This paper is about scheduling parallel jobs, i.e. which can be executed on more than one processor at the same time. Malleable jobs is a special class of parallel jobs. The number of processors a malleable job is executed on may change during the execution. In this work, we consider the NP-hard problem of scheduling malleable jobs to minimize the total weighted completion time or mean weighted...

In this paper, a novel multi-objective bus stop location model is proposed, which considers not only the coverage of demand and minimization of access time but also the necessities of suitable stops for transit network design phase. Three objective functions are considered including minimizing (I) sum of the total access distance (time), (II) the weighted combination of stops, and (III) the num...

In this paper we study the scheduling problem in which each customer order consists of several jobs of different types, which are to be processed on m facilities. Each facility is dedicated to the processing of only one type of jobs. All jobs of an order have to be delivered to the customer at the same time. The objective is to schedule all the orders to minimize the total weighted order comple...

We introduce a novel global constraint for the total weighted completion time of activities on a single unary capacity resource. For propagating the constraint, an O(n) algorithm is proposed, which makes use of the preemptive mean busy time relaxation of the scheduling problem. The solution to this problem is used to test if an activity can start at each start time in its domain in solutions th...

Job scheduling is concerned with the optimal allocation of scare resources with objective of optimising one or several criteria. Job scheduling has been a fruitful area of research for many decades in which scheduling resolve both allocation of machines and order of processing. If the jobs are scheduled properly, not only the time is saved but also efficiency of system is increased. The paralle...

In this paper, we address the scheduling problem with rejection in which we can choose a subset of jobs to process. Choosing not to process any job incurs a corresponding penalty. We consider the following problem for the first time: scheduling with rejection to minimize the total weighted completion time with the constraint of total penalties on identical parallel machines, where the number of...

We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS’s) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved approximation schemes, and their design is a primary goal of this research agenda. We present EPTAS’s for the scheduling problem of a set of jobs on uniform...

In this paper we study an extension of the single machine scheduling problem with the total weighted completion time objective, where there is a single non-renewable resource consumed by the jobs, having an initial stock and some additional replenishments over time. We prove that this problem is NP-hard in the strong sense, and provide an FPTAS for a special case with two supply dates.