This research is purely economic. Information related to the hospitals of the Ecuadorian Institute of Social Security (IESS) from several years ago to the present was considered because, frequently, a problem related to medical supplies occurs; expired medicines or shortages and overprices. Many of these cases did not consider an adequate mathematical calculation for optimization. Here is the objective of applying mathematical models for inventories for probabilistic or deterministic optimal order quantity (EOQ). They are essential for correct decision-making in the administration of hospitals and thus avoid shortages of medicines and supplies. In addition, correct the abundant stock in inventories so that these do not expire in hospitals as has happened in recent years. Through monthly contributions, users who come to the IESS are affiliates who deliver to the institution to obtain decent health care so that they are not affected by additional expenses regarding drugs or medical supplies. These are side effects that affiliates often suffer in treating their disease throughout the country. It was concluded that more than 59 million dollars were made in purchases of medicines and supplies from 2017 to 2020 in contracts to buy direct from the supplier due to shortages; with the help of deterministic and stochastic inventory models, they can solve these problems. Problems and obtain an optimization of resources.La presente investigación es de carácter netamente económica. Se consideró información vinculada a los hospitales del Instituto Ecuatoriano de Seguridad Social (IESS) de varios años atrás hasta la actualidad, debido a que, de manera frecuente, se presenta un problema relacionado a los insumos médicos; medicinas caducadas o desabastecimiento y sobreprecios. Muchos de estos casos no tomaron en cuenta un cálculo matemático para la optimización de recursos. Aquí nace el objetivo de aplicar modelos matemáticos para inventarios para cantidad óptima de pedido (EOQ) probabilístico o determinísticos, sumamente necesarios para realizar una correcta toma de decisiones en la administración de los nosocomios y así evitar el desabastecimiento de medicamentos e insumos. Además, corregir el abundante stock en los inventarios, para que estos no caduquen en los hospitales como ha sucedido en los últimos años.