191,400 research outputs found
Move-optimal schedules for parallel machines to minimize total weighted completion time
We study the minimum total weighted completion time problem on identical machines, which is known to be strongly -hard. We analyze a simple local search heuristic, moving jobs from one machine to another. The local optima can be shown to be approximately optimal with approximation ratio . In case all jobs have equal Smith ratios, the approximation ratio is at most
Scheduling with Outliers
In classical scheduling problems, we are given jobs and machines, and have to
schedule all the jobs to minimize some objective function. What if each job has
a specified profit, and we are no longer required to process all jobs -- we can
schedule any subset of jobs whose total profit is at least a (hard) target
profit requirement, while still approximately minimizing the objective
function?
We refer to this class of problems as scheduling with outliers. This model
was initiated by Charikar and Khuller (SODA'06) on the minimum max-response
time in broadcast scheduling. We consider three other well-studied scheduling
objectives: the generalized assignment problem, average weighted completion
time, and average flow time, and provide LP-based approximation algorithms for
them. For the minimum average flow time problem on identical machines, we give
a logarithmic approximation algorithm for the case of unit profits based on
rounding an LP relaxation; we also show a matching integrality gap. For the
average weighted completion time problem on unrelated machines, we give a
constant factor approximation. The algorithm is based on randomized rounding of
the time-indexed LP relaxation strengthened by the knapsack-cover inequalities.
For the generalized assignment problem with outliers, we give a simple
reduction to GAP without outliers to obtain an algorithm whose makespan is
within 3 times the optimum makespan, and whose cost is at most (1 + \epsilon)
times the optimal cost.Comment: 23 pages, 3 figure
Geometry of Scheduling on Multiple Machines
We consider the following general scheduling problem: there are m identical machines and n jobs all released at time 0. Each job j has a processing time pj, and an arbitrary non-decreasing function fj that specifies the cost incurred for j, for each possible completion time. The goal is to find a preemptive migratory schedule of minimum cost. This models several natural objectives such as weighted norm of completion time, weighted tardiness and much more.
We give the first O(1) approximation algorithm for this problem, improving upon the O(loglognP) bound due to Moseley (2019). To do this, we first view the job-cover inequalities of Moseley geometrically, to reduce the problem to that of covering demands on a line by rectangular and triangular capacity profiles. Due to the non-uniform capacities of triangles, directly using quasi-uniform sampling loses a O(loglogP) factor, so a second idea is to adapt it to our setting to only lose an O(1) factor. Our ideas for covering points with non-uniform capacity profiles (which have not been studied before) may be of independent int
Minimizing the number of tardy jobs with precedence constraints and agreeable due dates
AbstractMinimizing the number of precedence constrained, unit-time tardy jobs is strongly NP-hard on a single machine. We study a special case of the problem where a job is tardy if it is finished more than a fixed K time units after its earliest possible completion time under the precedence constraints. We prove that the problem remains strongly NP-hard even with these special due dates. We also present polynomial time solutions for the weighted version of the problem if the precedence constraints are out-forests or interval orders. In the process, we also present a polynomial time solution for a special case of the minimum weight hitting set problem
Client-contractor bargaining on net present value in project scheduling with limited resources
The client-contractor bargaining problem addressed here is in the context of a multi-mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity-on-Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two-party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights
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