Scheduling With Families Of Jobs And Delivery Coordination Under The Batch Availability

Scheduling with delivery coordination is an important modern scheduling model in scheduling research. In this scheduling model, the jobs are first processed on the machines. Then, they are delivered to the customers by the vehicles. The goal is to minimize the completion time of the delivery.In this thesis, we consider the scheduling of families of jobs in which processing and delivery are coordinated together. In these problems, only one vehicle is available to deliver the jobs to specified customers. The jobs in the same family can be processed together to form a processing batch. But, jobs from different families cannot be transported together by the vehicle. In addition, setups of batches are required when the machine is changing from a processing batch of one family to a processing batch of another family. The objective is to minimize the time when the vehicle finishes delivering the last delivery batch to its customer and returns to the machine. Under the batch availability, the four scheduling problems can be denoted as follows:(1) 1â†'D,f|v=1,si,ci,ti|Cmax(1DFB).(2)1â†'D,f|v=1,si,ci,ti=tCmax(1DFB(t)).(3)1â†'D,f|v=1,si=s,ci,ti|Cmax(1DFB(s)).(4) 1â†'D,f|v=1,si=s,ci,ti=tCmax(1DFB(s, t)).In the second chapter, we study the scheduling problem 1DFB. Under the group technology (GT) assumption, problem 1DFB is equivalent to F2‖Cmax and can be solved optimally by Johnson’s rule. Then, we use the Equal-Size Partition problem for the re-duction to show that problem 1DFB is NP-hard without the GT assumption. Finally, we provide an approximation algorithm with a performance ratio of 7/4.In the third chapter, we consider problem 1DFB(t) which is a special case of problem 1DFB with all jobs having the identical delivery time, i.e., ti= t. We show that the approximation algorithm of problem 1DFB established in Chapter 2 is a 5/3=pproximation algorithm for problem 1DFB(t).In the fourth chapter, we consider problem 1DFB(s) which is a special case of prob-lem 1DFB with all families having the same setup time, i.e., Si=s. Based on the approxi-mation algorithm of problem 1DFB established in Chapter 2, we provide a approximation algorithm with a performance ratio of 5/3 for problem 1DFB(s).In the fifth chapter, we consider problem 1DFB(s, t) which is a special case of prob- lem 1DFB with all jobs having the same delivery time and all families have the same setup time, i.e., ti= t and si= s. Based on the approximation algorithm of problem 1DFB established in Chapter 2, we present an approximation algorithm with a performance ratio of 3/2 for problem 1DFB(s,t).