Background The challenge of keeping vaccines cold at health posts given the unreliability of power sources in many low- and middle-income countries and the expense and maintenance requirements of solar refrigerators has motivated the development of passive cold storage devices (PCDs), containers that keep vaccines cold without using an active energy source. With different PCDs under development, manufacturers, policymakers and funders need guidance on how varying different PCD characteristics may affect the devices’ cost and utility. Methods We developed an economic spreadsheet model representing the lowest two levels of a typical Expanded Program on Immunization (EPI) vaccine supply chain: a district store, the immunization locations that the district store serves, and the transport vehicles that operate between the district store and the immunization locations. The model compares the use of three vaccine storage device options [(1) portable PCDs, (2) stationary PCDs, or (3) solar refrigerators] and allows the user to vary different device (e.g., size and cost) and scenario characteristics (e.g., catchment area population size and vaccine schedule). Results For a sample set of select scenarios and equipment specification, we found the portable PCD to generally be better suited to populations of 5,000 or less. The stationary PCD replenished once per month can be a robust design especially with a 35L capacity and a cost of $2,500 or less. The solar device was generally a reasonable alternative for most of the scenarios explored if the cost was $2,100 or less (including installation). No one device type dominated over all explored circumstances. Therefore, the best device may vary from country-to-country and location-to-location within a country. Conclusions This study introduces a quantitative model to help guide PCD development. Although our selected set of explored scenarios and device designs was not exhaustive, future explorations can further alter model input values to represent additional scenarios and device designs.
Minimum cost flow problems on infinite networks arise, for example, in infinite‐horizon sequential decision problems such as production planning. Strong duality for these problems was recently established for linear costs using an infinite‐dimensional Simplex algorithm. Here, we use a different approach to derive duality results for convex costs. We formulate the primal and dual problems in appropriately paired sequence spaces such that weak duality and complementary slackness can be established using finite‐dimensional proof techniques. We then prove, using a planning horizon proof technique, that the absence of a duality gap between carefully constructed finite‐dimensional truncations of the primal problem and their duals is preserved in the limit. We then establish that strong duality holds when optimal solutions to the finite‐dimensional duals are bounded. These theoretical results are illustrated via an infinite‐horizon shortest path problem. We also extend our results to infinite hypernetworks and apply this generalization to an infinite‐horizon stochastic shortest path problem. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(2), 98–115 2017
Given the costs and a feasible solution for a minimum cost flow problem on a countably infinite network, inverse optimization involves finding new costs that are close to the original ones and that make the given solution optimal. We study this problem using the weighted absolute sum metric to quantify closeness of cost vectors. We provide sufficient conditions under which known results from inverse optimization in minimum cost flow problems on finite networks extend to the countably infinite case. These conditions ensure that recent duality results on countably infinite linear programs can be applied to our setting. Specifically, they enable us to prove that the inverse optimization problem can be reformulated as a capacitated, minimum cost circulation problem on a countably infinite network. Finite‐dimensional truncations of this problem can be solved in polynomial time when the weights equal one, which yields an efficient solution method. The circulation problem can also be solved via the shadow simplex method, where each finite‐dimensional truncation is tackled using the usual network Simplex algorithm that is empirically known to be computationally efficient. We illustrate these results on an infinite horizon shortest path problem.
The goal in external beam radiotherapy (EBRT) for cancer is to maximize damage to the tumour while limiting toxic effects on the organs-at-risk. EBRT can be delivered via different modalities such as photons, protons and neutrons. The choice of an optimal modality depends on the anatomy of the irradiated area and the relative physical and biological properties of the modalities under consideration. There is no single universally dominant modality. We present the first-ever mathematical formulation of the optimal modality selection problem. We show that this problem can be tackled by solving the Karush-Kuhn-Tucker conditions of optimality, which reduce to an analytically tractable quartic equation. We perform numerical experiments to gain insights into the effect of biological and physical properties on the choice of an optimal modality or combination of modalities.
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