To the best of our knowledge the work reported here is the first to provide a formal modeling framework for decision making with respect to outreach. As with any model-based approach, our work has some limitations and certain facts are worth keeping in mind. First, our results apply mainly to rural outreach settings with relatively lower population densities; in densely populated urban settings coverage models could clearly be much more complex. However, since most urban centers tend to have health posts or clinics with regular hours, outreach generally is focused on rural locations. Second, we assume that the social planner is not biased in favor of
outreach plans where the travel is shorter or across easier terrain (which is sometimes the case in practice), and that the plans from our model can be implemented in an unbiased fashion. Third, in general it could be difficult to predict the exact type of coverage applicable to a particular application environment. However, the models could be run under different assumptions of coverage, and as the results indicate, in many instances the optimal locations are identical (e.g., with N=6 locations), with only the estimates of the populations served being different. In other cases there may be some common locations and some that differ (e.g., with N=3), in which case the social planner would make a subjective decision on the locations to select.
In addition, when it is not possible to specify the coverage assumption, a robust approach can be applied by creating a model that combines aspects of the different models into one model or by using a minmax regret evaluation of the solutions found by the different models as shown previously. Similarly, if there is uncertainty about parameter values then the model can be run for different parameter values, either separately or in a combined manner, in order to find a robust solution. For example, the first and second radius of model 2 can be assumed to be 4km and 6km in one model run and 5km and 8km in a second model run or have both parameter sets incorporated into one robust model. Moreover, in the robust formulation for addressing demand uncertainty, if the total demand is unchanged and the deviation percentage in each village is the same, the optimal solution of the nominal problem is the same as that of the robust problem.
In summary, outreach is a critical component of EPI vaccination programs in low and middle income countries. However, there are no standard guidelines for outreach and these activities tend to be conducted in a fairly ad hoc fashion. In particular, the problem modeled in this paper is motivated by vaccination activities in India, and our approach is based on adapting facility location models to the outreach coverage problem. Based on past and ongoing work
related to vaccine logistics that we have done with a number of countries in Asia and sub- Saharan Africa, we feel that these models can aid decision makers when they are establishing outreach policies. The resulting outreach plan affects the performance of the entire vaccine supply chain because the demand for vaccines at all levels of the supply chain will vary with the outreach plan and the resulting vaccine coverage.
3.0 MODULAR VACCINE PACKAGING TO INCREASE PACKING EFFICIENCY
3.1 INTRODUCTION
Currently, individual vaccines vials and their component packaging vary significantly in overall length, width, and height. This is because the vaccine packaging size is determined by the dimensions of both individual cylindrical vials (each containing one or more doses of vaccine) and rectangular inner packs that typically contain 10, 20, 50 or 100 vials of a particular vaccine. The variability of inner pack and vial dimensions may hinder efficient vaccine distribution because it constrains packing of cold boxes and vaccine carriers to quantities that are often inappropriate or suboptimal in the context of country-specific vaccination guidelines. In particular, estimating storage space requirements is more difficult with non-standard sizes and in a resource constrained system it may not be possible to take all the vaccines needed in a carrier because of the inefficient packaging.
Modularized packaging is one way to address this because the consequent increase in packing efficiency has the potential to reduce storage space requirements and replenishment frequencies. The standardization of packaging also has the benefit of making operations much simpler for personnel since vaccines can be more easily packed and space requirements can be more easily estimated. While vaccine vial size has been a recent topic of academic and policymaker interest, explorations of alternative packing configurations have not yet addressed
inner packs (Assi, et al., 2011; Dhamodharan & Proano, 2012; Parmar, Baruwa, Zuber, & Kone, 2010; Lee, et al., 2011; Lee & Burke, 2010; Assi, et al., 2013; Brown, et al., 2014; Drain, Nelson, & Lloyd, 2003). The packing analysis in this paper proposes that a solution to inefficient packing caused by inner pack and vial size variability is a modular packaging system (where vial and inner pack dimensions are more consistent between different vaccines) that allows for more effective packing into cold boxes and vaccine carriers.