Research On Optimal Production Scheduling Of Supply Chain Based On Switched System

With the rapid change of global economic pattern and the increasing pressure of market competition,supply chain has gradually developed into a complex dynamic network system.Because the inventory state of products in the supply chain network changes constantly,in order to reduce the cost,the manufacturer needs to adjust the production strategy according to the inventory state.Therefore,the optimal production scheduling for inventory changes has been a hot issue in supply chain management.The main content and innovation points of the thesis include the following:Firstly,the optimal production scheduling problem of supply chain to reduce inventory cost is studied,the optimal scheduling model of linear switching system is constructed,and the linear branch and bound method is designed.Since the inventory cost is a linear structure with respect to the inventory state in supply chain,the thesis constructs a dynamic lower bound system of the linear cost functional by matrix transformation and matrix trace operation.In each production stage,the lower bound is compared with the current optimal value,and the branch and bound algorithm is designed based on the depth-first search strategy.Numerical experiments verify that the algorithm can search for the global optimal solution in the linear scheduling system with high efficiency.Secondly,the optimal production scheduling problem under safety inventory is studied,the optimal scheduling model of the linear-quadratic switched system is constructed,and the linear-quadratic branch and bound method is designed.In response to the supply risk of market fluctuations,search for an optimal production scheduling sequence,make the inventory state as far as possible to maintain near the safety level with multiple stages,the thesis expresses the cost functional into a quadratic structure with respect to the inventory state,and then using the matrix theory and semi-definite programming techniques to build a new dynamic lower bound system of the quadratic cost functional.Based on the new lower bound,the linear-quadratic branch and bound method is designed,and numerical experiments verify the effectiveness of the algorithm in searching all global optimal solutions for linear-quadratic optimal production scheduling problems.Thirdly,the optimal production scheduling problem that restrains the switching frequency is studied,the optimal scheduling model of hybrid switched system is constructed,and the exact branch and bound method is designed.Because the frequent production scheduling is not conducive to the operation in the production cycle and seriously affects the service life of equipment,in order to choose a more stable scheduling sequence,the thesis introduces the total variable function with respect to the scheduling sequence to measure its changing frequency and amplitude.For this kind of hybrid optimal scheduling problem,the thesis constructs an exact dynamic lower bound system for the cost functional,which enables the branch and bound method to exactly search for all the global optimal solutions under any regularization parameter.Numerical experiments verify the efficiency of the algorithm in searching the global optimal solution in hybrid scheduling systems and the inhibitory effect of the total variable function with respect to the scheduling sequence.Finally,the optimal production scheduling problem with transaction delay is studied,the optimal scheduling model of time-delay switched system is constructed,and the time-delay branch and bound method is designed.Because the transaction process between upstream and downstream members often has delay phenomenon in multiple stages,the cost functional in the supply chain is influenced by the current state,the time-delay state and the production scheduling sequence,the thesis uses the dimension expansion technique of matrix to decouple the state and the scheduling signal.Then the cost functional is converted to the standard quadratic form with respect to the initial state equivalently,and an exact dynamic lower bound system is constructed.Thus the time-delay branch and bound method is designed based on the depth-first search strategy.Numerical experiments further verify that the algorithm can search for the global optimal production scheduling sequence in the time-delay scheduling system.