The competition between modern agri-businesses is not only the competition between production enterprises but also the competition between the agri-food supply chain networks (ASCN) including the core production enterprises.To improve the competitiveness of ASCN,the strategic decision of optimal design of ASCN is crucial.The optimal design of ASCN is effective to improve the operation efficiency of ASCN and reduce the operation cost and operation rise For traditional design of ASCN,all parameters including demand quantity and cost coefficients are assumed to be deterministic.Nevertheless,the uncertainties of supply,production and demand often exist in practice.Therefore,in this study we investigated the problem of robust optimal design of ASCN considering the uncertainties of supply and demand faced by ASCN.The aim is to develop a mathematical model for the robust optimal design of ASCN and is to present an effective optimization method to obtain robust solution for the addressed problem.In the first part,firstly the robust design problem of multi-echelon agri-food supply chain network (ASCN) with single non-perishable product is stated in detail.Then the parameters and variables of the optimization model are explained.Lastly,a mixed integer linear programming (MIP) model is presented for robust optimal design of ASCN,in order to minimize the sum of total cost of ASCN and the risk cost of uncertainty.The model integrates the decisions on facility location,capacity selection and transportation mode selection.In the model,the demand uncertainty and raw material price uncertainty are considered and are described by the scenario-based method.In the second part,a meta-heuristic named particle swarm optimization (PSO) is adopted to solve mid-to-large scale problems because the problem of robust design for ASCN belongs to the NP-hard problem.To avoid the stagnation of search of basic binary PSO (BBPSO),a newly proposed modified binary PSO (MBPSO) is utilized,which adopts the updating mechanism based on the concepts of the genotype-phenotype representation and the mutation operator.Moreover,an adaptive mutation operator is developed and embedded into the MBPSO.In the adaptive MBPSO (AMBPSO),the mutation probability is automatically increased if the global best particle keeps unchanged more than ten generations.For comparison purpose,the BBPSO with adaptive mutation operator (called ABBPSO) is also presented.The implementation procedure of the PSO approaches through LINGO and VC++ 6.0 is lastly described.In the third part,three cases of apple supply chain are constructed in order to test the effectiveness of the MIP model as well as MBPSO and AMBPSO.Using the three cases,the validity of the developed model is verified by analysis of case computation via LINGO.Then,the AMBPSO is compared with the existing BBPSO,MBPSO and ABBPSO against three cases.The comparison results show the effectiveness of the AMBPSO for robust design of ASCN.The computation results also indicate that the proposed AMBPSO is superior to existing BBPSO and MBPSO.In addition,the following conclusions are drawn through the comparison study:the MBPSO is better than the BBPSO with respect to exploration ability,and the adaptive mutation operator is helpful to improve the global optimization ability.In summary,the proposed MIP model for robust optimal design of ASCN problem is valid and the developed AMBPSO is effective and efficient to solve the problem of robust optimal design of ASCN.The comparative study shows that the updating mechanism of MBPSO based on genotype-phenotype representation and the adaptive mutation operator are able to improve BPSO's global optimization ability.%针对产出单一产品的多级农产品供应链网络(agri-food supply chain network,ASCN)鲁棒优化设计问题,以降低不确定性风险和总成本为目标,建立了集成生产设施选址、产能决策和物流网络运输模式选择的混合整数规划数学模型.模型中同时考虑了需求和农产品原料价格的不确定性,并采用情景法来描述有关不确定性.通过案例计算分析验证了模型的有效性.采用一种基于基因型-表现型概念的改进二元粒子群(Binary Particle swarm optimization,BPSO)算法并融合自适应变异技术,发展出一种自适应改进BPSO算法(AMBPSO)求解ASCN设计问题.通过将AMBPSO与基础BPSO(BBPSO)、带自适应变异的BBPSO(ABBPSO)算法和改进BPSO(MPSO)就三个案例的计算对比,验证了算法的有效性.计算结果表明AMPSO优于现有的BBPSO和MBPSO算法.
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