Optimization Algorithm For A New Multitasking Scheduling Model With Rate-Modifying Activities And Delivery Times

As the largest industry in China,manufacturing industry maintains the lifeline industry of Chinese economy,which has been keeping a good development trend.However,with the change of market environment at home and abroad,the traditional manufacturing industry is faced with the problems of high financing cost,overproduction,rising manufacturing cost,shortage of labor force and so on.It is urgent to reform and develop the manufacturing industry.And this must be put on the agenda,that is,the thinking and innovation of the existing production and manufacturing mode.At the same time,with the continuous development of the social economic environment and the technological environment,the mode of production has evolved accordingly,including mass manufacturing,agile manufacturing,lean production,flexible manufacturing,mass customization and intelligent manufacturing,etc.It is of great significance to study scheduling problem,establish reasonable production scheduling model and propose optimization algorithm in the new manufacturing mode.Firstly,we introduce the background and significance of the scheduling problem,and expatiate on the domestic and foreign scheduling research hot issues and related research status,and put forward the basic problems studied in this paper.Secondly,we propose a scheduling model with multiple rate-modifying activities and past-sequence-dependent delivery times in multitasking scheduling.The processing time is not a constant,but a function based on position and job.Multitasking is common in the actual operation and management activities of enterprises.In multitasking,when a primary job is being processed,it is unavoidably interrupted by the waiting jobs.Thus the multitasking function on a single machine consists of two parts,i.e.,the switching and interruption functions.The actual processing time of the primary job consists of three parts:the unfinished part of the primary job,the switching time and the interruption time.At the same time,workers and machines will be tired and worn out after working for a period of time.Productivity will be reduced.A rate-modifying activity is an activity that changes the production efficiency of a machine.The rate-modifying activity takes a certain amount of time during which the machine cannot process the jobs.However,jobs may need additional operation before they are delivered to the customer.For example,electronic components require demagnetization.Similar to other literatures,the delivery time of each job is proportional to the job's waiting time for processing.In addition,with the increase of processing time,workers and machines will have learning and aging effects.Processing time function in this paper is based on the function of the job and the processing position of the job.Thirdly,we consider multitasking scheduling problems with general multiple rate-modifying activities and past-sequence-dependent delivery times on a single machine and parallel machines.In the single-machine setting,the objectives are to minimize the makespan and the total completion time.In the parallel-machine setting,the objectives are to minimize the total completion time and the total machine load.We show that all the problems under study are polynomially solvable.In particular,the multitasking scheduling problem in which only the processing time function is based on the processing location is further discussed in single machine environment.SPT/LPT polynomial time algorithm is proposed for minimized makespan and total job completion time.The time complexity is just O(nlo n)Finally,we use the LINGO tools to illustrate the working of the proposed solution algorithms by numerical examples.As a result,we verify the feasibility and effectiveness of the algorithm.