scheduling for job shop is very important in both fields of production management and combinatorial op-timization. however, it is quite difficult to achieve an optimal solution to this problem with traditional opti-mization approaches owing to the high computational complexity. the combination of several optimization criteria induces additional complexity and new problems. in this paper, we pro...

In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS). 1998 ACM Subject Classification F.2.2

The criterion of total weighted completion time occurs as a sub-problem of combinatorial optimization problems in such diverse areas as scheduling, container loading and storage assignment in warehouses. These applications often necessitate considering a rich set of requirements and preferences, which makes constraint programming (CP) an effective modeling and solving approach. On the other han...

Lagrangian relaxation is a powerful bounding technique that has been applied successfully to many / /9-hard combinatorial optimization problems. The basic idea is to see an ./K~-hard problem as an "easy-to-solve" problem complicated by a number of "nasty" side constraints. We show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower boun...

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processin...

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive sche...

this paper discusses the problem of allocation of constrained renewable resource to splittable activities of a single project. if the activities of stochastic projects can be split, these projects may be completed in shorter time when the available resource is constrained. it is assumed that the resource amount required to accom-plish each activity is a discrete quantity and deterministic. the ...

In this paper we establish a mean value property for the functions which is satisfied to Laplace–Bessel equation. Our results involve generalized divergence theorem and second Green’s identities relating bulk with boundary of region on differential Bessel operators act. Also design fractional weighted operator, study its boundedness, obtain maximal inequality spherical get boundedness. The conn...