Production Scheduling Problem With Learning Effect And Resource Allocation

Scheduling is a very important combinatorial optimization problem.Its background is mainly in the production workshop area.Now it has been widely used in many fields such as management science,medical and health care,corporate management,modern service,and industrial production.It is also a very important branch of operation research.The learning effect plays a very important role in production scheduling.The processing time of the job will decrease with the factors such as the machine running-in degree increasing,the proficiency of skilled workers improving,and so on.and by adding resource inputs such as manpower,material,and financial resources into the job,the manager can also cut down the processing time of the job.Therefore,it is of vital importance to study scheduling problems that consider both learning effects and resource allocation.Single-machine environment is a very important and basic processing environment in production scheduling.No-wait flow shop scheduling problem is also a very important and common type of scheduling problem in industrial production,and no-wait two-machine permutation flow shop scheduling problem is the basic problem in flow shop scheduling problem.This paper studies the scheduling problems in these two processing environments.The processing time of the job is a given function related to its position in the processing sequence and the resources allocated to the job.For different practical application backgrounds,we consider the linear resource consumption function and the convex resource consumption function separately.At the same time,all jobs have a common due date that needs to be determined.We need to make aion to confirm the common due date,the allocation of resources,and the processing sequence of the jobs.The objective function is the minimization of the total earliness,the total tardiness,the common due date cost,and the total resource cost.We found that the problem is polynomially solvable under the proposed model and finally gave an algorithm to solve the problem.This paper enriches the variable production scheduling theory of processing time and provides theoretical bases for the research of more complex processing environments such as parallel machines and mixed flow shop at the theoretical level.Meanwhile,it provides relevant guidance and advice for the production process of the company at the practical level.