Incorporating Driving Range Variability in Network Design for Refueling Facilities

To stimulate and facilitate the use of alternative-fuel vehicles, it is crucial to have a network of refueling or recharging stations in place that guarantees that vehicles can reach (most of) their destinations without running out of fuel. Because initial investments in these stations are restricted, it is important to choose their locations deliberately. A fast growing stream of literature therefore analyzes the problem of locating refueling or recharging stations. The models proposed in these studies assume that the driving range is fixed, although reality shows that the driving range is highly stochastic. These models thereby misrepresent the actual coverage a network of refueling stations provides to drivers. This paper introduces two problems that do take the stochastic nature of the driving range into account. We first introduce the Expected Flow Refueling Location Problem, which is to maximize the expected number of drivers who can complete their trip without running out of fuel. The Chance Constrained Flow Refueling Location Problem is to maximize the number of drivers for which the probability of running out of fuel is below a certain threshold. We prove the problems to be strongly NP-hard, propose novel mixed-integer programming formulations for these problems, and show how these models can be extended to the case that the driving range varies during a trip. Furthermore, we extensively analyze and compare our models using randomly generated problem instances and a real life case study about the Florida state highway network. Our results show that taking the stochastic nature of the driving range into account can substantially improve the network coverage, that optimal solutions are highly robust with respect to data impreciseness, and that the potential gains of stochastic models heavily depend on the driving range distribution. Based on the results, we discuss policy implications

The benefits of combining early aspecific vaccination with later specific vaccination

Timing is of crucial importance for successful vaccination. To avoid a large outbreak, vaccines are administered preferably as quickly as possible. However

Literature review: The vaccine supply chain

Vaccination is one of the most effective ways to prevent and/or control the outbreak of infectious diseases. This medical intervention also brings about many logistical questions. In the past years, the Operations Research/Operations Management community has shown a growing interest in the logistical aspects of vaccination. However, publications on vaccine logistics often focus on one specific logistical aspect. A broader framework is needed so that open research questions can be identified more easily and contributions are not overlooked.In this literature review, we combine the priorities of the World Health Organization for creating a flexible and robust vaccine supply chain with an Operations Research/Operations Management supply chain perspective. We propose a classification for the literature on vaccine logistics to structure this relatively new field, and identify promising research directions. We classify the literature into the following four components: (1) product, (2) production, (3) allocation, and (4) distribution. Within the supply chain classification, we analyze the decision problems for existing outbreaks versus sudden outbreaks and developing countries versus developed countries. We identify unique characteristics of the vaccine supply chain: high uncertainty in both supply and demand; misalignment of objectives and decentralized decision making between supplier, public health organization and end customer; complex political decisions concerning allocation and the crucial

Literature Review - the vaccine supply chain

Vaccination is one of the most effective ways to prevent the outbreak of an infectious disease. This medical intervention also brings about many logistical quest

Resource location games

In this paper, we introduce and analyze resource location games. We show core nonemptiness by providing a set of intuitive core allocations, called Resource-Profit allocations. In addition, we present a sufficient condition for which the core and the set of Resource- Profit allocations coincide. Finally, we provide an example showing that when the sufficient condition is not satisfied, the coincidence is not guaranteed

The most efficient critical vaccination coverage and its equivalence with maximizing the herd effect

‘Critical vaccination coverages’ are vaccination allocations that result in an effective reproduction ratio of one. In a population with interacting subpopulations there are many different critical vaccination coverages. To find the most efficient critical vaccination coverage, we define the following optimization problem: minimize the required amount of vaccines to obtain an effective reproduction ratio of exactly one. We prove that this optimization problem is equivalent to the problem of maximizing the proportion of susceptibles that escape infection during an epidemic (i.e., maximizing the herd effect). We propose an efficient general algorithm to solve these optimization problems based on Perron- Frobenius theory. We study two special cases that provide further insight into these optimization problems. First, we derive an explicit analytic solution for the case of two interacting populations. Second, we derive an efficient algorithm for the case of multiple populations that interact according to separable mixing. In this algorithm the subpopulations are ordered by their ratio of population size to reproduction ratio. Allocating vaccines based on this priority order results in an optimal allocation. We apply our solutions in a case study for pre-pandemic vaccination in the initial phase of an influenza pandemic where the entire population is susceptible to the new influenza virus. The results show that for the optimal allocation the critical vaccination coverage is achieved for a much smaller amount of vaccines as compared to allocations proposed previously

Dose-optimal vaccine allocation over multiple populations

For a large number of infectious diseases, vaccination is the most effective way to prevent an epidemic. However, the vaccine stockpile is hardly ever sufficient to treat the entire population, which brings about the challenge of vaccine allocation. To aid decision makers facing this challenge, we provide insights into the structure of this problem. We first investigate the dependence of health benefit on the fraction of people that receive vaccination, where we define health benefit as the total number of people that escape infection. We start with the seminal SIR compartmental model. Using implicit function analysis, we prove the existence of a unique vaccination fraction that maxi- mizes the health benefit per dose of vaccine, and that the health benefit per dose of vaccine decreases monotonically when moving away from this fraction in either direc- tion. Surprisingly, this fraction does not coincide with the so-called critical vaccination coverage that has been advocated in literature. We extend these insights to other compartmental models such as the SEIR model. These results allow us to provide new insights into vaccine allocation to multiple non-interacting or weakly interacting populations. We explain the counter-intuitive switching behavior of optimal allocation. We show that allocations that maximize health benefits are rarely equitable, while equitable allocations may be significantly non-optimal