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We consider a multi-echelon joint inventory-location (MJIL) problem that makes location, order assignment, and inventory decisions simultaneously. The model deals with the distribution of a single commodity from a single manufacturer to a set of retailers through a set of sites where distribution centers can be located. The retailers face deterministic demand and hold working inventory. The distribution centers order a single commodity from the manufacturer at regular intervals and distribute the product to the retailers. The distribution centers also hold working inventory representing product that has been ordered from the manufacturer but has not been yet requested by any of the retailers. Lateral supply among the distribution centers is not allowed. The problem is formulated as a nonlinear mixed-integer program, which is shown to be NP-hard. This problem has recently attracted attention, and a number of different solution approaches have been proposed to solve it. In this paper, we present a Lagrangian relaxation-based heuristic that is capable of efficiently solving large-size instances of the problem. A computational study demonstrates that our heuristic solution procedure is efficient and yields optimal or near-optimal solutions.

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Introduction The essential components of a vaccine delivery system are well-documented, but robust evidence on how and why the related processes and implementation strategies drive catalytic improvements in vaccination coverage are not well established. To address this gap, we identified critical success factors that may have led to substantial improvements in routine childhood immunization coverage in Nepal from 2000 through 2019. Methods We identified Nepal as an exemplar in the delivery of early childhood vaccines through analysis of DTP1 and DTP3 coverage data. Through interviews and focus group discussions at the national, regional, district, health post, and community level, we investigated factors that contributed to high and sustained vaccine coverage. We conducted a thematic analysis through application of implementation science frameworks to determine critical success factors. We triangulated these findings with quantitative analyses using publicly available data. Results The following success factors emerged: 1) Codification of health as a human right, along with other vaccine-specific legislation, ensured the stability of vaccination programming; 2) National and multi-national partnerships supported information sharing, division of labor, and mutual capacity building; 3) Pro-vaccine messaging through various mediums, which was tailored to local needs, generated public awareness; 4) Female Community Health Volunteers educated community members as trusted and compassionate neighbors; and 5) Cultural values fostered collective responsibility and community ownership of vaccine coverage. Conclusion This case study of Nepal suggests that the success of its national immunization program relied on the engagement and understanding of the beneficiaries. The immunization program was supported by consistent and reliable commitment, collaboration, awareness, and collective responsibility between the government, community, and partners. These networks are strengthened through a collective dedication to vaccination programming and a universal belief in health as a human right.