Decentralized beneficiary behavior in humanitarian supply chains: models, performance bounds, and coordination mechanisms

Abstract

Effectiveness in humanitarian supply chain operations depends on the critical last mile between beneficiaries and needed supplies or services. Often, the last mile is traveled by the beneficiaries themselves. This paper’s focus is on systems in which beneficiaries make autonomous decisions about where to seek supplies or services using a utility function that captures distance, congestion, and the relative importance of the two factors. We model beneficiary behavior as a network congestion game where the resources are a set of facilities from which individuals choose. Importantly, our models capture the fact that the relative importance of distance and congestion may be specific to both the individual and the facility; we represent this using a factor called the congestion weight. We prove new bounds on the system performance that results from decentralized beneficiary decisions in comparison to centralized optimal assignments, and we introduce mechanisms for achieving centrally optimal outcomes even in the presence of decentralization. We demonstrate the methods with data from the international public health response to the Haiti cholera epidemic.

Appendix 1

Figures 9, 10, 11, 12, 13 and 14 display average initial congestion weights, optimized congestion weights, and the difference between them for six selected facilities. The magnitude of change required for both HCD1 (Fig. 9) and HCD2 (Fig. 10)is higher than for LCD2 (Fig. 12). However, the change in the negative direction is largest for LCD2, greatly encouraging some individuals to choose this facility.

The modifications to players’ congestion weights for HCD1 and HCD2 discourage individuals from two and three sections, respectively, from choosing those facilities. In dense areas, it is most beneficial to spread demand across multiple facilities in order to ease congestion. Changes in congestion weights concerning LCD1 (Fig. 11) encourage individuals from one section to choose it while discouraging individuals from another section. Due to its lower capacity and urban environment, LCD1 has the potential for overcrowding. Thus, the optimum congestion weights encourage individuals nearby to choose LCD1, but discourage individuals who are further away. Finally, the optimum solution greatly encourages nearby beneficiaries to choose LCD2 by decreasing the associated congestion weights. At the same time, individuals further away are discouraged from choosing LCD2.

Fig. 9

Initial (a) and optimized (b) congestion weights for HCD1, a high capacity facility in a densely populated area; the average change in individuals’ congestion weights for this facility (c)

Fig. 10

Initial (a) and optimized (b) congestion weights for HCD2, a high capacity facility in a densely populated area; the average change in individuals’ congestion weights for this facility (c)

Fig. 11

Initial (a) and optimized (b) congestion weights for LCD1, a low capacity facility in a densely populated area; the average change in individuals’ congestion weights for this facility (c)

Fig. 12

Initial (a) and optimized (b) congestion weights for LCD2, a low capacity facility in a densely populated area; the average change in individuals’ congestion weights for this facility (c)

Fig. 13

Initial (a) and optimized (b) congestion weights for HCR, a high capacity facility in a rural area; the average change in individuals’ congestion weights for this facility (c)

Fig. 14

Initial (a) and optimized (b) congestion weights for LCR, a low capacity facility in a rural area; the average change in individuals’ congestion weights for this facility (c)