A Stochastic Scheduling Problem with Intree Precedence Constraints

1988 ◽  
Vol 36 (6) ◽  
pp. 937-943 ◽  
Author(s):  
Esther Frostig
Keyword(s):  
Stochastic Scheduling ◽  
Precedence Constraints ◽  
Scheduling Problem

scholarly journals Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Constraints ◽  
2021 ◽  
Author(s):  
Jana Koehler ◽  
Josef Bürgler ◽  
Urs Fontana ◽  
Etienne Fux ◽  
Florian Herzog ◽  
...  
Keyword(s):  
State Of The Art ◽  
Precedence Constraints ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Automated Manufacturing ◽  
Scheduling Problem ◽  
Tasks Scheduling ◽  
Optimization Modulo Theories ◽  
Coupled Tasks ◽  
Np Hardness

AbstractCable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

scholarly journals Bi-objective unrelated parallel machines scheduling problem with worker allocation and sequence dependent setup times considering machine eligibility and precedence constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Reza Alizadeh Foroutan ◽  
Javad Rezaeian ◽  
Milad Shafipour
Keyword(s):  
Precedence Constraints ◽  
Setup Times ◽  
Scheduling Problem ◽  
Multi Objective ◽  
Worker Allocation ◽  
Sequence Dependent ◽  
Machine Eligibility ◽  
Sequence Dependent Setup ◽  
Dependent Setup Times ◽  
Sequence Dependent Setup Times

<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

scholarly journals Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 246
Author(s):  
Yuri N. Sotskov ◽  
Еvangelina I. Mihova
Keyword(s):  
Graph Coloring ◽  
Precedence Constraints ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Mixed Graph ◽  
Coloring Problem ◽  
Release Times ◽  
Schedule Length ◽  
Graph Coloring Problem

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness for integer due dates to the scheduling problem, where along with precedence constraints given on the set of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set . We prove that the extended scheduling problem with integer release times of the jobs to minimize schedule length may be solved as an optimal mixed graph coloring problem that consists of the assignment of a minimal number of colors (positive integers) to the vertices of the mixed graph such that, if two vertices and are joined by the edge , their colors have to be different. Further, if two vertices and are joined by the arc , the color of vertex has to be no greater than the color of vertex . We prove two theorems, which imply that most analytical results proved so far for optimal colorings of the mixed graphs , have analogous results, which are valid for the extended scheduling problems to minimize the schedule length or maximal lateness, and vice versa.

Strategy evaluation for stochastic scheduling problems with order constraints

1991 ◽  
Vol 23 (01) ◽  
pp. 86-104 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Single Machine ◽  
Stochastic Scheduling ◽  
Theoretical Framework ◽  
Precedence Constraints ◽  
Scheduling Problems ◽  
Strategy Evaluation ◽  
Order Constraints

A single machine is available to process a collection J of jobs. The machine is free to switch between jobs at any time, but processing must respect a set Γof precedence constraints. Jobs evolve stochastically and earn rewards as they are processed, not otherwise. The theoretical framework of forwards induction/Gittins indexation is used to develop approaches to strategy evaluation for quite general (J,Γ). The performance of both forwards induction strategies and a class of quasi-myopic heuristics is assessed.

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