In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is th...

We consider parallel, identical machine scheduling problems where the jobs are subject to precedence constraints, release dates, and the processing times of jobs are governed by independent probability distributions. The objective is to minimize the expected value of the total weighted completion time ∑w j C j , where w j 0. Building upon a linear programming relaxation by Möhring, Schulz, and ...

Linear precedence (LP) rules are widely used for stating word order principles. They have been adopted as constraints by HPSG but no encoding in the formalism has been provided. Since they only order siblings, they are not quite adequate, at least not for German. We propose a notion of LP constraints that applies to linguistically motivated branching domains such as head domains. We show a type...

Suppose jobs, in the Johnson's two-machine n-job flow-shop scheduling problem, are grouped into disjoint subsets within which a job order that may not be preempted is specified. Furthermore, suppose that a precedence relation between these subsets is given such that the processing of a subset must be completed, on each machine, before the processing of another subset begins on the machine. This...

We consider an online linear optimization problem over the set of permutations under some precedence constraints. In this problem, the player is supposed to predict a permutation of n fixed objects at each trial, under the constraints that some objects have higher priority than other objects in each permutation. This problem is naturally motivated by a scheduling problem whose objective is to m...

Given a set T of tasks, each of unit length and having an individual deadline d(t)∈ Z, a set of precedence constraints on T , and a positive integer k6 |T |, we can ask “Is there a one-processor schedule for T that obeys the precedence constraints and contains no more than k late tasks?” This is a well-known NP-complete problem. We might also inquire “Is there a one-processor schedule for T tha...

This paper presents an efficient method to determine minimum System-OnChip (SOC) test schedules with precedence and power constraints based on simulated annealing. The problem is solved using a partitioned testing scheme with run to completion that minimizes the number of idle test slots. The method can handle SOC test scheduling with and without power constraints in addition to precedence cons...

We consider the classic problem of scheduling a set of n jobs non-preemptively on a singlemachine. Each job j has non-negative processing time, weight, and deadline, and a feasibleschedule needs to be consistent with chain-like precedence constraints. The goal is to computea feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan[Annals of ...