and so on. Noteworthy, a lack of orchestrated decision management in PSC exerts negative influences over the total cost and unsatisfied demand.

At the blood collection centers, an incentive mechanism to increase the number of available donors is the essential point, especially in developing countries that the number of donors is much lower than in developed countries (Zahiri & Pishvaee, 2017). In blood product supply chain, the first echelon (collection) depends on various issues from population densities, the number of collection facilities and production methods (through apheresis or from whole blood), up to the overall capacity of the registered donors during and after working hours, which is limited by the number of physicians, devices and gender of donors. Given the fact that women cannot donate through apheresis because of the increasing rate of vasovagal reactions and also the less amount of obtained donated blood units (Tomita et al., 2002), it is remarkable to consider donor’s gender in designing and planning. Moreover, laboratory centers’ reliability, the transportation infrastructure, the number of medical centers, and their various requirements affect the PSC.

Living in heights, cities with air pollution, as well as heavy smoking rise erythropoietin in the human body which consequently, cause polycythemia (Tefferi, 2005). Polycythemia categorizes into the primary and secondary types. The patients’ blood of primary polycythemia is useless, and consequently, the taken blood units are completely disordered. On the other hand, most blood proportion of the second type is useful, as secondary polycythemia patients are recommended to donate blood four times a year (https://ibto.ir). Accordingly, the number of available ordinary donors and secondary polycythemia donors should be determined. As stated before, decision-makers (DMs) have a strong desire to persuade donors to donate regularly. This matter impels them to pay more attention to the procurement issues and apply blood extraction technology (BET) at efficient medical centers. Evaluating medical centers’ efficiency to allocate BET, based on the number of crucial criteria, is expressed as suppliers’ effectiveness.

Due to the short life-span of PLTs, donors are always needed, while only 5% of the eligible people practically donate their blood (Schreiber et al., 2006). Considering social announcement may assist collection facilities to motivate people for donating blood. Besides that, by focusing on promoting the number of booked donors, the total logistics cost will be decreased. From this viewpoint, social announcements, such as banner-ads, social-media, and newspaper, for blood donation can be applied to promote blood donation. Noteworthy, each type of social announcement grabs a different number of donors.

Production planning is another momentous decision in PSC. As far as the health care service’s provision addressed, the more it passes through the life of PLTs, the more is the risk of bacterial contamination. Accordingly, PLT demand, based on requirements, can be categorized into three types, including fresh, young, and old. For long-time treated patients, one-day fresh PLTs are applicable which generally obtain through apheresis. Two or three-day young PLTs are mainly applied to patients with extreme rupture or hematology cases. Old PLTs, which are titled to PLTs with more than three days old, are appropriate for general surgery (Harmening, 2012). Remarkably, there is a natural uncertainty in the quantities of patients’ consumption as demand may increase sharply in some periods. Therefore, one of the major concerns for DMs is demand fluctuation which compelled them to apply uncertainty programming in their models.

In this study, using social announcement growth as an incentive, we attempt to orchestrate PSC model in a tactical decision-making process. To create a more realistic model, we submit various social announcements in the collection facilities for increasing the number of available donors. In the proposed model, in each social announcement, the donor’s motivational rate is different which leads to attracting the various types of donors. In the investigated problem, different production procedures are considered. Also, three types of donors have been prioritized and incorporated into the model as (1) first-time secondary polycythemia donor, (2) experienced secondary polycythemia donor and (3) regular donor. Moreover, the gender of donors has assumed as the woman are not able to donate platelets through apheresis, and the obtained blood units from women are lower than those of men. Additionally, we address different ages for PLTs based on patients’ consumptions. To tackle natural demand uncertainty and shortage, we assume that hospitals prefer to hold extra PLTs of different ages as safety stock in the blood banks. In order to indicate the usefulness of the proposed models, we apply them to a real case study. The incremental contributions of this paper are as follows:

• Presenting social announcements in collection facilities to promote the number of available donors.

• Assessing hospitals’ efficiency as suppliers for allocating BET regarding to different types of available donors.

• Developing the donor appointment reservation including, booked and non-booked donors within and after working hours in an integrated PSC.

• Considering donors’ priority and incorporating it into the model as (1) first-time secondary polycythemia donor, (2) experienced secondary polycythemia donor and (3) regular donor.

• Identifying the optimal level of PLT units drawn from each procedure (i.e. apheresis and whole blood) and gender.

The rest of this paper is organized as follows: In Section 2, relevant articles are structured. In Section 3, the methodology of the evaluation is dedicated. Managerial insights through numerical experiment are defined from solution methodology in Section 4. At last, conclusions and future opportunities are discussed in Section 5.