New Models And Algorithms For Due-Window Scheduling Considering Outsourcing And Rate-Modifying Activities

With the development of economy,science and technology,the transformation from made in China to mind in China is becoming more and more urgent.Resources are becoming scarce,so reducing costs,improving service level and market response ability of supply chain production are necessary.To achieve these goals,we should establish an accurate math model to reflect the real production environment,meanwhile use efficient algorithms to improve the operation capacity of supply chain scheduling.By using scheduling,this paper will reflect the realistic production environment and common problems,we will expand and refine the traditional scheduling model,at the same time,reduce the production cost,improve the resource utilization,production flexibility and market satisfaction.JIT production,to a large extent,reflects the market requirements for flexible manufacturing and personalization,which are important for enterprises competitiveness.The deadline and due-window model in the scheduling field can reflect the background of flexible manufacturing.The deadline model sets the delivery date as a time point while the due-window model sets the delivery time as a period of time,so the due-window model is more realistic than the deadline model.The due-window model is divided into common due-window and slack due-window respectively,we will discuss these two models respectively,the common duewindow assumes that all the jobs share a same delivery window,differently the slack duewindow assumes that each job has its own delivery window,it’s due-window length depend on job’s actual processing time and the common flow allowance,therefore the characteristics of each job can be reflected.Appropriate due-window needs to balance the advance cost,delay penalty,opportunity cost and due-window size cost.When the job is completed ahead of duewindow,it will cost additional storage cost and management cost,while the job delay will incur a penalty to the customer.An earlier due-window start time can improve customer satisfaction,however,it will put more pressure on the manufacturers.A larger due-window size can make production more flexible,but the cost is also higher.Since the processing time of jobs is affected by many factors in real production environment,we will change the traditional classical assumption that the processing time of jobs is fixed,consider the aging constraints based on the job’s location and job itself,and ratemodifying activities,resource allocation,etc.The machine will continue to age,so the later the job is processed,the longer the processing time will be,that is the aging effect of the machine.Arranging an rate-modifying activity at appropriate time can adjust the machine to the initial state,improve the efficiency of the subsequent job processing.Additional resource allocation such as fuel or capital can reduce the processing time of jobs,the earlier the due-window be,the greater the tardiness cost,job processing time compression can prevent excessive tardiness cost caused by setting premature due-window.The above factors are related to processing time,beyond these,we also consider outsourcing.When the order does not match the machine,and enterprise cannot bear its production cost,they can outsource orders(commonly named rejection in scheduling),outsourcing gives the manufacturing industry a more flexible choice,the traditional scheduling assumes that all jobs should to be produced the enterprise itself,this is one of the innovations of this paper.Under these constraints,we should jointly seek the optimal self processed jobs collection and their sequencing,the location of rate-modifying activities and resource allocation.In this paper,two kinds of due-window models(common due-window and slack duewindow)are combined with the above constraints,and two kinds of resource allocation functions are considered,linear resource constraints and convex resource constraints respectively,the due-window models and resource allocation functions combined to form four scheduling problems.Finally,the data experiments of the four models are demonstrated and compared through Python,and the conclusions are analyzed,which puts forward reliable suggestions for controlling the cost of real manufacturing industry under the background of JIT.