Mathematical modeling for global good

Earthquakes like the ones that took place in February 2023 in Southeast Turkey near the northern border of Syria represent a major threat for humankind. The humanitarian community estimates that, in addition to more than 50,000 deaths, over 8.8 million people live in areas most affected by these earthquakes. So, an effective and timely response like the one provided through the research developed by Professor Serrato in collaboration with researchers from Turkey and Mexico is crucial to support affected populations after these kinds of disasters take place.

An estimated 80% of disaster relief operations involve making aid, food, and other resources available to the affected people in a timely and adequate manner. In many countries, during the immediate aftermath of a disaster, some key inventory items are positioned at the origin of the relief supply chain through in-kind donations, which can account for up to 80% of all collected items. These donations range from human resources, bedding, and medical supplies to food, clothing, and personal hygiene products, among others, and they can come through governments, the private sector, or citizens.

In such humanitarian supply chains, inventory is usually accumulated and handled at various points throughout the network, ranging from the collecting centers to on-site distribution centers. So, developing effective policies to adequately manage this inventory is essential to attending to the affected communities in a timely and adequate fashion. Classical inventory strategies and decision-making policies hardly adjust to the diverse conditions faced in a crisis, creating a challenge for the practitioners in the field of humanitarian assistance to develop customized policies, strategies, and models to efficiently manage and distribute the inventories of supplies in the case of emergency and disaster response.

“This research was initiated several years ago through one of the doctoral students within our group,” said Professor Serrato. “She leveraged previous research that we and others developed, to identify and outline this need. Collection centers are continuously confronted by the uncertainty in the quantity and nature of in-kind donations that they receive, as well as the requested aid coming in from the affected communities. The convolution of these two variables creates complications in the operations management of collection and distribution centers, and the decisions to be made regarding the size and frequency of shipments. Inspired by this challenge, and after a period of direct observation and mapping at the Red Cross, we developed a mathematical model based on a Markov Decision Process (MDP) to model the daily operations in collection centers and support their decision-making process.”

Professor Serrato explains that this model addresses the decision to send shipments to the affected areas, based on the available inventory and backlogged demand, while considering the tradeoff between the implications of unsatisfied (or late-satisfied) demand and the cost of frequent shipments. Such a model has provided valuable insights to decision makers who face this problem in developing countries like Mexico or Turkey, during the critical and chaotic period of disaster response.

Despite the importance of in-kind donations in humanitarian response, little research had been conducted to address the uncertainty of such in-kind donations and the uncertainty on demand in settings such as a natural disaster and its subsequent relief operations. This research addressed this challenge, while focusing on the minimization of unsatisfied demand.

“The decision is to take a shipment action at the beginning of each decision epoch, based on the available inventory, the current accumulated demand, and the expected value of demand for the next period. The costs involved are logistics ones, such as shipping and inventory holding costs, as well as the penalty for unsatisfied demand in a critical situation associated with timely humanitarian response. Solving this model produces a policy, indicating the optimal actions to be taken at the beginning of each decision epoch given the current state of the system: the at-hand inventory, the backlogged demand, and the expected incoming demand for that decision epoch. For this problem structure, we proved the existence of a Monotone Optimal Non-Decreasing Policy (MONDP), which is appealing to the decision makers for its ease of applicability.”

This research was featured by the International Federation of Operational Research Societies (IFORS) in its  March 2023 News issue. Further details of the work conducted by Professor Serrato and this group of researchers is also available through Springer.

About Professor Marco Serrato.

Marco Serrato serves as professor of global strategy and business analytics at Thunderbird School of Global Management at Arizona State University, and as Associate Vice President of Arizona State University's Learning Enterprise. He has experience developing initiatives with private, governmental, and nongovernmental organizations in the United States, Latin America, Europe, Asia and the MENA region, including serving as former chair and emeritus board member of the International Consortium for University-based Executive Education (UNICON). Dr. Serrato has published more than thirty research papers on international peer-reviewed and conference journals, four books, and three book chapters. His contributions have been featured by international media including the World Economic Forum and the United Nations, among others.