Single Machine Deterioration Type Scheduling Problems With Resource Constraints

With the speed of the global economic growth slowing,the growth rate of Chinese economy is declining,which is particularly serious in productive enterprises.Due to the influence of the multiple factors such as the decrease of cost advantage and the large amount of resource consumption,the production efficiency of the productive enterprises is low.Therefore,scheduling problems have a great deal with how to increase production efficiency,drop production costs and reduce resource consumption in productive enterprises.The paper mainly studies how to find the optimal scheduling that minimizes the job's actual processing time and minimizes the consumption of resources in the production scheduling of enterprise.There are many factors affecting the actual processing time of jobs in actual production scheduling.In this paper,the single machine scheduling problems are mainly studied,where the actual processing time of jobs has a deterioration effect and a convex resource constraint.And the following two models are studied separately:(1)the single machine scheduling problem with deteriorating effect,convex resource constraints and due date is studied.And from the point of resource consumption quantity,the problem explores two objective functions that minimize the cost of resources and the due date cost of all jobs;(2)the single machine position-dependent weights scheduling problem with deteriorating effect and convex resource constraints is studied.The goal is to find an optimal schedule that minimizes the weighted sum of the tardiness of job at each position and the cost of resource consumption.Then three problems of the two models have been established.Some mathematical methods,including mathematical induction method and Lagrange multiplier method,have been used.Some lemmas and theorems of the problems are given,and then the optimization algorithms are proposed.Finally,the paper shows that these problems are polynomial solvable.