Robust Models For Location And Allocation Decisions In Emergency-grain Depots Considering Demand Uncertainty

In recent years,frequent natural disasters have brought enormous economic and life losses to China.In order to deal with natural disasters effectively,this paper studies the problem of emergency grain depots location with inventory and allocation.A grain emergency logistics system is established to supply sufficient grains timely and reduce losses.There exist many uncertainties in natural disasters,such as occurrence time,disaster scales and locations.Robust optimization is an effective way to solve uncertain problem by using uncertain sets to express uncertainties.Therefore,it is of great theoretical and practical significance to build robust models to provide effective solutions for the location,allocation and inventory of emergency grain depots.In construction of model,this paper first establishes a deterministic model that aims to minimize the total cost including grain depots construction cost,the grain inventory cost,and the transportation cost from grain depots to disaster points.Then,based on the deterministic model,considering the uncertainty of the food demand in disaster,three different robust optimization methods,box,ellipsoid,and polyhedron,are introduced respectively,and the corresponding robust optimization models are deduced.Programming in JAVA,CPLEX is called to solve each model separately and get corresponding solution.In the numerical experiments,this paper generates random samples based on the grain demands of Changzhou City and tests the deterministic model and different robust optimization models with the performance evaluation index of total cost and service level.By changing the robust parameter,the robust models are adjusted to make a trade-off between cost and robustness.The main conclusions of this paper are: 1)The deterministic model cannot provide a reliable emergency grain depots location,allocation and inventory plan in realistic disaster situations;2)The box robust model guarantees one hundred percent service level,but it leads to higher cost;3)By adjusting robust parameter,the ellipsoid robust model makes a trade-off between service level and cost,but it costs longer time and larger memory consumption for solution;4)By adjusting robust parameter,the polyhedron robust model reduces cost without decreasing service level much with short solution time and small memory consumption.The characteristics and innovations of this paper are as follows: 1)Considering uncertain grain demands in the disasters,different robust optimization methods are introduced to establish mathematical models and provide more realistic solutions comparing with deterministic model.2)Comparing and analyzing different robust optimization methods,appropriate robust model is provided under different requirement of cost and service level.3)Considering practical factors,the grain loss rates are different when the scale of food inventory is different and the maximum radius constraint is added for timeliness of emergency rescue.