Research On The Solution Methods Of The Cutting Stock Problems With Usable Leftovers

Reducing the consumption of material resources is one of the important ways for enterprises to realize green manufacturing.To make full use of materials and reduce material consumption to achieve the purpose of saving materials is not only a good way for enterprises to improve their economic efficiency,but also a social responsibility for enterprises to improve the environment.Cutting optimization is one of the most direct and effective methods to reduce material consumption.As a key source node to control the utilization rate of materials,cutting optimization technology can play a positive and significant role in reducing resource consumption and carbon emissions.The Cutting Stock Problem(CSP)is widely used in such aspects as the sheet metal and linear stuff(profile,pipe,wire,etc.)in metal products and machinery manufacturing,the wood in furniture manufacturing,the plate glass in the construction and decoration industry,the cloth in the clothing industry,etc.From the perspective of manufacturing operations,the CSP is to use materials resources and equipment resources to manufacture products at low cost and high efficiency according to constraints such as customer needs and production conditions.From the perspective of academic theoretical research,the CSP is a NP-hard combinatorial optimization problem.So far it is still unable to find an effective and accurate algorithm to solve the CSP.In the modern integrated manufacturing systems,manufacturing technology,information technology and management technology are intersecting and penetrating with each other.The cutting stock process of manufacturing enterprises involves factors of management and technology.The decision-making of cutting stock is closely related to various departments such as technology,production and inventory.Under the environment of modern integrated manufacturing,the decision-making CSP is the optimization problem of cutting stock under various complex constraints according to various integrated effective data information.To increase material utilization,simplify the cutting process and shorten the calculation time are the main considerations to solve the CSP.The issues studied in this paper are how to use the accumulated leftovers in the past production process to maximize the material utilization rate,how to improve the material utilization rate while maintaining the simple cutting process,how to improve the material utilization through the leftovers inventory in the multi-cycle production,and how to ensure a satisfactory cutting plan in a reasonable calculation time.This paper studies three cutting stock problems in different manufacturing industries from the perspective of utilization of waste materials.The main work and innovations are as follows:(1)To analyze the CSP in the modern integrated manufacturing environment,explain the correlation with the enterprise management system such as Enterprise Resource Planning(ERP)and Manufacturing Execution System(MES),analyze the relevance between the CSP and business activities,such as the supply,production and sales;summarize the characteristics of leftovers inventory,analyze the economic benefits of leftovers utilization and analyze the correlation between multi-cycle production and leftovers in order to find out the potential of leftovers utilization to reduce cost and increase efficiency of manufacturing enterprises.(2)For the paper and plastic film manufacturing industry,the requirements for the use of leftovers are proposed.According to the characteristics of paper and plastic film that can be pasted and spliced,dependingon if a reel can be divided lengthwise into subreels to form the reel-pyramid,the CSP can be classified into Divisible SCSP(DSCSP)and Indivisible SCSP(ISCSP).Two Models of Integer Programming(MIP)are proposed for DSCSP and ISCSP,respectively.Call CPLEX to solve the relaxation MIP,and get the lower bound of the solution to the CSP.To consider the solution time and efficiency,use the SVCTIP algorithm of the adaptive Sequential Heuristic Procedure(SHP)combined with the column generation method to find the cutting plan of two SCSPs,and use the backpack algorithm to find the the cutting pattern on the leftovers.The experimental results show that the optimization effect of the SVCTIP algorithm is better than that of the widely used Sequential Heuristic Procedure(SHP).The utilization rate of the SVCTIP solution is higher than that of the internationally renowned company Greycon.Those show that the SVCTIP algorithm can effectively utilize the leftovers of the paper roll and the plastic film,reduce the consumption of the finished paper roll,reduce the production cost of the product,increase the economic benefits of the enterprise,and promote the realization of green manufacturing in enterprise.(3)For the similar enterprises that manufacture motors,the number of types of wafer is small,and the demand for small batches and long-term repeated Wafer CSP(WCSP).On the basis of maintaining a simple cutting process,it is proposed to actively generate standard leftovers and the strategy of utilizing leftovers.As the buffer,the stocks are constrained by the total inventory limit to avoid increasing the backlog of funds and the difficulty of managing leftovers or increasing the diversity of leftovers by the upper limit of classified inventory to obtain higher materials utilization rate.The adaptive SHP for Wafer CSP with Normal Leftovers(AWNL)is used to find the cutting plan of the WCSP and the dynamic programming recursive method to find the uni-direction patterns.The experimental test results show that the active generation leftovers strategy can improve the long-term material utilization rate of the enterprise;the utilization rate of the rolling shearing under this strategy can be equal to the flat shearing,and even has a better trend;The simple cutting process brings about a significant drop in cutting costs.Only a small amount of storage space is needed to store the leftovers.The leftovers can be used as a beneficial supplement to the safety stock to help avoid stock-outs.These show that the AWNL algorithm can greatly reduce the production cost of WCSP while maintaining high utilization rate without increasing inventory pressure.(4)Different from previous studies on the utilization of surplus materials,this paper studies the one-dimensional CSP with Bounds on both the Number of leftovers and the number of leftover Types(1DCSPUL_BNT).A strategy for generating multiple leftovers using dynamic optimization methods is proposed,which increases the diversity of leftovers.The leftovers and the standard materials as multiple stock lengths 1DCSPUL_BNT to improve the material utilization rate.The TPBNT algorithm of SHP is used based on column generation and the MIP optimizer to solve the 1DCSPUL_BNT in two periods.The experimental results show that the TPBNT algorithm is better than the literature algorithm in reducing the cutting loss and reducing the leftovers in both single-cycle and multi-cycle situations.Compared with the specified the leftovers strategy,the optimized material type strategy in this paper has better performance in reducing operation times and storage space.To sum up,the research in this paper not only enriches and improves the basic algorithm theory of CSP,but also has practical guiding significance for the production and operation of related enterprises.