Optsting: Multi-objective optimization for supply network logistics of scorpion antivenom

Abstract

The lack of medicines (specifically antivenom) in Mexico, particularly in marginalized communities, is not only a limitation of the Mexican government. It is a nontrivial issue of logistic optimization. The lack of infrastructure means that delivery and administration in these communities suffer from multiple constraints. People that suffer from scorpion envenomation in some communities need to travel to other locations for treatment, this is critical as it is recognized by Mexican law that the first 30 minutes after suffering a sting are the most crucial for patients. This logistical problem is one that can be addressed using mathematical modeling, specifically network logistics. To model the allocation of resources towards medicine availability in some of these regions. Since these considerations are in competition with one another, the network can be used to formulate a multi-objective optimization problem that can be solved using evolutionary algorithms. Here we present a logistical network for the Mexican municipality of Yautepec in the state of Morelos. We use it to formulate a multi-objective optimization problem that is then solved using MATLAB.

Introduction

In the 1990s the government of Mexico invested significant resources into the development of safe and effective scorpion antivenoms. Combined with widespread prevention campaigns, Mexico experienced a significant reduction in scorpion sting envenomation (SSE) related deaths (Chippaux et al., 2020; Hernández-Muñoz et al., 2024; How Mexico Revolutionized the Science of Antivenom, 2025). However, scorpionism is still considered a public health risk, with Mexico suffering the largest number of SSE envenomation in the world with more than 300 thousand cases. SSE is not shared uniformly either geographically or temporarily. Envenomation follows seasonal patterns, with hot months being refer by local media as “scorpion season” (temporada de alacranes). Additionally, the problem is concentrated on a few states like Guanajuato, Guerrero, Sinaloa, Morelos, Michoacan, Jalisco, and Colima (Hernández-Muñoz et al., 2024; Trinidad-Porfirio et al., 2023). Within these states, marginalized, rural or semirural communities suffer the brunt of SSE. Not only do they have disproportionate sting rates, they have insufficient infrastructure that often makes them unable to properly offer treatment. In case of SSE the administration of an antivenom (Flaboterapico as the medicine is known in Spanish) is known to significantly increase the probability of surviving without long term effects. However, problems in the logistical supply to these areas makes it so that antivenoms and other important medicines are not available when they are needed (Chippaux et al., 2020; Hernández-Muñoz et al., 2024; Trinidad-Porfirio et al., 2023).

Mexico has suffered from shortages of multiple medicines in recent years. This stems from multiple factors, initially the Mexican government centralized purchase of medications to avoid corruption, however miscalculations and a lack of planning lead to problems with pharmaceutical providers. The Mexican government has been trying to avoid unnecessary costs in purchasing and distribution of medicine. Shortages are not only caused by lack of purchase at the federal level, but by logistical problems at state and local level. Health institutions have lackluster infrastructure to keep inventory of medication (specially in rural areas), additionally the Mexican government tries to safe money in transport costs as well, underdelivering many marginalized communities (Gobierno de México exhibe a proveedores farmacéuticos por incumplimiento en entrega de medicamentos, 2025; La Jornada: Un Problema de Distribución Ocasiona El Desabasto En Medicamentos, n.d.; José, 2025; Suárez, 2025).

The issue of shortages in antivenom stockpiles at the local level is one that has competing interests. Local physicians and politicians try to procure more medication, while the federal government, and pharmaceutical providers try to save money and maximize profit respectively. To solve problems like this the use of network representation of logistics has been implemented in the past. Supply chain network optimization involves determining the optimal configuration of nodes (suppliers, production sites, warehouses, retailers, and customers) and links (transportation routes and communication channels) such that overall cost is minimized while service levels are maintained or enhanced (Altiparmak et al., 2006; Chen et al., 2003; Chen & Lee, 2004). These networks can have multiple degrees of complexity, they can range from relatively straightforward, to complex programs that simulate unpredictable increases in demand or complex alterations to logistics (Ashworth et al., 2025; Chen & Lee, 2004; Margolis et al., 2018). Optimization of these networks often requires satisfying competing objectives, like maximizing met demand while minimizing fuel consumption. For this reason, these problems have been characterized as multi-objective optimization problems (MOOPs), that can be solved using metaheuristic methods. These methods, like evolutionary algorithms, generate a set of solutions where every solution is considered to be as good as the rest. The set of solutions is then called Pareto optimal solutions (Barbati et al., 2024; Coello et al., 2007; Margolis et al., 2018).

In this section, we present a small network logistics model of antivenom logistics for the municipality of Yautepec in Morelos, Mexico. We use the NSGA-II algorithm to solve a MOOP derived from the network.

Methodology

The full code implementation was done in MATLAB. The network was formulated at 3 levels: supplier, medical center, and locality. Suppliers were based on Laboratorios Silanes (the biggest producer of antivenom in Mexico) and Birmex, the government entity responsible for medication acquisition (Boyer, 2013; Hernández-Muñoz et al., 2024). Medical centers were based on the following healthcare centers: Yautepec, Oaxtepec, Cocoyoc, Oacalco, los Arcos, and Ignacio Bastida. These represent the largest of the 9 health centers in Yautepec. Geographical information for the localities inside the municipalities proved unreliable. To solve this we grouped nearby localities, resulting in 11 groups out of the 94 registered localities (INEGI, 1998). For the formulation of our problem, we have 4 objectives:

For the unmet demand of each locality k. Where d_k is demand and Σ_jf_c,local(j,k) is total antivenom delivered to that same locality.

