Abstract We consider a variant of the NP-hard problem assigning jobs to machines minimize completion time last job. Usually, precedence constraints are given by partial order on set jobs, and each job requires all its predecessors be completed before it can start. In this paper, we different type relation that has not been discussed as extensively is called OR-precedence. for start, require at ...

This paper presents makespan algorithms and scheduling heuristic for an Internet-based collaborative design and manufacturing process using bottleneck approach. The collaborative manufacturing process resembles a permutation re-entrant flow shop environment with four machines executing the process routing of M1,M2,M3,M4,M3,M4 in which the combination of the last three processes of M4,M3,M4 has ...

We study envy-free mechanisms for assigning tasks to agents, where every task may take a different amount of time to perform by each agent, and the goal is to get all the tasks done as soon as possible (i.e., minimize the makespan). For indivisible tasks, we put forward an envy-free polynomial mechanism that approximates the minimal makespan to within a factor ofO(logm), wherem is the number of...

abstract: this paper considers the problem of scheduling n jobs on m unrelated parallel machines with sequence-dependent setup times. to better comply with industrial situations, jobs have varying due dates and ready times and there are some precedence relations between them. furthermore sequence-dependent setup times and anticipatory setups are included in the proposed model. the objective is ...

this paper presents a new mathematical model for the problem of scheduling part families and jobs within each part family in a flow line manufacturing cell where the setup times for each family are sequence dependent and it is desired to minimize the maximum completion time of the last job on the last machine (makespan) while processing parts (jobs) in each family together. gaining an optimal s...

Definition 8.1.1 Let P = ∑ i∈J Pi. Clearly 1 ≤ OPT ≤ P . Since 1 ≤ OPT ≤ P , if we have access to a (1 + )-relaxed decision procedure we can use it O(logP ) times to do a binary search on different values of T (between 1 and P ) to find a (1 + )approximation. Since logP is polynomial in the input size, if the relaxed decision procedure runs in polynomial time then we have a (1 + )-approximation...

We consider a scheduling game, where a set of selfish agents (traffic loads) want to be routed in exactly one of the two parallel links of a system. Every agent aims to minimize her own completion time, while the social objective is the makespan, i.e. the time at which the last agent finishes her execution. We study the problem of optimizing the makespan under the constraint that the obtained s...