The number of people affected by natural disasters or displaced by conflict, persecution, violence or human rights violations has been steadily increasing, doubling in a decade and reaching 82 million in 2015. At least 440 000 people lost their lives in only two recent major natural disasters, Indian Ocean earthquake and tsunami and Haiti earthquake. Fortunately, there is a growing interest in a field of humanitarian logistics that aims to increase preparedness and improve how we respond to natural or man-made disasters.
A much more mature field is business logistics, that plans efficient storage and flows of goods from the point of origin to the point of consumption in order to meet all customers’ requirements. Common motivation is then to minimize logistics costs, such as the costs of opening the storage facilities, procurement of goods or costs of their transportation. Emergency plans in humanitarian logistics optimize a similar set of decisions. For example, we might need to decide on the number, location and size of storage facilities, the quantities of various types of emergency supplies (e.g. food, water, medicine) stocked in each facility and/or the distribution of the supplies to demand locations after an event. However, the problem settings differ greatly. Meeting all demand after an emergency is rarely possible and therefore the chief motivation is to maximize the response, i.e. provide relief to the greatest number of people possible.
Despite these differences being repeatedly acknowledged by most researchers in the field, an interesting trend can be seen in humanitarian logistics literature: the common objective is still to minimize costs. Since it cannot be imposed that all people in need must receive assistance, simply minimizing logistics costs would in this case yield no service provided whatsoever. In order to circumvent this, an economic value of human suffering is introduced and added to the objective. The motivation of an emergency plan then becomes to minimize the summation of logistics costs and these costs for unmet demand.
This might be perceived as somehow equivalent to maximizing the response. However, determining the penalty costs that monetize unmet demand is a significant challenge. As already explained, in an extreme case where these penalty costs are zero, such formulations become underspecified and produce a trivial solution that reaches no people. Reversely, very high unmet demand penalty costs will ensure that more people receive the needed assistance, but the logistics costs will also increase drastically, often beyond available or even reasonable budget limits. We therefore end up with a worthless emergency plan, as we have no means to actually carry it out. In most papers, these or similar values are merely introduced for a single case-study, without further elaboration or guidance on how to define them for other problem instances. Next to the difficulty in determining the penalty costs, assigning an economic value to human suffering is controversial due to its ethical implications.
For these reasons, we formulated an alternative mathematical model that, respecting the budget constraints, directly maximizes met demand. Besides avoiding the difficult task of determining the penalty costs for unmet demand, such a formulation gives insights to the decision maker about how changes in the available budget influence the emergency strategy produced and its objective. Since adjusting the budgets is much more straightforward than manipulating the completely intangible and controversial penalty cost for unmet demand, we consider this model to be more user-friendly for practitioners in the field.
We evaluate the two formulations using a case study focused on hurricane threat in the Gulf Coast area of the United States and a number of randomly generated instances. The optimal solution of the alternative model naturally always reaches more people in need (since the objective function maximizes the response directly) than the common model, and is obtained in comparable computation time.
More details about the two different mathematical models can be found in:
What our study therefore suggests is that putting a price on human life can and thus should be avoided. We encourage employing alternatives that are at no loss able to remedy this and a number of other issues in the literature, that we further examine in our work. Hopefully, this discussion leastwise invites researchers to elaborate the choice of specific objectives in their writing and opens the floor for further dialogue on the topic.