For total transportation costs between the 3 scales of the network, as a product of cost and the sum of distance traveled.

For total time traveled at speed v.

Which measures how evenly demand is met. A smaller deviation means a more equitable distribution.

Leaving the optimization problem as

To solve this problem we use Platemo, a multi-objective optimization platform in MATLAB. The demand for each group of localities was based on historical trends for those localities. Additionally, to represent the accumulation of antivenom in certain health centers we allowed unmet demand into the negative. Since it is generally reported that antivenom production in Mexico is enough to supply national demand, we did not include production as a constraint in the problem. We are focused on logistics as a driver of antivenom scarcity.

Results and discussion

The resulting network showed one, if not the limitations of the centralized logistical model currently employed Mexico. Silanes and Birmex are both located in Mexico City, around 100 to 140 kilometers from Yautepec. They are responsible for delivering not only to this municipality, but also to others in the country. This issue is not exclusive for antivenoms, while Silanes is the main provider of antivenoms, the Mexican government has centralized all purchases of medication (José, 2025; Suárez, 2025). The graphical representation of our simplified network shows how complicated this can be in Figure 1.

Figure 1. Representation of the simplified network used in this study

The results for the MOOP appear in figure 2. Our Pareto front shows the competition between unmet demand and transportation costs. Transportation costs high at base, since the scale of distance between layer 1 and 2 is considerable larger than between 2 and 3. While this model considers a single variable for the cost calculation between the 3 layers, this does reflect reality. At the local level, moving between these communities is hard, specially in the event of SSE. Walking is the most common method of transportation, car ownership is not common, and collectivized transportation is only available at certain times of the day. In reality the lack of medicine for any urgency in one medical center is a deadly constraint for patients, who are materially incapable of moving to larger population centers with better supplied facilities (Chippaux et al., 2020; Trinidad-Porfirio et al., 2023).

The pareto solutions show that more accumulated medication correlates with higher costs in transportation, and that lower delivery times are not necessarily correlated with the other 2. This opens route optimization as a potential option to reduce costs, if centralized logistical systems will continue to be the norm it is possible that they can be upgraded to reduce costs and time without causing shortages in remote communities (Margolis et al., 2018).

Figure 2. Pareto front showing transportation costs, unmet demand and average delivery time.

This model is simple, it can be expanded to account for more complicated behavior, like visiting multiple health centers in search of medicine, the augmented cost of transportation derived from dirt roads and poorly maintained roads, it could also be expanded to cover more communities. What the Pareto front reveals more broadly is that the problem has 2 scales. The federal centralized scale and the local scale. At the federal level the Mexican government is trying to reduce waist. Production of medications takes place mostly in a few big cities, primarily Mexico City. As such logistical distribution has to deal with high transportation costs for medication. Take into account that Morelos is a state next to Mexico city, so transport costs for antivenom to the south or the north states would probably be an order of magnitude higher. At federal level a model like this could be connected to a live database or inventory showing existing stockpiles of antivenom and of other medicines. Supply runs could be optimized to try to avoid both overstocking and shortage (Altiparmak et al., 2006; Margolis et al., 2018).

Equity within the pareto front shows the complications at the local scale. Equity is disparate, and time from community to care center varies. The model currently doesn’t really reflect the “choices” that inhabitants of Yautepec have during emergencies. At the local level the way to improve logistical outcomes is to upgrade infrastructure and ensure supply to the majority of healthcare centers, to avoid unnecessary transportation costs for inhabitants of these communities (Margolis et al., 2018). A model like this one can be enhanced to work with more realistic data and at a bigger scale and be used to reduce logistical costs associated with medication delivery. However, local limitations cannot be addressed at this scale. There is ample evidence that good logistical planning can significantly reduce cost and unmet demand, which is vital when it comes to quality of life of individuals, centralized supply chains by themselves should not be a limitation with proper management and planning (Ashworth et al., 2025; Chen et al., 2003; Margolis et al., 2018).

Recombinant antivenoms could help to reduce logistical limitations in Mexico. Systems like on demand production were developed to supply local zones with poor infrastructure, and they could help decentralize the supply chain. These systems are capable of producing multiple types of recombinant medicines, so they are useful beyond the issue of SSE, this is an area where investment into synthetic biology shows promise for marginalized area, which are common in Mexico. The development and deployment of these systems however would take time, so other tasks can be accomplished in the meantime (Crowell et al., 2018; Tang et al., 2023).

Conclusion

The model was able to be solved for a representation of a municipality in Morelos. Because of the metaheuristic nature of genetic algorithms, a similar implementation at state or federal level is possible, but ensuring accurate information for it is a non-trivial task. Models like this can work for planning centralized or even state level logistics, but they cannot solve the limitations of inhabitants of marginalized, and remote communities. Proper solutions require systemic changes at different scales, with participation of both state and federal agencies. While avoiding medical shortages and saving costs are competing objectives, they are not totally mutually exclusive as shown by our Pareto front. It is necessary for central planification to prioritize a sustainable model that allows for cost savings while maintaining supply in remote areas.