Dynamically optimizing the administration of vaccines from multi-dose vials

Abstract

Many vaccines are manufactured in large, multi-dose vials that once opened, must be used within a matter of hours. As a result, clinicians (especially those in remote locations) face difficult tradeoffs between opening a vial to satisfy a potentially small immediate demand versus retaining the vial to satisfy a potentially large future demand. This article formulates a Markov decision process model that determines when to conserve vials as a function of time of day, the current vial inventory, and the remaining clinic-days until the next replenishment. The objective is to minimize open-vial waste while administering as many vaccinations as possible. It is analytically established that the optimal policy is of a threshold type. Furthermore, an extensive sensitivity analysis is conducted that speaks to the benefits of consolidating demand, investing in buffer stock, and adopting different vial sizes. Lastly, a practical heuristic is evaluated and shown to perform competitively with the optimal policy.Keywords: Markov decision process, perishable inventory model, multi-dose vial, vaccine wastage * Corresponding author gitis, etc. A key step in achieving this goal is to reduce the large amount of vaccine "wastage", i.e., doses that are manufactured and shipped but then not administered while still viable, in developing countries. WHO (2005) estimates the overall global vaccine wastage rate to be a staggering 50% which varies with vial size, vaccine type, location, etc. More specifically, a recent study conducted in Bangladesh (Guichard et al., 2010) reports average wastage rates of 85.1% for BCG (tuberculosis), 71.2% for measles, 36.6% for TT (tetanus), and 44.2% for DPT (diphtheria, pertussis, and tetanus combination). Reducing wastage has been mandated by WHO (2005) and identified as a key factor in maintaining the financial sustainability of immunization programs in the world's poorest countries (Kamara et al., 2008) and in increasing the delivery of vaccines to patients. In the overall effort to improve vaccine coverage rates, it is critical that clinics manage vaccine supplies efficiently in the field to minimize wastage and maximize the number of immunizations administered.The primary driver of vaccine wastage is the fact that many vaccines are manufactured in large, multi-dose vials, which are more economical to produce than single-dose vials (Lee et al., 2010) but result in so-called open-vial waste (Guichard et al., 2010). Although unopened vials can be stored in reliable temperature-controlled environments for relatively long periods of time, for many vaccine types once a vial is reconstituted (i.e., "opened"), all of its doses must be used within a relatively short period of time

Customizing immunization clinic operations to minimize open vial waste

“…In Section 2.1, we describe the MDP model developed in Mofrad et al (2014), which is used to generate optimal vaccine administration policies. In Section 2.2, we introduce a new simulation model that is used to simulate the performance of a clinic under a given vaccine administration policy generated by the MDP model.…”

“…To clarify the modeling approach used in Mofrad et al (2014), we present Figure 1. Mofrad et al (2014) develop a finite horizon MDP model for vaccination sessions between two stock replenishments where Q vials are available at the beginning of each replenishment cycle and each vial consists of z doses. As seen in Figure 1, the replenishment cycle is divided into T sessions and each session is divided into η timeslots of equal length.…”

“…As previously stated, the existing literature on multi-dose vials is rather limited, and primarily focuses on the economic implications of single-vs. multi-dose vials. In contrast, Mofrad et al (2014) address another means for controlling OVW, namely that of vaccine administration from multi-dose vials, using a rigorous mathematical approach. They formulate a Markov decision process (MDP) model that maximizes the number of vaccinations between two consecutive vaccine stock replenishments (i.e., over one "replenishment cycle") by determining when to discontinue vaccinations as a function of time of day, the current vial inventory and the remaining number of vaccination sessions until the next inventory replenishment.…”

“…(Note that by "sessions" we mean the number of dedicated periods per cycle during which the clinic operates; a session typically corresponds to a working day, e.g., an eight hour session that runs from 8am-4pm.) Although they consider the same decision making problem considered herein, the focus in Mofrad et al (2014), is on model formulation, policy structure and limited sensitivity analysis under the single objective of maximizing the mean number of vaccinations administered.…”

“…The remainder of the paper is organized as follows. In Section 2, we provide an overview of the MDP model developed in Mofrad et al (2014) and a new simulation model created to evaluate additional performance metrics of interest. In Section 3, we conduct extensive computational analyses to generate insights on the relationships between day-to-day clinic operations and the vaccine administration policy.…”