Feasibility Identification for Networks with Generalized Precedence Relations (GPRs)

Production planning in Manufacturing-to-Order environments producing complex items must manage the execution of fabrication and/or assembling activities. In case of activities executed by workers, the committed effort can vary over time. To model this behavior, the Variable Intensity formulation has been proposed in the literature. In addition, the activities to be scheduled often represent whole production phases made of distinct production operations. Hence, the utilization of simple finish-to-start precedence relations does not correctly represent the real production process. In such cases Generalized Precedence Relations are used to allow overlapping among activities. However, since in Variable Intensity formulations the percentage execution of the activities is no more univocally related to their time execution, Generalized Precedence Relations cannot completely describe the constraints among activities. In this paper two mathematical formulations of precedence relations based on processing execution are presented to model overlapping between activities. The formulations are applied to an industrial case of production of machining centers and compared in terms of computational efficiency.

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Preprocessing the Discrete Time-Cost Tradeoff Problem with Generalized Precedence Relations

Mathematical Problems in Engineering ◽

10.1155/2020/6312198 ◽

2020 ◽

Vol 2020 ◽

pp. 1-19 ◽

Cited By ~ 1

Author(s):

Hanying Wei ◽

Zhixiong Su ◽

Yuan Zhang

Keyword(s):

Discrete Time ◽

Large Scale ◽

Polynomial Algorithm ◽

Time Cost ◽

Total Cost ◽

Project Completion ◽

Precedence Relations ◽

Path Lengths ◽

Time Float ◽

Generalized Precedence Relations

This study investigates the deadline of the discrete time-cost tradeoff problem (DTCTP-D) with generalized precedence relations (GPRs). This problem requires modes to be assigned to the activities of a project such that the total cost is minimized and the total completion time and the precedence constraints are satisfied. Anomalies under GPRs are irreconcilable with many current theories and methods. We propose a preprocessing technology, an equivalent simplification approach, which is an effective method for solving large-scale complex problems. We first study a way to deal with the anomalies under GPRs, such as the reduce (increase) in project completion as a consequence of prolonging (shortening) an activity, and discover relationships between time floats and path lengths. Then, based on the theories, we transform the simplification into a time float problem and design a polynomial algorithm. We perform the simplification and improve the efficiency of the solution by deleting redundant calculation objects.

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Solving multi-mode time–cost–quality trade-off problems under generalized precedence relations

Optimization Methods and Software ◽

10.1080/10556788.2015.1005838 ◽

2015 ◽

Vol 30 (5) ◽

pp. 965-1001 ◽

Cited By ~ 12

Author(s):

Kaveh Khalili-Damghani ◽

Madjid Tavana ◽

Amir-Reza Abtahi ◽

Francisco J. Santos Arteaga

Keyword(s):

Time Cost ◽

Trade Off ◽

Precedence Relations ◽

Multi Mode ◽

Generalized Precedence Relations

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The Fuzzy Project Scheduling Problem with Minimal Generalized Precedence Relations

Computer-Aided Civil and Infrastructure Engineering ◽

10.1111/mice.12166 ◽

2015 ◽

Vol 30 (11) ◽

pp. 872-891 ◽

Cited By ~ 23

Author(s):

José Luis Ponz-Tienda ◽

Eugenio Pellicer ◽

Javier Benlloch-Marco ◽

Carlos Andrés-Romano

Keyword(s):

Project Scheduling ◽

Scheduling Problem ◽

Precedence Relations ◽

Project Scheduling Problem ◽

Generalized Precedence Relations

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