Scheduling a sequence of tasks – in the acceptation of finding the execution times – is not a trivial problem when the optimization criterion is irregular as for instance in earliness-tardiness problems. This paper presents an efficient Dynamic Programming algorithm to solve the problem with general cost functions depending on the end time of the … Read more
It is with the aim of solving scheduling problems with irregular cost functions that this paper focuses on the continuous assignment problem. It consists in partitioning a d dimensional region into subregions of prescribed volumes so that the total cost is minimized. The dual problem of the continuous assignment problem is an unconstrained maximisation of … Read more
This paper presents a hybrid genetic algorithm for the Job Shop Scheduling problem. The chromosome representation of the problem is based on random keys. The schedules are constructed using a priority rule in which the priorities are defined by the genetic algorithm. Schedules are constructed using a procedure that generates parameterized active schedules. After a … Read more
In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is required to complete a set of operations in a fixed order. Each operation is processed on a specific machine for a fixed duration. A machine can process no more than one job … Read more
In this paper we consider the labor constrained scheduling problem (LCSP), in which a set of jobs to be processed is subject to precedence and labor requirement constraints. Each job has a specified processing time and a labor requirements profile, which typically varies as the job is processed. Given the amount of labor available at … Read more
For the $r$-stage open shop problem with identical parallel machines at each stage and the minimum makespan criterion, an approximation scheme is constructed with running time $O(nrm + C(m,\eps))$ , where $n$ is the number of jobs, $m$ is the total number of machines, and $C(m,\eps)$ is a function independent of $n$. Citation Discrete Appl. … Read more
The two-machine flow shop sequencing problem with arbitrary release dates of jobs and the minimum makespan criterion is considered. The problem is known to be NP-hard, and the best known approximation algorithms are those of Potts (1985) with a worst-case performance ratio of 5/3 and running time $O(n^3 \log n)$, and a polynomial time approximation … Read more
We consider the multi-stage multiprocessor flowshop scheduling problem with uniform machines at each stage and the minimum makespan objective. Using a vector summation technique, three polynomial-time heuristics are developed with absolute worst-case performance guarantees. As a direct corollary, in the special case of the ordinary flowshop problem we come to the best approximation algorithms (both … Read more