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The paper presents two robust models to solve the location-inventory problem occurring in the emergency grain depots (EGD) when demands are uncertain. The proposed model simultaneously determines the location of EGDs, the grain inventory at each employed EGD and the allocation of grain among emergency sites, with the objective of minimizing the system-wide cost which includes EGDs construction cost, grain inventory cost and grain transportation cost. Firstly, a mixed integer programming model is built for the deterministic problem. Secondly, two robust optimization models are established for the case when the demand volume of grain in each emergency site is uncertain. The two robust models, respectively, correspond to the Soyster [1] robust optimization model which is dedicated to the worst case, and the budget optimization model which was proposed by Brtsimas & Sim [2] and has the advantage to control the robust level. Extensive numerical experiments are conducted to show the benefits of the two proposed robust optimization models. Interesting insights related to the problem are presented as well. Keywords-location-inventory; uncertainty; robust optimization; emergency grain depots

Robust Models for Location and Inventory Decisions in Emergency-grain Depots