| In reality,the optimal layout of facilities often faces a large number of uncertainties,which inherently affect the optimal layout of facilities.The search for the optimal layout that performs well under various uncertainties has attracted the attention of many scholars.To solve the facility location problem considering uncertainty,it is necessary to clarify these uncertainties and choose appropriate modeling tools.In addition,the traditional deterministic facility location problem is often NP-hard,and the facility location problem considering uncertainty is even more difficult to solve.Therefore,it is necessary to pay special attention to the algorithm design and model solving of the geographic calculation of the facility location considering uncertainty.Therefore,from three perspectives of demand uncertainty,supply uncertainty and both demand and supply uncertainty,this study adopts robust optimization approach/method to carry out research on the geographical calculation of facility location problem considering uncertainty.Firstly,we construct the corresponding robust optimization model based on the characteristics of uncertainty,then design an efficient algorithm,generate random numerical examples for empirical analysis and develop a robust optimization layout system of facility location.Finally,the robust optimization models of facility location are applied to the optimal layout of the emergency material deposity in Guizhou Province.The main works of this study are as follows:(1)In view of the facility location problem under discrete demand uncertainty,we first theoretically proved the monotonic non-increasing nature of the stochastic probustness optimization model(p-SRO)and the robust parameter p always has a lowest critical p-value,and then a two-stage min-p robust optimization model(min-p RO)is proposed.Secondly,we theoretically proved the optimality of the nearest assignment strategy,and constructed the Lagrangian relaxation algorithm and the Teitz-Bart vertex substitution heuristic(TB)based on this strategy.Finally,the performance of the two algorithms is compared by numerical experiments,and the factors affecting the minimum p threshold are analyzed.The results show that:(1)The performance of TB is significantly better than the Lagrangian relaxation algorithm.(2)Whether the fixed cost of the facility is considered or not,the fluctuation range of data has a significant positive effect on the lowest critical p-value;(3)When the fixed cost of facilities is not considered,the number of new facilities has a significant positive effect on the lowest critical p-value;When the fixed cost of facilities is taken into account,the number of new facilities has a significant negative effect on the lowest critical p-value.(2)In view of the facility location problem under continuous demand uncertainty,we assumed that the number of customer points with large fluctuations in demand is limited and considered the maximum fluctuation range of customer points,then constructed a mathematical model of the facility location problem under limited customer fluctuation(FLPLCF).Then,the Lagrangian relaxation algorithm and the Teitz-Bart vertex substitution heuristic(TB)for solving FLPLCF are designed.Numerical experiments show that the performance of the TB is significantly better than the Lagrangian relaxation algorithm.(3)In view of the facility location problem under supply uncertainty,we assumed that all potential facilities will fail independently with a certain probability,but the failure probability of all facilities is extremely small(regarded as small probability event),then constructed the mathematical model of facility location problem under limited facility failure(FLPLFF).Then,we theoretically proved the two properties of the multi-level assignment strategy(MLA)and proposed three types of multi-level assignment: nearest multi-level assignment(NMLA),probabilistic nearest neighbor multi-level assignment(PNMLA)and random multi-level assignment(RMLA).Based on multi-level assignment strategy,Lagrangian relaxation algorithm and Teitz-Bart vertex substitution heuristic(TB)are designed.The numerical results showed that:(1)NMLA has the best effect,and RMLA has the worst effect;(2)When the number of newly built facilities P is less than 7,the maximum number of facility failures R can be set to P-1;When the number of newly built facilities P is greater than 7,the maximum number of facility failures R can be set to 7.(3)The performance of the TB is significantly better than the Lagrangian relaxation algorithm.(4)In view of the facility location problem under demand uncertainty and supply uncertainty(facility failure),we assumed that the number of customer points where demand fluctuates greatly is limited and the number of facilities that fail simultaneously in a given time is also limited.The mathematical model of the facility location problem under limited customer fluctuation and limited facility failure(FLPLCFLFF)is presented.Then we designed the Lagrangian relaxation algorithm and Teitz-Bart vertex substitution heuristic(TB)based on the multi-level assignment strategy.The numerical results showed that the performance of TB is significantly better than the Lagrangian relaxation algorithm.(5)In view of the facility location problem under demand uncertainty and supply uncertainty(partial interdiction of facility),we assumed that all potential facilities have a certain degree of reliability and all facilities shoulde loss their partial capacities or service capabilities due to the emergency.Using Stackelberg master-slave game theory,a mathematical model of the facility location problem under demand uncertainty and partial interdiction(FLPDUPI)is constructed.Then we designed five bi-level algorithms and the numerical results showed that the the performance of the bi-level Teitz-Bart vertex substitution heuristic(TBTB)is better than the other four algorithms.(6)We applied the facility location problem under demand uncertainty and supply uncertainty to the optimal layout of emergency material depository in Guizhou province.Regarding the layout of the municipal emergency material depository in Guizhou province(GZ88),the optimal results of FLPLCFLFF showed that:(1)The optimized maximal service distance(driving time)and average service distance(driving time)are reduced by 10.29% and 13.25% respectively from the actual layout;(2)When increasing the number of new facilities,we only need to add a new facility to the original best location.And the facilities are evenly distributed in various regions in Guizhou province.Regarding the layout of the county-level emergency material depository of Bijie city in Guizhou province(BJ250),the optimal results of FLPDUPI showed that: we can basically achieve one-hour service distance(driving time)by setting six county-level emergency material depository.(7)Using Visual Studio 2013 as the development platform,C# programming language and Arc GIS Engine 10.2,the robust optimization layout system for facility location is developed.According to the situation of demand uncertainty,supply uncertainty,uncertainty of demand and supply,the system realizes a variety o f robust optimization models and solution algorithms for facility location.The system can provide scientific decision support for the robust optimization layout of geographic calculation of facility location. |
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