Research on Joint Optimization of Reconfigurable Manufacturing Flow Line Configuration and Production Planning under Uncertain Demand
In the context of global competition,market demands have become increasingly volatile,with shorter lead times and a wider range of individualized products.These trends have presented significant challenges for intelligent manufacturing systems to adapt and meet customer needs effectively.The reconfigurable manufacturing system(RMS),as a cutting-edge smart manufacturing approach,offers the flexibility to reconfigure its manufacturing capabilities by adjusting machine tools.However,optimizing the configuration of an RMS is a complex task.Unlike traditional manufacturing systems,configuring an RMS requires not only acquiring appropriate machines but also making dynamic decisions in response to shifting demands.This means that the configuration decision is no longer a static one made at the start of production but one that evolves over time.Furthermore,the modularity of machine tools adds another layer of complexity,as reconfiguration decisions involve determining the optimal mix of modules rather than simple increases or decreases in manufacturing capacity.Additionally,determining the optimal configurations for different production processes is a significant challenge.Consequently,solving the configuration optimization problem in RMS is a complex task due to the large number of decision variables.To deal with this problem,this paper considers the uncertain demand and propose a two-stage stochastic programming model with the objective to minimize the configuration cost,the reconfiguration cost,the expected inventory and the deferred cost.The uncertain demand is described by using the sample average approximation(SAA)method.Due to the uncertainty of market demand,the decisions are divided into two stages.The first stage decisions are the configuration and reconfiguration decisions.The former refers to the determination of the number of reconfigurable machine tools on the production line,while the latter refers to the change of the configuration of the reconfigurable machine tools by adding or removing auxiliary modules,and after determining the configuration of the reconfigurable machine tools in each period,it is necessary to allocate the appropriate configuration for each procedure.The second stage decision is the recourse action after the uncertain demand is revealed.Since demand is constantly changing and difficult to predict accurately,the current RM FL configuration may not be able to quickly respond to future demand,and it is necessary to smooth production through inventory and stockout in a timely manner after future demand realized,in order to compensate for the first stage of decision-making.In this problem,the recourse action refers to the production planning decision,including the production volume,inventory and out-of-stock quantity of each product in each period.Due to the modular reconfiguration,this model has a large number of decision variables which results in the model difficult to solve.To address this problem,a Danzig-Wolfe(DW)decomposition is carried out to transform the original model to the set partitioning master problem and pricing subproblem.A solution algorithm based on the column-generation solution framework is proposed to solve the decomposed model,which dynamically adds the reconfiguration-related variables in the solution process.This method effectively controls the number of decision variables and reduces the difficulty of solving the problem.Numerical experiments are conducted to validate the performance of the proposed model and algorithm.First,numerical results show that the proposed model can significantly reduce the operational cost of a reconfigurable manufacturing system compared to a model that does not consider stochastic demand and production planning related decisions.The proposed model can effectively reduce the configuration and reconfiguration cost by nearly 20％.Meanwhile,the average inventory and deferred cost can be reduced by nearly 16％.Second,the proposed algorithm can effectively reduce the scale of the original problem,and can obtain a better feasible solution to the problem in a relatively short time.In terms of solution time,the column generation algorithm can reduce the average solution time by more than 20％.In terms of solution accuracy,the average gap between the objective of proposed algorithm and the optimal solution is 0.78％for small-sized problem.For large-sized problem,the average gap is 3.07％between our objective and the optimal solution or lower bound of Gurobi in 1800 seconds,with the maximum gap below 5％.In this paper,we present a model and method that can assist enterprises in addressing the configuration optimization challenge of reconfigurable manufacturing systems.The model offers the following managerial insights:(1)By considering demand uncertainty in the optimization of resource configuration and integrating it with production planning decisions,the proposed model enables more effective reduction of cost associated with reconfigurable manufacturing resource configuration,inventory,and deferred cost.(2)The decision to acquire reconfigurable machines often occurs early in the planning cycle.Later in the planning cycle,changes in demand are typically addressed through configuration reconfiguration decisions.(3)Given the enhanced production flexibility provided by reconfigurable machines,manufacturing companies must possess a higher level of production management decision capability.
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