The Donation Collections Routing Problem

Abstract

This paper introduces the donation collections problem (DCP), which is a network routing problem motivated by certain challenges that arise during the response phase immediately following large-scale disaster events. In particular, catastrophic events are often characterized by a dramatic surge of unsolicited donations and spontaneous volunteers that pose significant logistical problems for officials, and also inhibit the organized relief efforts of professional responders. The purpose of the DCP is to present a practical alternative for managing post-disaster logistics operations associated with material and volunteer convergence. The DCP is represented mathematically is an integer programming problem. We propose a host of common sense heuristic policies to generate routes for the DCP, and then evaluate the performance of these heuristic methods through computational experimentation. Our results indicate that longer routes are generally preferable to shorter ones based on the DCP objective function, and that network nodes characterized by rapid accumulation of donations should be served during the latter portion of a route’s execution. Our findings also show that routing strategies that would be potentially appealing to inexperienced volunteers produce extraordinarily undesirable results. The collections routing literature almost entirely focuses on the development of optimal or near optimal solution algorithms. However, the humanitarian contexts that motivate the DCP warrant examination of simple heuristic policies that can be easily implemented in practice. This approach seems to represent a unique line of inquiry in the domain of collection routing.

Appendix: Problem Instances for Computational Experiment

In Table 8, $a_{\lambda _{i}}$ and $b_{\lambda _{i}}$ represent the lower and upper bounds of a uniform distribution associated with randomly generated λ values. Similarly, $a_{c_{ij}}$ and $b_{c_{ij}}$ are lower and upper bounds for randomly generated c _ij values. In particular, recall that the computational experiment conducted in Sect. 5 consists of 240 problem instances—10 replications for each of the 24 scenarios shown in Table 8. Each of the 10 problem instances for each scenario is based on a randomly generated accumulation rate λ from a uniform distribution with parameters $(a_{\lambda _{i}},b_{\lambda _{i}})$, and randomly generated travel times c _ij , i, j = 1, …, n from a uniform distribution with parameters $(a_{c_{ij}},b_{c_{ij}})$. The uniform distribution parameters $(a_{\lambda _{i}},b_{\lambda _{i}})$ and $(a_{c_{ij}},b_{c_{ij}})$ in Table 8 are obtained by solving the following system of equation for the given values of $(\mu _{\lambda _{i}},\sigma _{\lambda _{i}})$ and $(\mu _{c_{ij}},\sigma _{c_{ij}})$, respectively:

$$\displaystyle\begin{array}{rcl} \frac{a + b} {2} & =& \mu {}\\ \frac{(b - a)^{2}} {12} & =& \sigma ^{2}. {}\\ \end{array}$$

Table 8 Experimental design parameters for computational study

1.1 Sample Route Duration Results

See Table 9.

Table 9 Route durations for special case of $\sigma _{\lambda _{ i}} = 0$