Mathematical Model for Locating a Pre-Positioned Warehouse and for Calculating Inventory Levels

Abstract

A mixed integer non-linear mathematical model is proposed to efficiently provision necessary supplies for the dignified survival of people affected by hydrometeorological disasters that are usually experienced in the state of Veracruz, Mexico. In the context of damages to property and infrastructure in the municipalities affected by such natural disasters and to develop resilience, a model that combines the problem of locating facilities with the problem of determining inventory levels for uncertain demand is developed, facilitating the timely supply of survival kits. The number of survival kits required is determined according to the needs of the affected people in terms of food products, equipment, water, and medicine. Requirements for food products and equipment are based on the human life cycle, from the stages of early childhood until old age; those for water and medicine on total demand. The model is tested in the Capital Region, one of the ten regions within Veracruz, because the municipalities that comprise the region have experienced numerous declarations of emergency registered in the Natural Disasters Fund. The Capital Region comprises 33 municipalities, 17 of which have experienced this type of declaration in 2016. Therefore, our model has been developed to determine the optimal location of a pre-positioned warehouse in the Naolinco municipality, including the optimal levels of inventory that would satisfy 99% of the affected population in this region. Our model can serve as a tool through which individuals involved in the decision-making process can select the locations that have not been impacted by the hydrometeorological events, including pre-positioned warehouses that in turn safely store the survival kits. This model can be utilized not only in Mexico but in any part of the world by individuals involved in the decision-making process associated with providing relief to affected people.